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MEASURING THE ALLOCATION OF CONTROL
CN 6 DEGREE OF FREEDOM HITMAN-COMPUTER INTERACTION TASKS
Maurice R. Masliah
A thesis submitted in conforrnity with the requirements for the degree of
Doctor of Philosophy
Graduate Department of Mechanical and industria1 Engineering
University of Toronto
O Copyright by Maurice R. Masliah 200 1
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Measuring the Allocation of Control in 6 Degree of Freedom Human-Computer interaction Tasks
Maurice R Masliah, PhD., 200 1
Department of Mechanical and industrial Engineering
University of Toronto
Abstract
Trajectory information can be analysed in both the time and space dimensions via a new
metric called the W-metric. The W-menic is a measurement definition which quantifies the
allocation of control across multiple degrees of fieedom. Allocation of control is defined as the
product of hvo components, the simultaneity of control and the efficiency of control,
corresponding to the time and space dimensions respectively. The existing hurnan factors,
biomedical. and motor control literature serves as the foundation for the development of the W-
metric. The 7X-metric has several limitations including dependency upon the chosen coordinate
system. assumptions of optimal trajectorïes, and the lack of fiequency domain analysis,
A six degree of freedom longitudinal virtual docking task experiment tested the R-
metric's validity and usefulness. Results fiom the docking experiment showed that operators,
rather than controlling al1 six degrees of fieedom equaIly, allocate theü control to the rotation and
translation degrees of Freedom separately, and switch control behveen the hvo groups. This
switching of control is also a function of the input device and the allocation of control across a11
available degrees of freedom increases with practice.
Unlike a docking task, a tracking task specifies the time-space components of the
required tnjectory. A six degree of freedom longitudinal virnial tracking expriment was
conducted to confirm the validity of the previous findings. Even under the conditions where equal
ailocation of control across al1 the degees of freedom is required by the task, mbjects in the
tracking experiment still showed a preference to switch control between the translation and
rotation degrees of Freedom, though not as high as in the docking experiment.
Potential applications of the W-metnc inchde evaluation of input devices, understanding
of human motor control systems, and assessing neuroIogical damage. To lay the groundwork for
testing the W-metric as a possible diagnostic tooI the docking experiment was re-run with elderly
subjects. LVhile results fiom the docking experiment show that elderly subjects show lower
overall performance scores, no differences were found in the patterns of allocation of control
across degrees of freedom.
Acknowledgements
In the fa11 of 1994, dong with other supporthg papers, I mailed a paper titled "Manual
Control of Orientation" to Paul Milgram in the hopes of finding an advisor whose interests
matched my own. A mere three months later :-) 1 received a very positive response and Paul
invited me to visit. At the time 1 was concemed with finding an academic lab with a high calibre
of research, solid financial support, and a strong interdisciplinary environment. While 1 found al1
this and more, I also found something I had not thought to look for. Unlike the other things, you
won't End it listed in any university publication or on a C.V. So 1 have the honour of putting down
in print that [ found an advisor who first and foremost is a decent human being.
I would like to thank al1 the members of ETC lab, including David Dnsic, Kit Cheung,
Steve Ma, Doug Liversidge, Peter Lind, Miriam Kim, Ming Hou, Caroline Cao, Wenbi Wang,
Moncef Mestiri, Hanio Takemun, John Hajdukiewicz, Herman Colquhoun Jr., and Cathy
Courage for agreeing to spend hours in front of a computer manipulating tetrahedrons so that 1
would have pilot data, for their advice, and for their fiiendship.
Thanks to my committee- Scott MacKenzie, John Senders, and Julius Grodski who took
the time to guide my research and provided answers to questions I hadn't even asked, but should
have. Also special thanks to Christine MacKenzie for s e ~ n g as my extemal examiner, and
Simon Graham as my intemal examiner.
Even though 1 can probably count on one hand the number of times we have met in
person, I must also acknowledge the guiding work of my "academic elder brother", Shumin Zhai,
whose research cenainly paved the way for my own. Shumin laid the foundation and it is on his
shoulders that 1 am standing.
Without the four years of financial support frorn the Department of Mechanical and
Industrial Engineering, the University of Toronto, NSERC and the institute of Robotics and
IntelIigent Systems (IRIS), 1 would not have had the opportunity to pursue this research.
"Human movements are compler patterns which cannot be understood by
the laws of physics even if they are constrained by physics in every detail." (Morasso
and TagIiasco 1986 pg. 1)
"1 do not see any way to avoid the problem of coordination and still
understand the physical basis of life." H. H. Pattee as cited in (Wailace 1989)
Table of Contents . *
Abstnct ........................................................................................................................................u
..................................................................................................................... Acknowledgements iv
Table of Contents .......................................................................................................................... vi
List of Fipures ......................................................................................................................... xi
List of Tables .................................................................................................................................. .u
Between Versus Within Sources of VariabiIity ........................................................................ xix
................................................................................................ The So hvare ..................... .. xîx
1 Introduction ............................................................................................................................ 1
........................................................................................ 1.1 Human-Cornputer Interaction 2
1 . 2 Existing Perfomance Metrics ......................................................................................... 7
1.2.1 Time-On-Target ............................................................................................................. 9
.................................................................................................. 1.1.2 Relative Motion PIots LI
12.3 The Speed Accuracy Tnde-off ................................................................................... 12 1.2.4 Time. Space. and Frequency Domains ........................................................................ 14
1.2.5 Spatial or Temporal invariance .................................................................................. 14
12.6 Cross-Correlations ....................................................................................................... 1.)
1.2.7 IntegaIity ..................................................................................................................... 17
1.2.8 inefficiency ............................................................................................................... 18
1.3 Theory and Litenture on Multi-Degree of Freedom Human Control ............................. 19
L.3.1 How Movements are Learned ...................................................................................... 19
1.3.2 The Trajectory of the Working Point ........................................................................... 21
13.3 Leming to Coordmate Redundant Biomechanical Degrees of Freedom ................... 21
L.4 Summary and Research Goa1 .......................................................................................... 23
.................................................................................. 2 TheR-mettic for Docking Tasks ....... 25
............................ 2.1 Simultaneity of Conuol ... .................................................................... 25
.................................................................................................... 2.2 Efficiency of Control 30
2.3 Surnmary of the*-memc for Docking Tasks ................................................................. 32
2.4 A Note on the Time Dimension ..................................................................................... 3 3
1.5 Hypothetical Examples .................................................................................................. 33
..................................................................................................... 3 The Dociiing Experiment 39
Hypotheses ...................................................................................................................... 39
Subjects ...................................... .. ......................................................................... 40
Experimental Plattbrm .................................................................................................... 41
................................................................................................................................. Task 42
...................................................................................... Procedure 45
Design ................................................................................................... 45
.......................................................................................................................... Results 45
Discussion .................................................................................................................. 5 9
Summary of Docking Experiment ................................................................................... 61
....................................................................................... J The W-metric for Tracking Tasks 63
................................................................................................... 4.1 Sirnultaneity of Conno1 64
....................................................................................................... 4.2 Efficiency of Conrol 70
................................................................ 4.3 Summary of the%-metric for Tnc king Tasks 70
................................................................................... 4.4 The Traditional Forcing Function 71
4.5 The Modified Forcing Function ...................................................................................... 73
5 The Dynarnic Tracking Experiment ............................................................................. 7 8
....................................................................................................................... Hypothesis 78
Subjects ........................................................................................................................... 79
Experimental Platform ..................................................................................................... 79
Task ............................................................................................................................... 80
Procedure ......................................................................................................................... 81
Design ............................................................................................................................. -81
Results ............................................................................................................................. 82
Discussion ....................................................................................................................... 95
6 The ûocking Experiment with Elderly Subjects.. .......... " ............................................. 91
6.1 introduction: Newological assessrnent ......... ... ....................................................... 97 6.2 Motivation .................................................................................................................... 3 9
..................................................................................................................... 6.3 Hypothesis 100
6.4 Subjects ......................................... .. ............................ 100
6.3 Experimental Platform ................................................................................................. 101
6.6 Task ............................................................................................................................... 101
6.7 Procedure ....................................................................................................................... 102
6.8 Design ............................................................................................................................ 102
6.9 Results ........................................................................................................................... 103
.................................................................................................................... 6.10 Discussion 117
7 Conclusions .......................................................................................................................... 119
. . 7.1 The Original Monvation ................................................................................................ 120
............................................................................ 7 2 Experimental Conclusions Summary 121
8 Limitations of theW.metric. and Future Work ............................................................... 123
........................................................................................... 8.1 Limitations of the R-metric 123
8.2 Future Work ............................................................................................................. 124
8.2.1 Extending the %-memc into the Frequency Domain ................................................ 124
8.2.2 Two Handed Coordination ......................................................................................... 125
............................................ 8.2.3 Evaluation of Elastic and Multi-channel Input Devices 126
8.2.4 Evaluation of Transformed Axes ............................................................................... 126
8.2.5 The %-memc as a Measue of Expertise ............................................................... 127
8.2.6 Telcopention- Minimally invasive Sugery ............................................................ 178
.......................................................................................................... 8.2.7 Process Control 129
8.2.8 Assessrnent of Neurological Damage .................................................................. 129
Appendix A: Stationarity ................................................................................................... , 1 3 2
Testing for Stationarity ....... ... ............................. 133
The Runs Test (nonparamettic) ......................................................................................... . 133
Stationarity oCTracking Data ..................... ... ............................................................... 134
Panmetric Approaches ................ .... ............................................................................ 137
..................................................................... Conclusions as to the Stationarity of the Dats 138
Appendix B . W-metric Dockhg Calculations Example ......................................................... 139
............................................................................................................ Simultaneity of Control 140
................................................................................................................ Efficiency of Control 145
The %-mehic Score ......................... ............... ................................................... 145
viii
Appendix C: Algorithm for Computing the%-metric for Tracking Tasks .......................... 146
References ................................................................................................................................... 150
l n d e ~ ............................................................................................................................................ 157
List of Tables
Table 1 . Sumrnary of Zhai's findings wïth respect to input device resistance and transfer function . (Zhai 1995) ............................................................................................................................... 6
Table 2 . Metrics from Ellson (Ellson 1947) and Zhai & Senders (Zhai and Senders 1997a) used . .
to extend time on target into a coordination measure .......................................................... 10
Table 3 . Predicted performance measures . Colurnns A-G correspond to trajectories A-G shown
...................................................................................................... in Figure 10 and Figure 1 1 37
Table 4 . Actual performance measures tiom real data (sample size = 1) ..................................... 37
Table 5 . How the metrics of integrality, inefficiency, and the m-metric evaluate the different . . .......................................................................................................... trajectones in Figure 10 38
Table 6 . Two scenarios for assigning error reduction for the example in Figure 37 ..................... 66
Table 7. Traditional forcing function constants used by Zhai (Zhai 1995) .................................... 72
Table 8. Table ofconstants used in the modified forcing function for the dynmic tracking
experirnent .............................................................................................................................. 80
Tabie 9. Summary of hypothesises and experimental conclusions .............................................. 121
............................................................................................ Table 10 . Raw data and caicuIations 139
List of Fiqures
Pigure 1. A cornputer's cursor manipulated by a standard mouse has two degrees of fieedom ...... 2
Figure 2. An assortment of different input devices with more than MO degrees of freedom. A)
The "Cubic Mouse", designed by B. Frohlich & J. Plate (Frohlich and Plate 2000), is an
isotonic device with additional rod and button controls. B) The "Rockin'Mouse", designed
by R. BaIakrishnan. is a mouse with a cürved bottom and a Wacomm sensor for sensing the
angle of the mouse. C) The" M E 3 Glove", an isotonic device designed by S. Zhai (2hai
19951, consists of an Ascension Bird@ tracker and a clutch mounted on a glove. D) The
"FingerbaIl", an isotonic device designed by S. Zhai (Zhai 1995), consists of an Ascension
BirdO tracker in a ball. E) The "Bat", an isotonic device designed by C. Ware (Ware 1990),
consists of a Poihemusm tracker and a handle. F) The "EGG, an elastic device designed by
S. Zhai (Zhai 1995), consists of an Ascension Bird@ tracker mounted within an elastic
fiame. G) The SpacebaIlm, an isometric device manufactured by Labtec@. Ei) The
CricketTM, manufactured by Digital image Design inc., an isotonic device with a handIe. i)
The Magellan SpaceMouse distniuted by LogitechB JI The SpaceMaster rnanufacnlred by
Basys, Germany. K) The "ErgoPoint 3D" manufactured by ïïU Research, a device with four
touch sensors. t) iBM's ScroIIPointB Moust is a mouse combined with 2 degree of fieedom
isornemc joystick. hl) The "Padmouse" designed by R. Balakrishnan @aIaicrishnan and
................................................................... Patel 1998) is a moue combined with a touchpad 3
Figure 3. A taxonomy oftirne-space manual control tasks. (MasIiah 1999) ................. .... ..... 9
Figure 4. Hypothetical phase pIane plot, adopted fiom (Behbehani et al. 1988) "......................... 13
Figure 5 . Trajectory A showing separabie degrees of freedom, trajectory B showing integral
degrees of freedom. ................................................................................................................ 18
Figure 6. How ineflciency (Zhai und MiIgram 1998) is calculuted - ............................................ 19
Figure 7. How sirnultaneity is ca1cuIated by way of a nonnalised error reduction p p h for
docking tasks, for hvo degrees of freedom, x and y. .............................................................. 28
Figure 8. Two different error reduction cases. The top graph shows two error reduction curves
with very Iittle overlap, representing Iow simdtmeity. The bottom graph represents a fùgh
degree of overlap, representing hi& sllnultaneity .................................................................. 30
Figure 9. ïiIustration of how the eficiency portion of the R-meirïc is caIcuIated ........................ 3 1
Figure IO, Seven different hyphetical ûajectories for a docking task with 2 degrees of hedom.
Figure 11. Seven different trajectories from Figure 10 collected fiom real data, showing time
information. ............................................................................................................................ 35
Figure 12. Normalised error reduction functions over tirne for the seven different trajectories seen . - m Figure 9, collectsd fiom real data .........................~............................................................. 36
Figure 13. The docking task required manipulation of 6 degrees of freedom: translation along X,
Y, Z, and rotation about the X, Y, Z axes (RX RY, RZ) ....................................................... 41
Figure 14. Isometric and isotonic devices on the resistance continuum ........................................ 42
Figure 15. A depiction of the experimental setup used modeling the Fingerball, an isotonic input
device. An Ascension BirdC3 magnetic transmitter is on the right side of the table with a
receiver inside the Fingerball. The mode1 is wearing iMAX8 stereoscopic glasses, as worn
by the experimental subjects. The experimental room was darkened during the actual
experïment. ............................................ ........................................................................ 43
Figure 16. Monoscopic screen images of the docking task; the actual experiment setup is a
stereoscopic display. The user's cursor appears at the centre of the screen, while the target
appears at one of eight possible locations at the start of each trial. Besides position, the
cursor's corners are distinguished by lines, while stars adorn the target's corners. The cursor
is shown being manipulated ont0 the target. In the last Frame, the corners of the target change
colours to indicate a successful dock ..................................................................................... 44 Figure 17. Docking performance over time for the four subjects using the Spaceball (an isometric
input device). Raw data, session means (5 one-hour sessions with 216 mals per session) and
session standard deviations are shown ................................................................................... -46 Figure 18. Docking performance over time for the four subjects using the Fingerball (an isotonic
input device). Raw data, session rneans and session standard deviations are sho wn............. 47
Figure 19. Docking performance over time for both the isometric and isotonic devices compared.
Session means and standard deviations are shown ................. .. ....................................... -47
Figure 20. The W-metric scores in the docking experiment for only the isometric input device. ALI
bvo-way degree of freedom combinations are shown ....................................................... -..48
Figure 21. The M-metric scores in the docking experiment for only the isomemc input device. All
three-way degree of fieedom combinations are shown, ......................................................... 49
Figure 22. The W-rnetric scores in the dockhg experiment for only the isomemc input device. All
four-way degree of freedom combinations are shown , ...................................................... 50
Figure 23. The W-metnc scores in the dockhg experirnent for oniy the isometric input device. Al1
Five-way degee of fieedom combinations are shown ............................................................ 50
Figure 24. The W-metric scores in the docking experiment for only the isometric input device.
î h e six-way degree of freedom combination is shown ....................~....~....~----....--.-...-.-----.---- 5 1
Fi-ure 25. The W-metric scores in the docking experiment for only the isotonic input device. Al1
hvo-way degree of freedom combinations are shown. ................................~....~.~................... 52
Figure 26. The W-metric scores in the docking experiment for only the isotonic input device. Al1
three-way degree of Freedom combinations are shown. ............................................ . 5 2
Figure 27. The W-metric scores in the docking experiment for only the isotonic input device, Al1
four-way degree of Freedom combinations are shown ....................................................... .... -53
Figure 28. îhe W-metnc scores in the docking experiment for only the isotonic input device. Al1
fwe-way degree of freedom combinations are shown .................................... . ............... .. ...... 53
Figure 29. The W-memc scores in the docking experiment for only the isotonic input device. The
six-way degree of freedom combination is shown. ............................................. . . . 54
Figure 30. How the W-metric scores changes over time in the docking experiment. A set of
representative between translation and rotation degree of Freedom (X-RX) and a within
rotation degree of freedom (RX-RY) scores, for both the isometric and isotonic input
devices, are shown. .................................................................................. . .................. 5 5
Figure 3 1. How the W-memc scores changes over time in the docking experiment. A set of
representritivc between translation and rotation degree of Freedom (Y-2-RY) and a within
rotation degree of Fieedom (RX-RY-RZ) for both the isornetric and isotonic input devices are
shown ......................................................................................................................... . . 5 6
Figure 32. The W-metric scores over time in the docking experiment across al1 6 degrees of
tieedom ................................................................--................................................................. 57
Figure 33. The relationship between the two dependent variables task-completion time and th&-
metric for the X-Y combination for the docking experiment ................................................. 58
Fi-we 34. The relationship between the two dependent variables task-completion time and t h e -
rnetnc for the X-RZ comparison for the docking experiment. ............................................. 58
Figure 35. The relationship between the two dependent variables task-compIetion time and t h e -
metric for the RX-RY comparison for the docking experiment .,.....,........ ,.. .................- 59
Figure 36. Tavonomy of manual control tasks, emphasis on tracking tasks, Tracking tasks defme
both the required trajectory in space and the Pace at which the trajectory is to be followed.63
Figure 37. Case 4 shows the cursor lagging behind the target Case B shows the cursor leading in
front of the target. T represents time and shows the position of both the cursor and the target
and time TI and TL.. The numbers at the right next to the brackets indicate "units of errof.65
Figure 38. How simultaneity is calculated by way of a norrnalised error reduction graph for
trackiw tasks. ......................................................................................................................... 69 O
Figure 39. Position of the screen target as generated by the traditional sum of sines forcing
Function. One graphic unit = 1.4 cm (Zhai 1995). The traditional forcing functions for three
........................................................... degrees of fieedom are shown, as used by Zhai 1995. 72
Figure 40. The absolute value of the first derivative of the forcing functions fiom Figure 39. Each
degree of Freedom changes its position at a different rate .................................................. 73
Figure 41. Illustration of the difference between the traditional and modified forcing functions.
The modified forcing function is a mirror reflection of the traditional forcing function
accomplished via a sign change at the switch point. Switch points are selected so that the
target's trajectory appears relatively smooth to the subject ................................................ 74
Figure 42. Position of the screen target as genented by the modified forcing function. The
modified forcing function for t h e degree of freedom is shown ........................................ 76
Figure 43. Only one line is visible because ail thee translation degree of freedom have the same
absolute value of the first derivative for the modifred sum of sines forcing function ............ 76
Figure 44, Power spectral density for the traditional forcing function .......................................... 77
Figure 45. Power spectral density for the modified forcing function ............................................ 77
Figure 46. Tracking performance over time for the four subjects using the Spaceball (an isometric
input device). Raw data, session means (5 une-hour sessions with 60 trials per session) md
session standard deviations are show .................................................................................... 83
Figure 47, Tracking performance over time For the four subjects using the FingerbaIl (an isotonic
input device). Raw data, session means and session standard deviations are show II............. 84
Figure 48. Tracking performance over time for both the isometric and isotonic devices compared.
Session means and standard deviations are shown ................................................................ 84
Figure 49. The M-metric scores in the tracking experiment for only the isomemc input device,
with two-way degree of fieedom cornparisons shown. ........................................................ 85
Figure 50. The M-memc scores in the tracking experirnent for only the isometric input device,
with three-way degree of fkedom cornparisons shown. .................................................. 8 6
Figure 5 1. The M-metric scores in the tracking experiment Tor only the isornetric input device,
with four-way degree of fieedom comparisons shown ........................................................... 86
Figure 52. The M-meaic scores in the tracking experïrnent for only the isometric mput device,
with five-way degree of fieedom cornparisons shown .................................................... 8 7
Figure 53. The M-metric scores in the tracking expeciment for onIy the isometric input device,
with the six-way degree ofîkeedom cornparison shown. ................................................... 87
Figure 54. The M-metnc scores in the tracking experiment for only the isotonic input device, with
hvo-way degree of keedom compansons shown. .............................~...~~...~........................... 88
Figure 55. The M-metric scores in the tracking experiment for only the isotonic input device, with
three-way degee oE fieedom cornparisons shown. ............................................................ 89
Figure 56. The M-rnetric scores in the tracking experiment for only the isotonic input device, wvith
four-way degree of Freedom comparïsons shown ................................................................... 89
Figure 57. The M-merric scores in the tracking experiment for only the isotonic input device, with
five-way degree of freedom cornparisons shown, ................................... .... ........................... 90
Figure 58. The M-memc scores in the tracking experiment for only the isotonic input device, with
the six-way degree of freedorn comparison shown, ............................................................... 90
Figure 59. How the M-meûic score changes over time in the tracking experiment. A between
translation and rotation degree of freedom (Y-Z-RY) and a within rotation degree of freedom
(LX-RY-RZ) for both the isometric and isotonic input devices are shown ........................... 9 1
Figure 60. How the W-metric score changes over time in the tracking e.qenment. A between
translation and rotation degree of freedom (Y-Z-RY) and a within rotation degree of freedom
........................... (RX-RY-RZ) for bath the isometric and isotonic input devices are shown 92
Figure 61. The 3X-metric score over time in the tracking experiment for al1 6 degrees of freedom.
................................................................................................................................................ 92
Figure 62. The relationship between the two dependent variables RMS error and the X-memc for
X-Y combination for the tracking experiment .......... .. ...... .. .......................................... 9 3
Figure 63. The relationship between the two dependent variables RMS error and the X-metric for
................................................................. LX-RY combination for the tracking experiment. 94
Figure 64. The relationship between the two dependent variables RMS error and the W-metric for
X-RZ combination for the docking experiment ........................................................ 94
Figure 65. Docking performance over time for the four elderIy subjects using the Spaceball (an
isometric input device). Raw data, session means (5 one hour sessions with 120 mals per
............................... session) and session standard deviations are shown .... 104
Fieme 66- Docking performance over time for the four elderly subjects using the Fingerball (an
isotonic input device). Raw data, session means and session standard deviations are shown.
............................................................................................................................................. 104
Figure 67. Docking performance over time for both the isometric and isotonic devices compued
.............................. for eIderly subjects. Session means and standard deviations are shown 105
Figure 68. The W-metric scores in the docking experiment with elderly subjects for only the
isomemc input device. Al1 nvo-way degree of fieedom combinations are shown .............. 106 Figure 69. The W-mehic scores in the docking experiment for only the isometric input device. Ail
three-way degree of freedom combinations are shown. ....................................................... 106 Figure 70. The 2-metric scores in the docking experiment with elderly subjects for only the
isomemc input device. Ail four-way degree of fieedom combinations are shown .............. 107 Figure 7 1. The W-metric scores in the docking experiment with eIderly subjects for only the
isomemc input device. Al1 five-way degree of fieedom combinations are shown .............. 107 Figure 72. The W-meûic scores in the docking experiment with elderly subjects for only the
.................. isomemc input device. The six-way degree of Freedom combination is s h o w 108
Figure 73. The W-metnc scores in the docking experiment with elderly subjects for only the
................. isotonic input device. AI1 two-way degree of fieedom combinations are shown 109
Figure 74. The W-metric scores in the docking experiment with elderly subjects for only the
............... isotonic input device. Al1 threeway degree of Freedom combinations are shown 109
Figure 75. The W-memc scores in the docking experiment with elderly subjects for only the
................ isotonic input device. Al1 four-way degree of freedom combinations are shown 110
Figure 76. The 2%-metric scores in the docking experiment with elderly subjects for only the
isotonic input device. Al1 five-way degree O€ fieedom combinations are sho wn,............... 110
Figure 77. The W-metric scores in the docking experiment with elderly subjects for only the
..................... isotonic input device. The six-way degree of freedom combination is shown I l 1
Figure 78, How the W-metric score changes over time in the docking experiment with elderly
subjects. A between translation and rotation degree of freedom (X-RX) and a within rotation
degree of freedom (RX-RY) for both the isomemc and isotonic input devices are shown, 1 12
Figure 79. How the W-menic score changes ovrr time in the docking experiment with elderly
subjects. A between translation and rotation degree of freedom (Y-2-RY) and a within
rotation degree of Freedom (RX-RY-RZ) for both the isornettic and isotonic input devices are
shown .................................................................................................................................... 113
Figure 80. How the W-memc score changes over tirne in the docking experiment with elderly
subjects for al1 6 degrees of freedomAesuIts firom both the isometric and isotonic input
device conditions are shown ................... ........ .............................................................. 114 Figure 8 1. The relationship between the two dependent variabtes task-completion time and t h e -
rnetrïc for the X-Y combination for the docking experiment with elderly subjects ............. 115
Figure 82. The relationship berneen the two dependent variables task-completion time and the?#-
memc for the X-RZ combination for the dockïng experiment with eIderIy subjec ts,......... I l 5
Figure 83. The relationship between the nvo dependent variables task-completion time and the%
mecric for the RX-RY combination for the doclcing elcperiment with elderly subjects -...... 116
Figure 84. Docking performance over tirne showing both the younger and older subject by input
device condition .......................................................................................................... 1 17
Figure 85. Two hypothetical trajectories with identical W-metric scores but different fiequencies.
...................... ,, .......... ..+.. -...... + .................................... + ........ . ......................... L25 Figure 86. Runs distribution of tracking data from 228 series, divided into 2.5,2.9,3.3, and 4.0
second segments. The 0.05% tails are shown for the different tests. in order for a process to
be considered stationary, 90% of the number of runs shouId be between the left and right
tails ..................................................................................................................................... 136
Figure 87. The auto-correlation function of the Y translation error fiom a single 40 second
tracking mal ................ - ........ - .~~....~...~....~~~................................................................ 137
Figure 88. Trajectory for fictional degree of freedorn "X' _erphed aIong space and time ,........ 141
Figure 89. Distance from the goal position of "X" (target position -cursor position) calculated
fiom Figure 87 .............................................................................................................. 141
Figure 90. Change in error for X per unit of time ............. .. ............................................. 142
Figure 9 1. Error reduction graph for X. Same as Figure 88 with error increasing values zeroed
out ,.......................................+.............,.....,....,.........,....................................................... 143
Figure 92. The area under the error reduction curve forX is normalised to 1. The same steps are
taken to compute the normalised error reduction curve for Y ......................................... 144
Figure 93. The minimum of the norrnalised error reduction curves of X and Y are graphed. The
area under this curve is equal to the simultaneity of control .......................................... 144
Preface
"We ntrrsr be carefid not io conjkîe data ivirh the abstractions we use to a n a l ~ e rhem. " Nilfiatn James (1 842 -l9iU), as cited in (Rice 1988) p. vi
The human factors profession does not have a set of standards or officiai guidelines for
statisticaI reporting. The Engineering Data Compendium, which c m be viewed as much of a
"bible" text as any in the human factors field, does not seem to follow any sort of standard in the
presentation of variability. For example, in volume II of the Compendium (Boff and Lincoin
1988) the error bars used in figure on page 938 are based on standard deviation, on page 1096 the
error bars are based on standard error, on page 1324 they are based on 1% and 5% t valries, on
page 1362 thty are based on inrerqiiarrile ranges, and the figure on page 1492 shows error bars
based on the higimt and lorvest val~res. Having such a multitude of representations for error bars
within a single volume of text requires extra effort fiom the reader to decode the graphs.
Part of the problem is that no one means of depicting variation is necessarily supenor to
any other. Also, knowing one measurernent of variance dong with details of the experimental
conditions often means being able to caldate other measures of variance. For exarnple,
standard deviation standard error = {where n are the statistical degrees of fieedom). The next best Jn thing perhaps is to use the standards of another well-estaidished cornmunity. In particuIar, the
medical cornrnunity has published wel1-detincd guidelines.
men possib fe, quanrifjlfidings and presetit firem ivith appropriate indicaturs of nieasirremerrr error or rtncertaiq (sicch as conjidence intervals). ... At a minirniirrt, reuderii shotild be ofered lite mean and standard deviation for mery appropriate oirtcorne variable. ....
'%tridelinesfor Starisdcaf Reporring in Articles for Medical Jotirnals" Annals of Inremal Medicine. 1988; 208: p.767 {BaiIur LY and Mosrefler 1988; Wilkinson 1999)
The standard deviation is a conservative (giving Iarge sized error bars) choice for
depicting error bars; for a normal disü-ïïution i- one standard deviatian will include 68% of the
raw data. Throughout this dissertation, standard deviation is used to depict variation because it
conveys a desired message, is conservative, and fotIows the above guideline cited fiom (BaiIar iII
and Mostetier 1988).
Behveen Versus Witbin Sources of Variability
Individual differences in performance do exist; of this fact there can be no doubt.
However, since analysis of individual performance data was not a goal of this dissertation, no
individual data is presented. For the purposes of this dissertation individual differences, formally
referred to as benveen subjecr d~jïere~ices, have not been presented in any detail. Therefore
standard deviahons used within this dissertation have been computed based on the combined
variance of both subject variability and trial variability. Formally this means that subjects have
not been treated as a separate independent variable.
The Software
This dissertation was written using Microsoft Word '97. Experimental data graphs were
made using Microsoft Excel '97, Lotus 1-2-3 Miiiemium Edition, and SPSS Sigrnaplot 6.0. The
bibliography was created using Niles Software Endnote 3.0.1. The customised MiTS
(Manipulation in Three-Space) software, originally written by Shumin Zhai, was coded in C.
Software for computing the W-mehic was written using Borland Delphi 4.0. Anova calculations
were conducted using ISTAT and Analyse-It 1.50. Spectral analysis were conducted using
MathWorks Matlab 4.0. Linear regression was calculated using Microsoft Excel '97.
xix
1 Introduction
As technologies for interacting with systems such as CAD workstations, process control
plants, computer-aided design, scientitic data visualisation, and remotely controlled robots
become more sophisticated, the necessity of controlling multiple variables simultaneously
increases. Once rare and expensive, 3D applications including computer graphics animation.
virtual reality, and 3D video games are now mamstream and can be run on many home
computers. These types of tasks are much more compIex than the traditional computer tasks of
word processing, email, and spreadsheet calculations requiring a very different type of interaction
than simple discrete single-key presses. Ofien users must be able to manipulate multiple degrees
of freedom simultaneously in order to accomplish their goals. Evaluation of the human interface
is necessaty in order to design appropriate computer systems for such complex tasks.
Historically, the answer to the question wha t does it mean to control6 degrees of
freedom simultaneously?" was not clear. Commercial computer pointing devices have claimed
sirnultaneity in their product brochures and on their websites by making statements like the
following:
"ErgoPoint 3 0 is a multiple points/states controller. You can maniprilate up tu four points or States independentiy and simdtaneously, which is not achievable b-v conventional pointing devices ... ErgoPoint 3 0 can generate translation cornmand (X Y. and Z mis movement) and rotation command (pitch, ymv, and roll) independentlv and sitntiltanro~~~Iy~ " (ITUResearch 2000)
However, commercial product claims like these in the past have never included published
experimental testing or quantifiable evidence to support whether users are actually capable of
taking advantage of an input device's mechical capabilities. Just because an input device allows
"simultaneous" control does not mean such contrai is actually viable given human cognitive and
motor limitations. Unfortunately, even claims of simultaneity in the experimental litemture are in
fact not always conc1usive. For example:
"lt ivm found that after 30 minutes of practice more than 80% of the srrbjects rvere able to control al1 6 degrees offreedom simtiltnneously. " @ai 1995, Chapter 6)
Zhai made this statement after dimmional analysis of a 6 degree of freedom trachg
task. The root-mean-square error for each degree of fieedom was computed separately. Analysis
of the results reveaIed that afier 40 minutes of pracùse the root-mean-square errors for the
degrees of freedom were not signiticantly different from each other, leading Zhai to conclude that
al1 the degrees of Freedom were being controlled simultaneously. However it is possible to have
two identical performance scores but with very different time-space trajectories. Identical root
mean square or task completion times does not rnean simultaneous control is occuning. For
example it is possible to achieve identical root mean square error scores for each degree of
fieedom yet never control any two variables simultaneously by instead rnanipulating only one
variable at a time.
1.1 Euman-Cornputer Interaction
Engineers and cornputer scientists refer to a cornputer mouse, used to manipulate the
cursor on a windows-type operating system, as a "two degree of Freedorn" input device. The two
variables controlled by the rnouse are the horizontal (the X-axis) and vertical (the Y-axis) position
of the cursor on the cornputer monitor; see Figure 1. The ability to rnove a cursor across three
dimensions (3D) means not only translating the cursor along X and Y, but also in and out of the
screen- the Z-axis. in addition, for tme 3D manipulation, the orientation of the cunor can be
rotated about the X, Y, and Z axes, for a total of six degrees of freedorn. The total number of
degrees of Freedorn in a task is defined here as the minimum number of continuous variables
necessary for describing the state of a systern, or in this case, the position and orientation of a
cursor. With redundancy it is possible to use an input device with a larger number of degrees of
fkedom than the minimum nurnber required for the task. More formally, degrees of tkeedom are
detïned as "the number of independent dimensions one must use to define unambiguously the
state of the systern" (Morrison and Newell 1998).
Figure I . A conrprirer 's airsor manipulated by a standard mouse has nvo degrees offieedom.
Figtire 2. An assortnient of different input devices ivitli more thari nvo degrees offreedonr. A) Tiie "Ctibic Mouse': rlrsigned by B. Frolrlich & J. Plate (Frohlich and Plate 2000). is an isotonic device with additional rod and btirton controls. B) The "Rockin 'Mouse ", designed by R. Balakrishnan, is a morrse with a uirved bottom and a Wacom mrserisorforsensing the angle of tire morue. C) fie" h1ITS Glove ", an isotonic device designed by S. Zhai (Zhai 19951, comisrs of an Ascension Bird@ tracker and a clutch nrounted on a glove. D) Tlie "FingerbaIl", an isotonic clevice designed by S. Zhai (Zhai 1995), consists of an Ascension Bird@ tracker in a ball. E) The "Bar': an isotoriic device designed by C. Ware (Ware 1990). cottsisrs of a Pdhemus TMtracker and a handk FI The "EGG", an elastic device designed by S. Zhai (Zhai 1995). consists of an tlscension Bird@ tracker rnotinted within an elastic fiame. G) The Spaceball Y an isometric device trranirfacrured by Labrec@. 4 î l e Cricket 'M nranufactrired by Digital inrage Design Inc., an isoronic device with a handle, 9 Tire Magellan SpaceMouse distributed by Logitech The SpacaW(1ster tnantrfacttrred by Basys. Germany. K) nie "ErgoPoint 30" manujàctured by ITU Research, a device iwVItIr four totich sensors. L) IBMS ScrollPoint@ Mouse is a niouse combined ivith 2 degree of freedom isomerric joystick M) The "Padnrouse " designed by R. Balakriihnan (Bafakrîrhnan and Patel1998) is a moiise combined with a touchpad
Not onIy are the tasks which requüe rnuItipIe degree of fieedom controI more compIex,
but so too are the input devices with which operators interact. A sampfe of the variety of different
designs for rnultidegree of fieedom cornputer input devices is shown in Figure 2. At the thne of
this writing the computer mouse is the dejàcto standard for interacting with desktop cornputers,
and rnany of the devices in Figure 2 are in fact variants upon the current rnouse design. New
devices with a p a t e r nurnber of degrees of fieedom in the past have been introduced on a
regular basis into the market or at professional conferences (e-g. ACM- Association of
Computing Machinery's CHI-Computer Human interaction, and SIGGRAPH- Special Interest
Group on Graphics and interachve techniques).
It is one thing to design and manufacture a computer input device, but it is quite a
different thing to assess the performance or usefulness of a design. Often the design of new input
devices is based upon available sensor technology (Zhai 1995), rather than designed to meet the
demands of the user, the task, and the environment. The mapping between costs of materials and
production to number of units sold at a specific pnce for profit is relatively straightfonvard based
on established econornic principles. in contrast. the mapping between the design of an input
device to quality of the interaction allowed to the user is not as direct or as well understood. What
is known about design factors which directly impact performance of input devices include the
following identified by Zhai (Zhai 1995):
O Muscle groups and joints. The physical size, shape. and Iocation of an input device
determines an input device's affordances. For example, a srnall dial is best manipulated by
rotation between the thumb and forefinger. An input device worn like a glove on the hand
(e.g. the MITS Glove (Zhai 1995)) may require wrist, arm and shoulder rnovements.
Different parts of the body have different proportions olbrain cortex allocated to their control
(Sage 1977). with the finger tips and hands having a much greater number of dedicated nerve
fibres than the larger wrist, elbow, and shoulder joints. Therefore one leveI of improvement in
perîbrmance can come by switching control to the fine muscle groups, e.g. the finger tips.
Zhai's research has demonstrated that, for complex applications requiring a 6 degree of
freedom device, performance may be improved by using as many available joints in the body
as needed and are appropriate to manipulate the input device. For example, optimal
performance on some tasks requiring a large amount of rotation can be obtained by using the
figers in addition to using the entire arm to interact with the input device (Zhai 1995).
0 Input device resistance. This is the physical force the user interacts with. Device resistance
refen to a continuum, with isomeaic (meaning an input device which does not move and
ïnstead senses the amount ofapplied force) devices atone end and isotonic (input devices
which exert constant resistance which, when zero, sense a position in space) devices at the
other end. AI1 other m e s of devices, such as elastic (resistance which increases with
displacement), viscous (resistance mcreases with velocity), and inemal (resismce increases
with acceleration) devices, should fa11 somewhere in between the two ends of the continuum.
By definition, isometric and elastic deviceç are self-centring; when the user lets go, the input
device returns to sarne position each time. Also, the amount of proprioceptive feedback
available depends on the input device resistance. Isometric input devices provide only force
resistance, isotonic input devices provide only displacement information, while elastic
devices provide both force and displacement information. Zhai (Zhai 1995) proposed that
elastic controllers are the most advantageous for 6 degree of Freedom manipulation when
cornpared to isornetric input devices.
Transfer functions. A transfer function is an engineering term for the transformation mapping
of a signal; in this case the mapping is from the input device to the cursor movement. A zero
order transfer function is a direct mapping from input device position (or pressure) to a
particular cursor position. Zero order control is a 1 to 1 mapping of cursor to input device,
and is therefore also hown as position control. Often in zero order control it is necessary to
have some sort of clutching mechanisrn, for example when the desired cursor position is out
of physicd reach of the user. By clutching (disengaging the input device fiom controlling the
cursor. usually by pressing a button) the position of the input device can be reset without
affecting the cursor position, effectively resetting the home position of the input device.
A first order transfer function involves integrating the input from the controlling
device. In other words, the velociry of the cursor is proportional to the position (or force) of
the input device. First order control is also known as rate control, since a particular position
(or force) applied by the user corresponds to a particular velocity of the cursor.
Higher order controls involve additional integntion of the input h c t i o n for each
additional order (e.g. a second order transfer function is a double integration of the input
signal). For human opentors higher than f i order control usually results in an unstable
mnsfer function for many applications.
in a series of experiments, Zhai (Zhai 1995) concluded that the transfer function
interfacing a device with a computer should be compatible with the physical constraints of the
device- Zhai identified that an interaction exits between the input device resistance and the
transfèr function, where isomemc device should be used with rate control while isotonic devices
shouId be used with position control. An additional finding 6om Zhai (Zhai 1995) was that,
although isotonic position control is more "intuitive" than isometnc rate control, with practice
performance becomes equal across both modes of interaction. However, isotonic position control
was also found to be more fatiguing and jerkier for target acquisition tasks. Zhai's concIusions
with respect to input device resistance and transfer function are sumrnarised in Table 1.
Table 1. Strtnmaty of Zhai's findings ivith respect to inptir device resistance and fransferfirncrion, (Zhai 1995)-
Isotonic Input Devices lsometric Input Devices
Optimal Transfer
Function I 1
zero order (position control)
Self-Centring
Performance
Trajectory
fmt order (rate controI)
Fatigue
No
initially superior to isometric
Yes
equivalent to isotonic with
practice
relatively fatiguing
tnjectory is somewhat jerky
compared to isometric
Most descriptions of transfer hct ions (Wickens 1986; Zhai 1995) may give the
impression that zero order, fust order, etc. .. are the only options available for transfer fimctions.
However, most input devices used for real world tasks do not fit cleanly into a well-defined slot,
dong the tnnsfer function continuum. For example, a typical computer mouse is operated neither
strictly in position control nor in rate control mode, but rather somewhere in between- For slow
movements a computer mouse is effectively in position control mode, while for quick movements
not very fatiguing
velocity control integration acts
like a low pass smoothing filter
L
Range oîcontrol
the amount of cursor displacement is not CO-linear with the amount of mouse movement.
Input devices do not fit cleanly on the resistance continuum either. The iBM
ScrolPointB mouse and the PadMouse (Balaknshnan and Patel 1998) are multi-channe1 or
"mixed resistance mode" devices, for which different types of interaction devices (such as
isotonic mouse, touchpad, and isomemc joystick) are merged together into a single device. So
within even the same device, some degrees of Eieedom may have an isotonic sensor, wtule otficr
degrees of fieedom may be based on isometric technology.
limited; usually requires
clutching or zero resetting
unlimited (when used with rate
conîrol)
The number of possible combinations is quite high. A six degree of freedom device
required for 3D tasks could potentialiy have a different resistance and transform Fiinction for each
degree of fieedom, not to mention different gains, different ranges of motion, and different form
factors requiring manipulation by different joint and muscle groups.
The National Research Council's Comminee on Virtual Reality Research and
Development has stressed the need for ways of evaluating manual interfaces and has stated that
the current technology has not been adequately assessed (Durlach and Mavor 1995). New
products that allow users to manua1Iy interact with cornputers are regularly appearing on the
market, yet little is being done to quanti@ the usability of these devices, For mass consumer
products such as video game consoIes, the marketplace would be expected to sort out different
products, with the "superiof' products, winning market share. However for cornplex and life
critical applications such as surgery or space teleoperation allowing the market to decide the
interface may not be the best way to go. While the quality of the hurnan-computer interface is no
doubt a factor in determining market share, it is not the only one. Things such as cost,
advertisinglimaghrand name, and software compatibility also influence the market share of
computer-based products. The more critical the application, the greater the need for a quantitative
evaluation of the manual interface,
What quantitative measures currently exist for assessing human performance using multi-
degree of freedom input devices? How welI do these measures provide an understanding of what
is happening in terms of the user's control in one degree of fieedom relative to the other degrees
of freedom? How applicable are the current memcs to tasks with more than two degrees of
Freedom? Are users able to control more than one degree of freedom at a time'? If yes, then how
many, and to what degree? Are the current metrics able to provide insights into what strategies
operators use when faced with compiex computer manipulation tasks?
The same control action in different environments could result in different performance
scores- do existing metrics reflect this (i.e. are they task dependent)? The following section first
defines manuaI control tasks and presents a taxonomy to categorisc the different types before
discussing existing measures for quanti@ing performance.
1.2 Existing Performance ~Metrics
The term ''worlcing point" refers to those "most important" points whose trajectory is
vitaI for executing a motor task (Latash and Turvey 1996a). A manuid control task is one where
the manipulation of a "working point" is accompiished by manipulation of the han& or fingers.
The working point need not even be in a permanent direct contact with the body- in most
compurer tasks, the screen cursor is the working point that must be appropriately positioned in
order to accomplish tasks.
Manual control tasks cm be considered to differ in at least two dimensions, time and
space. The time dimension includes whether the pace of the task is set extemally, or if the
operator sets the pace. Externally paced tasks are usually time-matching tasks, where the users
must contact a target at specified times, while self-paced tasks are usually tasks where users are
trying to minimise movement times (Meyer et al. 1990). In the space dimension, either the
contact point can be a single point in space, or the contact point can be distributed over a
sequence (either a series of points or continuum) of points with a specified order.
Figure 3 presents a taxonomy of manual control tasks broken d o m by their space and
time requirements (Masliah 1999). An example of extemally paced single location tasks includes
bal1 catching, where a target must be acquired at a specific point in both time and space. If there
is no external time requirement. the task changes fiom being a target acquisition task to a docking
task. A docking task is defined here as a task for which an object, such as a cursor, must be
moved fiom an initial position to a goal position, with no constraints on either the trajectories that
rnay be chosen or the maimum time allowed to complete the movement fiom initial state to goal.
Menu selection and peç-in-hole tasks are also considered to be docking tasks.
Dynamic tracking tasks are those tasks for which both the time and space domains of the
task are specified. Dynamic tracking tasks specie both when and where the user's cursor needs to
be in order to satisfjt the demands of the task. If there is no external time requirement, the task is
defined as a tracing task, for which only the space constraints of a trajectory and not the timing of
the trajectory is specified. Marking menus (Kurtenbach and Buxton t 993) and Çee drawing of
predeftned shapes are examples of tracing tasks,
That which is typically measured for each time-space combination is shown on the right
side of the time-space taxonomy in Figure 3.
Time Domain Externally Paced Self-Paced ( T i e Matchhg) (Ti Minimizing)
- D ynamic Tracking . target
gunnery . driwng at a constant
TaaCgetAcquis$ion - - , bail catching ' , instrument
playing at a tempo
- speed- ----
Target Da king -;---menu - _-. _ -
selection , pegin-hole
tasks
Trac ing , drawing , marking
menus _--- - -- ---
---- What is being --__ -- --.- measirred?,- -phase e m r -spatial e m r
-phase ermr -spatial e m r
c o q ktion
collisions
comp letion
-spatial e m r
Figure 3. A taronottp of tittle-space nianira1 control rash. fiMadiah 1999)
In order to develop an understanding of what operators are doing when mmipulating
many degrees of fieedom it will be necessary to go beyond basic measures such as task
completion tirne and hstead to apply memcs which examine the rrajecrory of the working point
during the task, The following sections review existing memcs from the human factors, motor
contrai, neurological, and human-computer interaction literature that have been used for assessing
human performance in genenl and specifically those metrics which analyse trajectory
information.
1.2. I Tirne-On- Tar.eet
Historically, in the human factors literature (Ellson 1947), interest in human multi-degree
of tieedorn performance arose chiefly fiom military interests. Research in the late 1940's and
early 1950's centred on anti-aircraft gunners' ability to hit targets, and time-on-target for each
degree of freedom was used mainly because it was feasible to compute at that time. (Percent
cime-on-target is computed as the ratio of the tirne on target, within a d e h e d area, divided by the
total task time.) Tnditionally, time-on-target was a performance measure. Poulton (Poulton
1974), however, has severely criticised time-on-target as "not a very suitable measure", because
m o n whïch are slightly off-target are penalised just as much as m o n which are far off.
UsuaIly time-on-target is computed for al1 degrees of fieedom simuIîaneously (Senders et
al. 1955). However, by computing each degree of Ereedom separately and comparing them to the
entire set of available degrees of freedom, ElIson (ElIson 1947) was able to extend time-on-target
to become a type of coordination mesure, Zhai and Senders have presented (Zhai and Senders
1997a) a senes of different time-on-target metrics which are çummarised in Table 2. Using time-
on-target as a metric is based on the following assumptions:
that, if the percent of simultaneous time-on-target (STOT) was equal to the product
of the individual time-on-target scores (TOTx*TOTy), then the degrees of freedom
may be considered independent
that if the percent of sirnultaneous time-on-target (STOT) was greater than the
product of the individual time-on-target scores (TOTx*TOTy) then the degrees of
freedorn may be considered positively correlated
that if the percent of simultaneous time-on-target (STOT) was less than the product
of the individual time-on-target scores (TOTx*TOTy) then the degrees of freedorn
may be considered negatively correlated
Tabie 7. ~Ilecricsfionr Eiison (Ellson 1947) and Zhai & Senders (Zhai and Senders 1997a) used to w e n d cime 011 targec into a coordination memre.
Variable
I time-on-target
NameAlescription
TOTs
simultaneous tirne on target
individual degree of Freedom
TOTb
I target
baseline time-on-target value
TOTrnin srnaIIest individual time-on-
Value
C
tirne on target for only one degree of freedom-
computed for each degree of fieedom separately
KY, Z, RX, RY, RZ)
coordination coefficient
rime on target over al1 available degrees of
freedom/total task tirne
product of time-on-target over al1 the individual
degrees of freedom
TOTuYTOTy *TOTz*TOTEtx*TOTRy*TOTRz
(STOT - TOTb)l(TOTmin - TOTb)
h critica1 analysis of the data in (Zhai and Senders 1997b) for a 6 degree of freedom experiment
shows that TOTmin, STOT and TOTb show signs of asymptoting, as opposed to showing
continuous improvement for a (relatively) short one hour expenment. Zhai and Senders found
chat their coordination coefficient did not improve with practice, and in fact became slightly
smaller over time. In their paper Zhai and Senders admit that they did not understand why C did
not increase. Zhai and Senders did however conclude that subjects' performance was
"coordinated" for their 6 degree of fieedom tracking tasks- but not by much.
Zhai and Senders used a different slim of nventy sine waves for each degree of Freedom
as the forcing function dnving the target's motion. Using a sum of sines forcing function
traditiona1Iy has been an acceptable and standard practice for dynamic tracking tasks because it
produces a complex trajectory suficiently unpredictable to subjects (PouIton 1971; Zhai 1995).
Zhai and Senders' study emphasised an "operator's ability to coordinate two or more dimensionsn
(Zhai and Senders 1997a). Even without an explicit definition of coordination it is argued in the
present thesis (see sections 4.1 and 4.5, pages 71 and 73 respectively) that the forcing fict ion
must in some way be "coordinated" and that independent forcing fumions are by the nature of
their independence not "coordinated". The forcing fict ion used in (Zhai and Senders 1997a) for
the target motion was driven by six indeperident forcing hctions, so it is unclear how strong
conclusions may be drawn from an experiment to claim coordination where all available degrees
of Freedom are moving differentty.]
1.2.2 RelariveMotionPlors
Grieve (Grieve 1968) was interested in how "coordinated changes of timing and
amplitude of movement" come together to produce different gaits in humans. PreviousIy,
coordination has been studied by graphing single joint angle changes agauist a rime axis. instead,
by p p h i n g one joint angIe against another joint angle, Grieve was able to present cyclic patterns
cIearly on a single graph and at the same time deal with beginning and end discontinuities,
Presenting movement pattern in graphical format relies on pattern recognition for identmg
deviations fiom the nom.
Many extensions in order to quanti@ the data that Grieve depicted graphicaiiy have been
developed. To "desmie accuateIy changes in the movement pattern of one Limb segment in
relation to another or to compare the motion of different Iimbs" (Sparrow et aI. 1987) has been
the goal in each case. For example, a reIative motion plot is fundamentaiIy an angle-angle plot,
which is a graphical representation of motion. A summary of methods that can be used to
12
quantfi the information that is being presented graphically is provided by (Sparrow et al. 1987).
They include:
cross-correlation- the angles between temporally successive data on two angle-angIe
diagrams are cross-conelated
auto-correlation- successive data in a single time series are "auto-conelated"; that is, a tirne
series is cross-correlated with itself
centroid- computation of the centre of a relative motion plot
area and perimeter -usually involves linear approximations on adjacent data points to
calculate areas and lengths of a relative motion plot
orientation- the orientation of an angle-angle diagram is computed by using a Iinear
regression of y on n. The arc-tangent of the dope of the regression line of the y coordinates
on the n coordinates is used as the orientation of a relative motion plot in relation to the
horizontal.
asymmetry and normality indices- A weighted ratio of an individual's perimeter, a m ,
cennoid radius, and centroid angle to the mean of normative data. (Instead of using the mean
of the raw scores, the ratio of the individual's score to that of a mean derived €rom normative
data was used.) This has been used mostly to assess abnormalities and asymmetry in hurnan
gait.
discriminant analvsis- similar to the asymmetry and normality indices, this measure includes
weiçhts for Iinearly combining different measures.
1.2.3 nze Speed Acniracv Trade-off
Faster movements result in lower accuracy, and highly accurate movements must be
conducted slowly. Fitts' law is one of the most "robust, highly cited, and widely adopted
rnodeIs"(Mackenzie 1991) whose reach has extended beyond psychology. in fact for some
publications Fitts' law has been so accepted as fact sometimes it is not even cited (Bohan and
Chaparro L998; Bohan et al. 1998). Fitts' Iaw is defined as folIows (Mackenzie 1991):
Movement Time = a + 6 logz -+ c (: 1
Movernent Time = a + b * ID
a, b are empirically determined constants
c = 0,0.5, or 1.0
Targe ts Maximum
Phas/ Plane Area
Figure 4. Hypotltetical phase plane plot, adopred from (Belibehani et al. 1988).
The "coordination index", proposed by Behbehani et al. (Behbehani et al. 1988) is a
measure of accuracy multiplied by a measure of velocity, which is based on Fitts' speedlaccuracy
made-off law. Figure 4 is an illustration of an ideaIised phase plane plot for two consecutive target
jumps in a "nndom step tracking task" (a task wheiere the target, after acquired, will shifi its
position by a random arnount thereby starting the task overagain.) Behbehani et al.'s
"coordination index" is computed by using the maximum velacity and the area circumscribed by
the phase plane plot. n i e greyed area in Figure 4 is proportional to the maximum velocity and
total displacement and is used to index coordination (Behbehani et aI. 1988). This coordination
index has been used in biomedical research as a means of quant img upper extrernity
performance in Parkinson patients.
1.1.4 Time, Space. and Freqziencv Domains
An excellent compilation of existing quantitative human performance rnethods for
measurernent in the tirne, space and fiequency domains is presented by (Yu et al. 1997). The
definitions given in Yu et al. are the following:
Trajectory Measures
lengths of the trajectones
rise tirne- time it takes for each variable to reach its respective target for the first time.
tirne to contact to the target- a dynamic measure of the time that is rernaining for a variable to
move frorn its current state to the lower boundary of the target region, given its current
instantaneous velocity
area under time to contact
Oscillation measures
oscillation duration- time between the end of the rise time and the time when each variable
çoes into and stays on the target
peak- the percentage deviation with respect to the target value of each variable
number of oscillations- number of overshoots plus undershoots
area of deviation per unit time- the totaI area of deviations outside of the target region divided
by the duration of the oscilIation penod.
Variance variables
time shifi- time tiom stan of trial to first action taken
action frequency distributions- a distribution of the settings operators set different
components at
Trajectory measures are measures in the space domain. Variance measures are measures
in the tirne domain. Oscillation measures are measures in the tkquency domain.
1 .X Spatial or Temporal Invariance
A comrnon theme in the motor control Iiterature is to use the amount of invariance in a
repeated movement as a measure of coordination. Moi-nson & NeweIl wrote: "...coordination
refers to the degree of spatial or temporaI invariance, or both, in the motion of the respective Iimb
effective units." (Momson and Newell1998) Measurement in the time domain is done by
computing cross-correlations, while measurernent in the fiequency domain is through coherency
and phase analysis. (Morrison and Newell 1998) This means of analysis is generally useFu1 only
for repeated rhythmic motions, such as walking, m i n g and jumping.
I.26 Cross-Correlations
Estimating the cross-correlations arnong error terms or joint angles (Vereijken et al.
1992) is another method for quantitjing coordination (Zhai and Senders 1997b). Unfortunately,
this method usually restricts analysis to only two variables at a time. Estirnating multivariate
cross-correlations becomes computationally very intensive thereby limiting what in pnctice cm
be achieved for 6 degree of Freedom data.
Zhai (Zhai and Senders 199%) conducted a 6 degree of fieedom tracking study and
analysed the results by cross-correlating al1 pairs of degree of fieedom error terms. The goal of
(Zhai and Senders 1997b) was "to gain insights as to whether translation and rotation were
integnted or sepanted aspects of 3D object manipulationn- Twenty-six subjects perfonned 6
degree of fieedom tracking in phases, where each phase consisted of 3 to7 minutes of pnctice
and four 40 second tracking trials. The correlation coefficient was then computed for every two
degrec of lieedorn pairing (a total of 15 different pairings) and graphed in a histogram, creating a
distribution of cross-correlation coefficients. Note that Zhai & Senders estimated the correlation
coefficient only for a time lag = O (no tirne lag). Zhai & Senders resuits could potentially be very
different if the subjects' motor control lag had been taken into account.
Interestingly, the correlation distributions showed that subjects were able to contro1 a11
the degrees of fieedom equally. The rnean values for the correlation distributions was just p a t e r
than zero. at around 0.2. However, sirnply correlating the error tems does not take into account
task related performance, in that two errors which are decreasing, or even increasing,
simultaneously will both result in high correlation coefficients. In fact the data from Zhai &
Senders showed that the highest correlation coefficients were found between translation and
rotation. Zhai & Senders concluded that subjects were treating translation and rotation in an
integral manner.
One problem with the Zhai & Senders study was that each degree of fieedom had a
sepante forcing hction, which meant that each degree of fieedom was completely independent,
so it could be possible that the target could have large motion in one degree of freedom and
minimal motion in the remaining degrees of fieedorn. Using cross-correIations as a rneasure of
coordination is based on the premise that mulrrjlle errors arereduced simultaneomly. However, if
ertors are not being created sirnultaneously is it reasonable to expect that an operator should
reduce them simultaneously?
Another potentiar problem with the Zhai & Senders study is that tracking trial length was
too short as compared to the wavelength of the forcing fùnction driving the target. Zhai &
Senders used the followïng forcing fùnction for the X degree of freedorn (Zhai and Senders
w m ) :
19
~ ( t ) = C s i n ( 2 d p i t + 4.r (i)) i=O
where
t = time
A = 3 . 5
p = l . Z
fo =0.01
4.r ( i ) = a randorn nurnber between O and 2z
This equation is the sum of 20 sine waves with different wavelengths and amplitudes.
The sine wave corresponding to i = O has a penod of 125 seconds; more than three times longer
than the sampling period of 40 seconds per tracking trial. This is probably what accounts for the
large distribution ofmeasured cross-correlation scores, a range of -0.5 to 0.9 out of a possibIe
range of -1 to 1. For example, if the cross-correlations are computed for a non-moving cursor,
that is a tracking task with no human operator, under the same expenmental conditions as Zhai &
Senders, the range of cross correlation scores wouid range fiom -0.9 to 0.9 (unpub1ished
simulation by the author). Ideally in such a situation a measure of coordination should r e m a
consistently low score, nther than a range of possible scores, some of which are very high, The
onIy way to obtain that whiIe using cross-correlation coefficients would be to have the sampiing
period much longer than al1 the wavelengths of the forcing fùnction. Unfortunately, it is not
practical to expect subjects to be able to track continuously for hours and hours, and a forcing
h c t i o n made up predominantly of shorter sine waves would be too difficult to track.
Besides of the unequal creation of error across different degrees of fieedom and the
sampling size issues, Zhai & Senders study did not show several results that should have been
expected, That is, no differences in cross-correlation distributions were seen between isomemc
and isotonic input device conditions. As wiIl be shown in this dissertation, the method of
interaction between the Spaceball and Fingerball are very different, and this difference shouM be
apparent in the cursor trajectories and thus the correlation coefficients. Also, subjects did not
show improvement with time (phases of the experiment). With practice, any measure of human
coordination should be expected to show improvement, However, the average cross-correlation
distribution scores actually went down from the first phase to the fifth phase. The most likely
conclusion from this is that the experimental conditions, combined with the particular method of
computing the cross-correlations, is not an appropriate measure of coordination.
1.7 7 Inte,gralitv
While most metrics in the literature deal with the motor control side of coordination,
there is also the perceptual side of coordination. How different variables, or dimensions, are
perceived obviously affects the performance reaction. According to Garner, two stimulus
dimensions are considered integral if they are perceived as a single task dimension or separable if
the dimensions seem umelated (Garner 1974). Whenever two stimulus dimensions are perceived
as integrai and they are varied in a correlated manner, reaction time is faster than if the stimulus
was varied in only one of the dimensions (Garner 1976). Separable dimensions, on the other
hand, can not easily be perceived as one; instead they are selectively attended to.
Jacob et al. (Jacob et al. 1994) have argued that the physical structure of an input device
must match the perceived structure of the stimulus. Thus an integral stimulus shouid be matched
with an integral device. and a separable stimulus should be matched with a separable device.
(Jacob et aI, 1994) have proposed a means of quantimng the degee to which a movement
trajectory can be considered integral or separable, based upon whether or not movement exists
simultaneously in al1 degrees of freedom.
Jacob et al. (Jacob et al. 1994) defined intepnlity as whether it is easy, or even possible,
to move diagonally across degees of Ereedom. In Figure 5, trajectory A is showing evidence of
"city-block"(Garner and Felfoldy 1970, p.226), or "stair-step" (Jacob et al. 1994), movement
between the (x and y) degrees of Freedom, Trajectory B exhibits what (Garner and Felfoldy 1970,
p. 225) termed "Euclidean" movement- movement that cuts diagonally across the degrees of
freedom. integrality, as defined by Jacob et al. is a task independent measure; that is, movement
of any kind is considered integral regardIess of whether or not the movement is contributing
towards reaching the goal.
Integrality (Garner 1974: Garner and FelfoIdy 1970) is not strictly a coordination
measure, though it has been used in that way. Balakrishnan (Balaiaïshnan et al. 1997) for
example, used integrnlity to demonstrate that subjects could controt three degrees of fieedom
simultaneously with a two translation + one rotation degree of Ereedom device, the Rockin'Mouse
(Balakrishnan et al. 1997).
Figure 5. Trajectory A sliorvhg separable degrees ojfreedom, trajectory B showing integral degrees of freedom.
[ntegrality is measured by first segrnenting into equal time units the trajectory of each
degree of freedom (Jacob et al. 1994). Each segment is then checked for the presence or absence
of movement above a chosen threshold. Foreach time segment, trajectory movement in al1
degrees of fieedom classifies that segment as Euclidean, whereas the end result is a ratio of
Euclidean to city-block movements for a given task. This ratio is a measure of the integrality of
control of a given input device, which can then be compared to the integrality ratio of other input
devices for the same task. Integrality as a measurement is concemed only with the timing of
movements, and places almost no emphasis (for movements above the threshold) on the
magnitude of the movements. For this reason, integrality is measurement in the time domain only.
1.7.5 hefficiencv
Zhai and Milgram (Zhai and Milgram 1998) have proposed a definition of coordination
which takes task performance into account. Theü measure is based on ineflciency, where
coordinated movement is genenlly recognised as being an eflcient movement. Applicable to
docking tasks only, inefficiency is computed as the ratio of the length of the actual cursor path
followed divided by the length of the shortest path, as illustrated in Figure 6. With this unified
mehic, al1 the degrees of Ereedom are combined to produce a single length, so it is not possible to
make any conclusions as to relative efficiency across individual degrees of fieedom. inefficiency,
as defined by Zhai & Milgram (Zhai and Milgnm 1998), is entirely a function of the magnitude
of the movements made across the degrees-of-keedom, and not of the timing of those
movements. For this reason, inefficiency is a measurement in the space domain only.
Inefficiency is measured as a ratio o f the length of - the actual trajectory over the length of the optimal trajectory
Length of actual trajectory across al1 the degrees of freedom
;. Lrngrh of the optimal trajectory _...- -'
across al1 the degreen of fieedom
Figure 6. How ineficiency (Zhai and lClilgram 1998) is calculared.
13 Theory and Literaîure on Multi-Degree of Freedom Euman Cootrol
The need to understand how operators manipulate many degrees of Freedom assumes that
human behaviour is not arbitnry and instead that operators exhibit specific types of behaviour
and apply strategies when performing motor control tasks. But what kind ofstrategies do
operators use when manipdating six degrees of fieedom in an object manipulation hsk? How
does an expert's motor actions differ fiom a novice's other than in stnctly time or accuracy
improvements? Do novices exhibit qualitative différences in behaviour? To what extent does the
design of the input device affect the strategy operators use to accomplish tasks? If a satisfactory
tool did indeed exist for understanding trajectory information then hypotheses related to motor
control could be formally tested in experimental settings.
The following subsections survey what is akeady known about motor control in generaI
and how people interact with everyday abjects and l e m new motor skills. The goal of this
literature review is to take what is known about motor control and apply it to human-computer
interactions, thus providing hypotheses that c m be tested and used to pcedict performance
strategies.
1.3.1 How Movements are Learned
"everything started with a dog" N. A, Bernstein (Latash and Turvey 1996a, pg. 173).
Russian physiologist 1. P. Pavlov, in a series of classical experiments, demonstrated that
if a hun,gry dog is eqosed repentedIy ta the samt stimulus just pior to feeding, over time that
dog will start salivating in response to the stimulus, regardless of whether or not the food is
evennially presented. This development ofa new action, which Pavlov called conditioned
refle'res (Latash and Turvey L996a, pg. 174) (Hilgard 1962, pg. 17-19), took hundreds of
combined signal and feeding presentations in order to produce the simplest of responses such as
salivating. Nonetheless, PavIovTs experiments were taken as evidence that learning of al1 kinds of
behaviour occurs through basic repetition.
This repetition-based development mode1 has been applied to hurnan motor control. The
traditional theory for the development of motor contro1 is summarised by Reed (Reed and
Bhndine 1996, pg. 435) as follows:
1. Movements are the units of actions.
1. Movements are either the results of central nervous system commands or reflexive.
3. Movements are more IikeIy to be repeated when they become associated wîrh pleasurable
feelings or outcomes.
4. The repetition of movements, leadinç to changes in the frequency ofgiven movements, is the
central mechanism in action leming.
[n other words, the cIassic approach is that people learn a cumplex movernent by
performing an action over and over again until the neural path for that action becomes strong,
Learning is reduced to the mere strengthening of the appropriate neural pathways fiom the brain
to the controlled muscle group. An opposing view is given by Bernstein, who summarised his
ideas as "repetition without repetition":
"Lit is ven, ivrong io idenrlfv the elaboraiion of a ski1 ivith the beating of a nertral parh in the brain. The coeficienr of er$cacy of this method woriid be orrrrageousiy iorv.for erample, to spend many hundreds of thorcsands of kilogram-meters of work on ntrmerous repeticions of a pole vault in order to move a ferv molecules in rhe brain that had been blocking the neuralputh. The actual imporrance of reperitions 13 quite diferen. Reperirions of a movemenr or action are necessasr in order ;O soive a motor problem many rimes (bercer and berter) and to find the besr ways of solving it. Repetifive solirtions of a problem are also necessas, because, in natural conditions, aternal condirioru nwer repear themselves and the course of the movemenr i3 never idealij reproduced. Coriseqrrenrly. it is necessary to gain erperience relevant to al1 various mod$carions of a ta&, primarily. ro ail the impressions chut underlie the sensory corrections of a movernent. .. " N, A. Bernstein (Latash and Turvey 1996a, pg. 175)
Bernstein's defmition of motor skill is "an ability to solve one another type of motorproblern" and
~tot "a formula of permanent musde forces imprinted in sorne motor control" (Latash and Turvey
1996a, p. 176). Bemstein also points out that living creatures in the real worId, unIike the dogs in
Pavlov's experiment, are not passive with respect to acquirùig sensations From the environment.
Rather, living creatures actively catch and gmb their perceptions From the world mund them
(Latash and Turvey 1996a, pg. 175). The importance of Bernstein's ideas is the emphasis it
placed on the dualism of perception and action. as opposed to treating them as separate concepts.
1 - 3 2 fie Trajecrorv of the Working Poitir
In the 19201s, Bernstein (Bernstein 1967) studied professional blacksrniths hitting an
anviI with a harnrner, workers wvho had been doing the same motor control task €or years. In the
case of the bIacksmiths, the tip of the hamrner is the workingpoint whose trajectory must be
conaolIed (Latash and Turvey 1996b) to properly strike the anvil. Bernstein observed that, while
the trajectory of the cip of the harnrner remained reIatively constant, the trajectories of the
individual joints of the body were much mure variable. Assuming that the blacksrniths had
deveIoped an optimal and standardised pattern of achieving their goals, it is perhaps surprishg
that their motor actions wouId show such a degree of variability. Latash haç argued that whatever
is being encoded into a blacksmith's brain for a given task must be the trajectoy of the working
point, nther than joint specific cornrnands (Latash and Turvey 199th). A blacksmith's body
manipulation cm take multiple different trajectories, yet still achieve the same working point
trajectory, thereby accomplishing the given goal.
Latash's arguments have direct implications for understanding how operators rnay
interact with a cornputer in an object manipuIation task. Even though the brain does not know (or
perhaps even care) which joints move in w h t way in carrying out a movement, the trajectory of
the wvorking point will still follow expected patterns for expert opentors. Therefore studying the
trajectory of the working point, the actual focus of the opentor's attention, may in fact be more
fiuitful in understanding behaviour than the study of individual joint angles which are more likeIy
to show variability fiom trial to trïaI.
1.3.3 Learnin,g ro Coordinare Redundant Biomechanical Dewees o f Freedom
The "Bernstein question" refers to how one coordinates redundant degrees of fieedom-
As the Level of anaIysis becomes more micro ( h m joints to muscles to motor units) the nmber
of degrees of freedom goes up. NeweII and McDonald have pointed out that prdonged practice
leads to qiialitative improvements in performance, not just quantitative (Neweü and McDonald
1994).
Learning new rnotor skills is usually complex, and Bernstein proposed that people reduce
the complexity of the task by reducing the number of degrees of Eeedom they are controlluig.
When Q i n g ro solve an unfarniliar motor problem, a novice must consciously conuol a large
number of joints. This can be accomplished by Iocking or "Freezing" joints in the body so that
they are rigid, which has the et'fect of reducing the number of variabIes that need to be monitored,
thereby makinp the task easier. Another reduction in the available degrees of freedom can be
accomplished by having two or more joints move in phase with each other, essentially as a tightly
coupIed single unit (Vereijken et aI. 1992). For e.wmpIe, an athlete who is leaming a new move
or sport may be tord by the coach to "loosen up" or "relax". What the coach is reaIIy saying is
"use al1 of your avaihble deprees of freedorn". The athlete has locked or coupled joints in the
process of leaming how to move and the coach is trying to counter the athlcte's reductionism.
Bernstein proposed two stages in the development of a new motor control skill. The k t
stage involves the slow Ioosening of the joints that were fiozen, During this phase a person leams
how ro use al1 of the available joints towards accomplishing the task. Joints that were previously
rigid now collaborate as a single functional unit, what Bernstein called "synergies," and today is
referred CO as "coordinative structures" {Kugler et al. 1980). A coordinative structure is deFined as
a group of muscles constrained to act as a single task-specific unit (Tuwey 1990).
The second phase involves not just the utilisation of al1 the available joints but the
optimisation, or efficient use, of those joints. Greene provides the following description of an
optima1 exploitation of existing reactive, Frictional, and mornentum forces to place a jug of milk
in a refrigerator.
Using momenttinl means tliat the arm srvings with litle artention. Ir is also ensier. When i p a a gallon of ~nilk on the bortom sherofthe refigeram, TI l@ed it in some rrrbitrary way, I'd be rired harrvay throiiglt. Insteud, holding it wifh my a m hanging doivn. I walk toivard rhe refrrgerator making the miikswing backic-rird like a pendrrlrim. Istop, and the milkswings into the refrigerator with no e o r t on tnypart. (Greene 1982. p,276-277)
While Bernstein's theories of motor skiil acquisition were first published in English in
1967, no empirical corroboration existed until 1 W2, in the fonn of a IongitudinaI slaiom ski
simdator expenment (Vereijken et al. 1992). Five novices trained on a slalom ski apparatus fur a
fou1 of 140 minutes each dismluted over a 7 day periad- Ten points on the subjects' body were
tracked during ûaining; the shoulders, hips, knees, ankies, and feet. initiaIIy subjects' joint angles
showed only a srnall range of movement, as rneasured by theu standard deviations and ranges of
angular motion. The cross-correlations of the joint angles between different joints, on the other
hand. were quite high. With practice, the range of movement of the joints increased while the
cross-correlations behveen different joints decreased.
Vereijken et al. (Vereijken et al. 1992) have surnrnarised their experimental results
according to the following:
While learning has traditionally been defined as the process of reducing variability in
performance, the development of coordination involves "the search for optimal rnovement
strategies within the biological workspace".
There is no one-to-one mapping behveen the variability in the avaiiable degrees of freedorn
and the variability of the resulting performance.
Freezing out degrees of Freedom in order to reduce the complexity of a coordination problem
may be a genenl stntegy for acquiring skill.
1.4 Summary and Research Goal
As previously mentioned, the-on-target scores are limited in their ability to accurately
reflect what is occurring in a multi-degree of Freedom task, since errors which are slightly off-
target are penalised just as much as errors which are far off (Poulton 1974). Relative motion plots
and spatiaVtemporal invariance measures are usehl only for repetitivekyclic motions and are
usually Iimited to only hvo degrees of fieedom at a tirne. Cross-correlating errors or joint angles
is computationally too intensive to be practical for more than two degrees of freedorn at a time,
Behbehani et al.'s coordination index based on Fitts' Law (Behbehani et al. 1988) is applicable
only to two degree of freedom target docking or tarçet acquisition tasks. integrality (Jacob et al.
1994) and inefficiency (Zhai and Milgram 1998) are not restricted to only two degrees of Fieedom
at a time but are Iimited to measurement in either only the time domain or only the space dornain
respectively.
This thesis argues that none of the existing metrics is satisfactory for understanding the
trajectory information from complex, more than two degree of Eeedom, human-compter
manipulation tasks. The goal is to develop an understanding of what is happening in one degree
of fieedom relative to the other degrees of freedom in multiple degree of fieedom tasks; is. how
a user is distributing their control across the avaiIable degrees of fieedom, However, before
achieving this goaI it is essentiaI first to develop a merrk for evaluating the allocation of control
across multiple degrees of Freedom. This thesis proposes a new research tool, to be caIled the W-
rrierric, with the following attributes:
trajectory-based analysis
applicable to two or more degrees of fieedorn
incorporates rneaswement in the space dornain (efficiency)
incorporates measurement in the time dornain (simultaneity)
task dependent, which mrans that if the task changes then the same control action can
receive a different performance score (c.f. In the case of integrality (Jacob et al.
1994), changing the task does not change the integrality score if the users control
actions rernain constant.)
How the W-rnetric is computed depends upon the type of task.
2 The %-metic for Doc king Tas ks
The X-meüic is based on the supposition that assessrnent of ahcation of contrd across
an n (where n f 2) degee of Eeedom docking task m u t take into account both the simultaneity
and the efficiency of control across the degrees of Freedom. A docking task is defined here as a
task for which an object, such as a cursor or a graphic object, must be moved Grom an initial
position to a goal position, with no conmints on either the trajectories that may be chosen, and
only optimisation constraints on the time allowed to cornplete the movement Eom initial state to
goal. Such tasks can thus be considered self-paced, or time-minimising (Meyer et al. 1990). In
this chapter it is shown how assigning one a i s to the space dimension (amount of movement)
and one ~ x i s to the time dimension (the timing of movement), the corresponding surface area
measures the allocation of control in two dimensions, time and space. Overlapping nomalised
surface areas allow comparisons across multiple degrees of freedom measured in different units.
(Each individual degree of freedom is normalised by dividing by a number measured in the same
Ar cm units (ex. - = 1 no units cm divided by cm) thus resulting in a unit-less number.) As justified x cm
in the foIlowing, it is the prodm of simdtaneity and efficiency that defines the W-metic.
2.1 SimuItaneity of Control
Simriltaneiy of control is calculated by computing first the normaiised error reduction
firrrctiori for each degree of fieedom separately. Error for each degree of freedom is d e h e d here
as the difference between the goaI position and the current position. Error reduction is a hc t ion
that quantitatively characterises the action of reducing error. It is defined as the instantaneous
amount by which the difference between the goal position and the current position is reduced (i-e.
the error tenn moves closer to zero). Error reduction is a funçtion of time and is set equaI to zero
during time periods in which the error may have actualIy increased (i.e. movement away fiom the
goai), in mathematical tenns, the emor reductionjinction represenis the instantaneourr value of
the negative derivalive of the error term, but only for positive values of the derivative. In other
words. during periods of error reduction the derivative of the error will be negative. In order to
have a positive error reduction fimction the negative of this derivative is taken. During periods of
error increase (positive derivative) the error reduction h c t i o n is set to zero.
Al1 "information" contained during portions of the task where the operator is moving the
working point away fiom the target is removed and essentialty '"lost". However, a fundamental
assumption of the W-metric is that the valuable trajectory information is contained within the
portion of the trajectory in which the working point is being "controlled" where control is defined
here as error reduction. If error is increasing, then by definition the working point is not being
controlled, and the %-rnetric does not take uncontrolled motion into account. The W-metric is
intended for analysing tasks where the task inchdes a requirement that the working point is to be
manipulated in a purposeful manner towards a goal. Uncon~olled movements are assumed to be
un-purposefut and therefore less interesting.
The error reduction function for each degree of fieedom is norrnalised by dividing it by
the total distance moved towards the goal over tne entire docking task for that degree of freedorn.
Thus, when al1 the normalised error reduction hctions are gnphed against time, the areas under
each curve al1 have a value equal [O one. n i e error reduction function is normalised for two
reasons, 1) different degrees of tieedorn rneasured in the same units c m be directly compared,
even if different amounts of error were reduced, and 2) different degrees of fieedom rneasured in
different units can now be directiy compared.
More formally, the Normalised Error Reduction Function, NERFi(t) (where i = 1,2, ... n are the degrees of Freedorn being analysed, and t is tirne), is defined as:
-dE(r) 1 NERFi([ ) =-*- . f o r ~ ~ ( t ) c 0
dr ACT,,
where Ei(t) = instantaneous error (goal position - cursor position)
and ACTi =total actual error reduced over the entire duration of a task for the ith degree of
fieedom. in other words, ACTi is equal to the area under the non-normalised error reduction
fict ion and can only be computed when the task is over.
Docking Error, E.&)
E(t) = target position - c ursor position
Cornpute the change in error over tirne (derivati w function)
CHANGE IN ERROR
Consider only intervals in wfiich
C ertor is reduced- O ~ ~
.ü Le. truncated O
3 values of -dE,(r)
dt d CHANGE
IN ERROR
period of cursor rnoving away fiom tacget
DOF "X"
priai of cursor "4' approachg target
period of cmor approachhg target
End of task \ hrge t acquire4
Time
L DOF "X"
Time
4. Nomalise area under the error Area under reduction curve.
Normalised Error Reduction,
NERF,(t)
Time
5 . Repeat steps 1-4 for each DOF. Area under each Y"
Normalised Error Reduction
NERF,(t) and NERFJt)
Time
6. Compute the area of overlap between the normalized error reduction curves.
Normalised Error Reduction NERFJt) 3 NERFy(t)
between the DOFs.
Figrrre 7. How simdtaneity is calmlated by WQJJ of a n o d i s e d error reduction graph for docking tasks. for two degree~ offieedoom, .r and y.
Figure 7 illustrates graphically how sirnultaneity is calculated for two degrees of fieedom
using normalised rrror reduction curves. The six steps shown in Figure 6 are
Cornpute the error fuction for each degree of fieedom separately.
Cornpute the change in error over time for each degree of freedom separatdy (i.e, the
negative of the derivative). Error is defined as the difference between the cursor position and
the target position.
Error can either increase (cursor moves farther h m the target) or decrease (cursor moves
doser to the target), or remain unchanged (cursor doesn't move). Since computing thex-
metric involves using only decreasing enor data, error increasing values are zeroed out.
The error reduction curves are normalised, so that the area under the curve for each degree of
Freedorn equals 1. Normalisation is accomplished by dividing each value by the total area
under the curve (which is equaI to the amount of error reduced by cursor movement).
Steps 1-4 are repeated for each degree of tieedom.
When placed on the same graph, the area of overlap across different error reduction cwves
represents the amount of simuitmeity for the corresponding degrees of freedom. Since the
area under each curve is equaI to I (step 41, the areas of overiap between multiple curves c m
cake on values between O and 1.
The m a of overlap between the curves is defied as the amount of simultaneity of
control- Figure 8 shows one normalised error reduction graph with a control simuitaneity z 1 and
one graph with a control simultaneity z O. The gcaphs in Figure 8 ilIustrate the control
simultaneity between hvo degree of tieedorn curves. However, any number (n p 2) of degrees of
Freedom m q be anatysed by computing the overlaps between pairs of normaIised error reduction
curves. In addition, any subset of the total available degrees of &dom may be analysed
separately.
MathematicaIIy, simuItaneity of control (SOC) for al1 n degrees of freedom is computed
according to:
where hiin() returns the minimum vaiue over ail NERFi(r)'s for each t, and T = total taçk
completion time. As inustrated m Figure 8, the minimum fiinction (Min) defines the contour of
the curve to be integrated, for computation of the area of overlap. Note that, even when the
example shown in Figure 8 is extended to n>7 degrees of freedom, the intersechons that define
the SOC function are stilI hvo-dimensional areas.
.- 5 B K
control simultaneity 5 ri
W .- - E- Z
Figure 8, Tkvo differenr error reduction cares. The top graph shows nvo error reduction curves with vety little overlap. representing low simultaneity. The bottom graph represents a high degree of overlap. representing high simultaneity.
2.2 Efficiency of Control
Allocation of control encornpasses not only simttltaneotcs enor reduction but also
eflcient emor reduction, where error reduction is defined as a controlled movement towards the
goal. The argument is that a movement that is strîctly simultaneous but not eficient is not
optimally controlled. An additional efficiency component is necessary for cornputhg the
aIlocation of control because the normalisation of the error reduction function in the sirnuhaneity
pomon of the R-mettic has the side effect of removing ineficiencies from the simdtaneity
calcuIation.
There are two main differences between the efficiency metric discussed in this section
and the original inefficiency meû-ic descnbed by Zhai and Milgram (Zhai and MiIgram 1998) in
section 12.8. Zhai and Milgram's metric is referred to here as a measure ofineficiency because it
is a ratio of the user's actual trajectory over the optimal trajectory, and the resulting ratio ranges
in values from 1 to infinity. The ratio discussed in this section uses the opposite, the ratio of the
optimal trajectory over the actual trajectory, as depicted in Figure 9, and is defined as the
efficiency cornponent of thex-metric, which has a value range between O and 1. The second
difference deals with whether the rnetric is computed across al1 the degrees of freedom or for each
degree of freedorn separately. Zhai and Milgram's inefficiency metric is based upon the Iength of
the actua1 trajectory across al1 the degrees of freedom together. A single number represents the
inefficiency for al1 the degrees of freedom. The efficiency component of the W-rnetric is
computed for each degree of freedom separately; therefore movement in one degree of fieedom
does not affect the efficiency scores for the other degrees of freedom, which is not mie for Zhai
and Milgram's ineficiency measure.
s t a 2 Goal y - Position
f' Position
b Efficiency = afb
Figirre 9. Illiisrrution of ltow the efficiency portion of the W-rnetric is calculuted.
The eficieticy component of the %Y-metric is a weighted average of ratios for each degree
of fieedorn, tvhere each ratio is the length of the optimal trajectory (OPT = length of the optimal
error reduction function tnjectory) divided by the length of the actual mjectory ACT ( A n =
Iength of the total actua1 error reduced over the duration of a task for the ith degree of tieedom)
for that degree of fieedom. Eficiency (EFF) is thus defmed here as:
where the weights, N;; are set equal to:
and k = number of members in the same subset as the ith degree of freedom. A subset of the total
degrees of fieedom is defined as a grouping of (k) degrees of fkeedom that are similar in nature
and measured in the same units. For example, al1 of the translation degrees of fieedom wouId
normally make up one subset, while al1 of the rotation degrees of Freedom would comprise
another.
The purpose of the weights, K., is two-fold: 1) to weight degrees of freedom of the same
units by their respective optimal trajectory magnitude, and 2) to deal with degrees of Freedom
which might be measured in different units. Note that the weights are defined such that their sum
rnust be unity. Thus, for example, the Cc values for X-Y-RZ (where X, Y are translation degrees
of freedom, and RZ is a rotation degree of Freedom about the Z axis), for a three degree of
freedom case in which the OPTr Rz values are 4 cm, 5 cm, 60' respectively, would be:
Appendix B contains a step-by-step example of a docking W-metric calculation.
23 Summary of the W-rnetric for Docking Tasks
The object of the 24-metric is to measure how control has been allocated among different
degrees of fieedom during a task and to express this via a value between O and 1. A bounded
normalised interval of O to t is straightforward and easily understood. A value closer to 1
indicates "efficient" and essentially synchronous control across degrees of freedom. A value
cioser to O on the other hand mdicates either a switching of control between the degrees of
fieedom or relatively ineficient control, or possibly both.
The nvo cornponents of the 24-metric have been defined with tiüs in mmd, çuch that the
'IK-metric = SOC x EFF. The simultaneity and efficiency components are mdtiplied together to
maintain a O to 1 interval. Averaging the two components wouid aIso result in a range between O
and 1, but in such a case situations involving one degree of freedom at a time control
(simultaneity = O ) would not give W-metrics scores of O.
To summarise, the primary features of the W-metric are the following:
measures the allocation of control
is equal to the product of sirnu!taneity and efficiency where
> simultaneity is equal to the overlapping area under the normaIised error reduction curves
> efficiency is the ratio of the length of the optimal trajectory over the actual trajectory
returns a value behveen O and 1, where values closer to O means separation or inefficiency of
control and values doser to 1 rneans simultaneous and eficient conroi
is computed for any nurnber of degrees of freedom (2 or more) and subsets of the total
available degrees of fieedom
may be computed across degrees of fieedom encompassing different measurement uni& (e.g.
cm, pixels, degrees)
2.4 A Note on the Time Dimension
The final W-metric score is not a function of the total length of time taken CO complete a
docking task, even though the memc explicitly takes into account the time dimension. What the
"time dimension" refers to here rather is the timing of control actions. In other words, what the
W-metric measures is the degree of simuItaneous error reduction occurring in multiple degrees of
freedom. as opposed to measuring whether the error reduction took a particular amount of time to
complete. There is therefore not necessarily a correlation between the W-rnetric vaIues and time-
to-completion performance measures for any particular docking task
2.5 Eypothetical Examples
This section contains some examples used to illustrate the W-metnc and to compare its
results in relation to inregmiity, a measurement onIy in the time domain (Jacob et ai. 1994), and
ineficiency, measurement only in the space domain (Zhai and Milgram 1998). Seven different
hypothetical two degree of Eeedom mjectories are shown in Figure 10.
C
Goal Position
Stan Position ?
I Stan Position
B a
Goal Position
Siart Position
Figtire IO. Seven different hypothetical trajectories for a docking rask wifh 2 degrees offieedom.
Triai A Trajectory Trial 6 Trajectory 0.3 seconds sampling 0.1 sea>rds m p r i q
Trial C Trajectory Trial D Trajectory a. t secniuts sampling O. r seconds mpiicg
.tm a too am m a X W i Piel Position X-Axis Phal Po-n
--
Trial G Trajectory 0.1 seconds sampiing
Figure I I , Seven diferennr trajectories from Figure I O collected from real data, showing rime information.
Trial A Normalized Error Reduction
Time (seconds)
Trial C Normalized Error Reduction
Time (seconds)
- Trial E Normalized Enor Reduction
Time (semnds)
Trial G Normalized Error Reduction
Tirne (seconds)
Trial B Normalized Error Reduction
Time (semnds)
Trial D Normalized Enor Reduction
Time (smnds)
Trial F Normalized Error Reducüon
Time (seconds)
Figure II. Nornraiised error redtrction funcrions over rime for the seven different trajectories seen in Figure 9. coIiected from reai data.
The seven trajectories from Figure 10 were used to guide a piIot expetiment, for the
purpose of replicating those trajectories using an isometric joystick on an i3M Iaptop. The resutts
from that experiment are shown m Figure L 1. in this case the subject's task was CO ptrrposely
generate seven different trajectories. Tbe jagged jumps in the data tvith the joystick are a
chancteristic of IBM's Trackpoint joystick and have been observed previously by (Douglas and
Eviithal 1997). Each tnjectory was executed only once.
Before analysing the real Trackpoint data, ordinal predictions were made as to the
relative scores the different metrics would produce, as shown in Table 3. Table 3 contains
idealised data, useful for comparing to the actuar trackpoint data, shown in Table 4.
Table 3. Predicted per$orrnance nieuswes. Colrrmns A-G correspond to trajectories A-G shotvri ilr Figure 10 and Figtrre I I .
Table 4. Acnral peflormance nieasrrres fiom real dara (sa~nple size = I ) .
Integnlity
Inefficiency
W-rnetric
Range
integrality I
Range
O to =
1 to 2
O to 1
thresholds)
inefficiency 1 to = I
A
- - -
1
I
Compiiting an integnlity (Jacob et al. 1994) score for the 2 degree of fieedorn exarnple
requires bvo decisions to be made: 1) the size of the threshold to use, and 2) the size of the time
window to use, Integrality was caIculated for two different threshold sizes, O and 1 pixel
mavements, and a value oFO.1 seconds was used for the size of the time tvindow.
B
O
> 1
O
C E
C=
> 1
«I
D F
a
»l
« 1
O
»1
O
G
e
»I
«< 1
c-
> 1
< 1
Table 5. Hoiv the met* of integrality, inefficiency. and the W-metric evaluute the different trajecro fies in Figtire 10.
Table 5 shows how the three metrics evaluate the seven different trajectories in order of
best to worst performance. The important differences between the %Y-metric, inteplity, and
inefficiency seen in the table are:
integrality
[nefficiency
W-memc
r Integnlity is unable to differentiate between trajectories A, D. & F.
r Inefficiency is unable to differentiate between trajectories B, D, & E.
Wo6t
Performance
B,C
B,C
r The W-metric is able to differentiate behveen trajectories A, B, D, & E.
The W-memc is thus abie to differentiate benveen different trajectories where integrality
and inefficiency fail to do so.
c
Performance
G
G
c
Performance
E,G
CE
E,F
<
Performance
BP.E
D
Best
Performance
A
A
3 The Docking Experiment
With the W-metrïc as a new tool for analysing multi-degree of freedom control
behaviour, the question becomes "what can it tell us about manual control tasks that isn't already
hown?" A fotmal controlled expenment in an area that has previously been studied could
potentially show the usehlness of the W-metric. Strong support for the vaiidity of thm-metric as
an analysis tool would exist if the X-metric were to provide empirical evidence that was
previously undiscovered. but in line with existing theory.
This chapter discusses a six degree of tieedom docking task that was implemented using
the same platforni as Zhai (Zhai 1993; Ztiai 1995). Performance under these conditions had
already been published but no allocation of control differences had been identified previously.
The previaus published conclusions are:
correlation analysis had concludeci that "there was little fundamental conflict in
controlling 6 degrees of tieedom" (Zhai and Senders 1997b) and
coneiation analysis had found that "more than 80% of the subjects were able to
control d l 6 degees of tieedom simultaneousIy" (Zhai 1995, chapter 6)
Similar to what has been observed in the motor control litenture (Vereijken et al. 1992)
and based on Bernstein's theories O E human coordination (Bernstein 1967), it is predicted that
novice operators attempting tu control a large number of degrees of Eieedom wiII not allocate
their control equaIly across al1 the degrees of freedom. Instead, subjects wilI cont.01 certain
subsets of the total number of degrees of fieedom at any time and switch control between those
subsets. Furthemore, the particular subsets controlled will not be arbitrary; nther, it is expected
that rotation and translation degrees of freedom will be treated separateiy. Irnrti and Garner (Imai
and Garner 1963) have identified a perceptual preference in discriminabiiity between translation
and rotation dimensions. This perceptuat preference is hypothesised to exist as an action
preference also. SpecificalIy, for a 6 degree of fieedom virtual docking task, operators will tend to
allocate their control gIobalIy between the three translation and three rotation degrees of fieedom,
and switch back and forth between them.
input devices which support more "natuni" modes of interaction (Le. resembling real-
world motor manipulations) are predicted to show a more uniform allocation of contml across al1
6 degrees of freedorn. Therefore, the isotonic input device, the Fingerball, should allow users to
brtter dlocate their control behveen translation and rotation degrees of freedom when compared
to the isometric input device, the Spaceball.
FinaIly, as expertise develops, and concurrently task completion time performance scores
are likely to improve, one of two behavioural tendencies is predicted likely to ernerge:
1. ûpentors will continue to sivitch their control between the translation and rotation degrees of
fieedom, and only their control performance will irnprove, or
2. Allocation of contra1 across al1 6 degrees of freedom will gradually become more unifonn
over t h e .
For hypothesis 1) the W-rnetric scores for the between translation and rotation degrees of freedom
are expected to show little increase over time while the within translation and within rotation
degrees of fieedom are expected to become higher with practice. Hypothesis 2) predicts the
opposite, that the W-metric scores for the benveen translation and rotation degrees of freedom
will be higher with practice while the within degrees of freedorn will not increase.
Corresponding to the above hypotheses, the experiment presented here was designed to
address three explicit questions:
I. How do people allocate their control across six degrees of freedom in a virtual docking task?
2. Are differences in the allocation of control device independent? Specifically are there
differences in allocation of control between isometric and isotonic devices, with isometric
and isotonic representing the two extremes of possible controller resistance?
3. How does allocation of control change over an extended period of practice?
3.2 Subjects
Twelve right-handed volunteen from the University of Toronto comrnunity were
recruited as subjects. Three subjects were rejected for failing to discern a binocular disparity of at
least 50 seconds of arc at 40 cm, as tested using the Randota Stereotest (Stereo ûptical Co., inc.,
Chicago, IL). A fourth subject was rejected for being unable to perform the docking tasks. The
remaining 4 male and 4 female subjects ranged in age fiom 25 to 32, with an average age of 28
y=. Subjects were paid $55 CND upon completion of the experiment. While most of the
subjects had extensive expenence interacting with computers, none of the subjects had previous
experience with any 6 degree of kedom computer input device. Some of the subjects had seen
3D movies in theatres before, however none of the subjects had any working experience with
stereoscopic displays.
3.3 Experimeatal Platform
ï h e expenment was conducted on a Silicon Graphics indigonr workstation with a 20
inch colour monitor, m i n g MiTS (Manipulation in Three Space) software, developed by Zhai
(Zhai 1995), to create a through-the-window virtual environment. For ail experimental tasks, the
origin was defined as the centre of the computer screen with the Z a i s pointing out towards the
subject, as shown in Figure 13. W B liquid crystal glasses (iMAX Ltd, Toronto, Canada)
openting at 120 Hz were used to provide stereoscopic viewing. For the isometric condition,
subjects used a SpaceballB (Mode1 #2003) manufactured by Labtec inc. (Vancouver, WA),
operating in rate control mode. The MITS software sampled subjects' data at 15 Hz. The
experiment was conducted in a darkened room and subjects were encouraged to adjust the
position and height of their chair so that they would feel comfortable.
Of the many possible input devices that could have been chosen, only two were selected
such that there would be one device representing each extreme of the resistance continuum, as
s h o m in Figure 14. For the isotonic condition, subjects used the Fingerball (Zhai et al. 1996;
Zhai and Senders 1997b) powered by a Flock of BirdsB (Ascension Technology Corp.,
Burlington. VT), operating in position control mode. These two devices have also been
extensively studied in experiments by Zhai (Zhai 1995), thus providing an existing knowledge
base to rnake comparisons.
Figure 13. m e docking task required manip dation of 6 degrees offeedom: rrandation a long X Y, Z. and rotation about tfte X; Y, Z ares (RI: RY. RZ).
Resistance Continuum
Isometric
Force sensing - (input device does not move)
Elastic lsotonic Position sensing - (input device moves without resistance)
A three-dimensional vimal docking task was uscd in this experiment, based upon the
MiTS software developed by Zhai (Zhai 1995; Zhai and Milgram 1998). See Figure 15 for a
photograph of the experimental setup. Subjects were told to align a tetrahedrally shaped cursor
tvith an identically shaped target tetrahedron as quickly as possible, as shown in Figure 16.
Whenever a corner of the cursor was successfully matched to its corresponding target, the comers
changed colour, indicating a correct docking. MI four corners had to remain docked for 0.7
seconds to complete the trial, which meant that "passing through" the target would not end a trial.
n i e sides of the tetrahedrons were colour coded and drawn in w-ke frame mode. The colour code
was selected so that the orientation of the target was unamtiiguous, and depicting the cusor as a
wireframe allowed ail sides to be visible at once. The size and coIour of the cursor and target
were identical, except for the corners. A single Iine marked the comers of the cursor, while a star
marked the corners of the target and the size of the lines. The radius of the stars indicated the
error target tolerance range for docking. The corner markings of the target wouId change colour
whenever the corresponding cursor corner would k within this tolerance range.
Figure 15. R depiction of the e~perimental setup rrsed modeling the Fingerball, an isotonic input device. An hcension Bird@ magnetic transmitier is on rhe righr side of the table with a receiver inside the Fingerball. The model is wearing IiGtctY@stereoscopic gCasses, as ivorn by the aperimentai suhjects. The qerimental room kvas darkened during the actrral aperiment.
For al1 trials, the initial position of the cursor was the centre of the screen, while the
target appeared in one of eight off-centre Iocations. Target lacations were selected so that an
essentially identical difference existed in al1 transIation and rotation degrees of fieedorn between
the t q e t and the cursor. Subjects ended each tria1 by manipulating aII four corners of the cursor
and maintainhg them witiiin the error range of the target for 0.7 seconds. The end of the trial was
indicated to the subject by a short beep. Text feedback then appeared on the screen showhg the
number of trials compieted and the task dockhg time of the last compIeted trial. This text
feedback was displayed for two seconds, wiiich was the minimum iime between trials. Subjects
could then initiate the next tria1 by either applying force co the SpacebaIl or retuming the
FingerbaIl to the home position, depending on which input device they were using. The MlTS
software indicated the start oCa new trial by somding a Iong beep.
Figitre 16. hfonoscopic screen images of the docking task; the acttrul erpetfment setup is a stereoscopic display- Die user's cursor appears ut the centre of the screen, while the targer appears at one of eight possible locations ut the sturt of each tria[. Besides position, the cursork corners are dis finguished hy fines, while stars adom the target 's corners. Tlie airsor ir shoivn being manipulared onto the target- In the Custfrarne, the corners of the rarget change colours to indicare a successfid dock
3.5 Procedure
Subjects were first tested for binocular disparity using the Elandote) Stereotest. A short
questionnaire was used as a screener to identifj experience with stereoscopic viewing and 6
degree of Freedorn control devices. The questionnaire also included questions from the Edinburgh
inventory (Oldfield 1971) to assess handedness. Subjects were then introduced to their contro1
device and asked to manipulate the cursor upldown, IeWright, idout, and then to rotate about
those corresponding a e s in a targetless environment. A cardboard mode1 of an mis system was
used to illustrate the axes of rotation.
This introduction to the control device took less than two minutes. Subjects were then
given a single docking trial as a traininglexplanation of the task. This single docking trial
preceded each day's session for the purpose of warming up the subject and testing that ail the
hardware and software were working appropriately. For al1 trials, subjects used only their
dominant hand to manipulate the input device.
3.6 Design
The experiment was a 2 x 5 x 2 16 between subjects design. The independent variables
were ris follows:
input Device: isometric rate, isotonic position
Session: 1,2, ... 5
Trial: 1,2, ... 216
The above conditions with 8 subjects represent a total of 8640 trials, collected over 40
houn of experimentation. A stratified random method was used to assign subjects to either the
isomemc rate or isotonic position conditions, such that each group was composed of 2 maies and
2 femaIes. The number of trials, 216 per session, was chosen so that each session would last about
an hou. Subjects completed one session per day over five consecutive days. The software
enforced a mandatory rest penod of 90 seconds afier every 24 trials. Each block of 24 trials
consisted of 8 randomly shuffled target locations selected three times.
3.7 Resuiîs
Although the number of trials, 216, was chosen so that each session would take about an
hour, in reality, the subjects' kt sessions took behveen 90 and 100 minutes to complete, while
the f i f i (fmal) sessions took only 40-50 minutes to complete.
The traditional performance measure for a docking task is mk completion time- Le. how
long did it take the subjects to dock the cursor onto the target. The raw completion tirne data,
session trial means (5 one hours sessions with 216 trials per session), and session standard
deviations for the isometric device condition are shown in Figure 17. Corresponding data for the
isotonic device condition are s h o w in Figure 18. Both docking performance graphç show
significantly (F(1.24) = 41.51, p < 0.0001) decreasing task completion tirnes with extended
pnctice, with the biggest improvement between the fmt and second sessions. Between the first
two sessions isometric times dropped h-om 13.9 s to 8.3 s (a 5.6-second or 40% irnprovement)
and the isotonic rimes went from 11.9 s tu 6.7 s (a 5.2 second o r 4 % improvement). The
performance improvement From the fourth to the fiRh session is much smaller with the isometric
times dropping from 6.2 s to 5.9 s (a 0.3 second or 5% improvement) and the isotonic times
dropping Frorn 4.4 s to 3.9 s (a 0.5 second or 1 1% improvement). Session means and standard
deviations for both devices together are shown in Figure 19. In Figure 19 the isotonic input
device has a 2 second shorter average docking time across al1 sessions; however this difference is
not significant (F(1,6) = 3.40 P = 0.1 15).
Trial Number
Docking Performance over Time lsornetric Rate Device
4 0 - -
Figure 17. Docking performance over tirne for the four mbjecrs using the Spaceball (an isometric input device). Rmv data. session means (5 one-how sessions ivith 2 16 tnak per session) and session standard deviations are shown.
- 35 rn
.. .. * ,
-< + Session Means
Docking Performance over Time lsotonic Position Device
-c Session Means
Trial Number
Figure 18. Doch?ngperjormrrce over rime for the four subjects using ~ h e Firigerball (an isotonic iriptir device). Raiv data, session means and session standard deviarions are sliown.
Docking Performance Over Time lsometric vs. lsotonic Input Device
(4 subjects per device)
+- Spacebali (içametric deviœ) + FingerbaIl (isofonic device)
Trial Number
Figure 19. Dockingperformance over tirne for bath the isometric and isoronic de~ices compared. Sessian meuns and standard deviarions are shorvn.
W-metnc scores were computed for al1 degrees of freedom (15 two-way comparisons, 20
three-way comparisons, 14 four-way comparisons, 6 five-way, and 1 six-way cornparison) for a
rotal of 56 different groupings. A rvithin grorrp srrbset is defined here as a set where al1 the
degrees of freedom in the set are either of the translation or rotation type. For example, for the 20
three-way comparisons, there are only 2 groups which are considered within group subsets, X-Y-
Z and RX-RY-RZ. An across grorip sribser (or benveen group srrbser) is defined here as a set
where at least one degree of freedom is of the translation type and at least one is of the rotation
type. So for the example of the 20 three-way comparisons, the eighteen remaining groups are
considered as across group subsets.
When the W-metric scores are computed for both devices collectively, no significant
differences were found. However, when they are computed for each input device separately, a
more detailed picture emerges, illustrating the differences between the two input devices. Figure
20 shows the 15 isometric two-way combinations, where the within translation and within
rotation pairings have significantly (paired t test, p < 0.0001, Bonfenoni) higher W-metric scores
than the pair-wise combinations across rotation and translation degrees of freedom. The within
translation combinations are an average 112% higher than the W-metric scores for the two-way
across combinations. Figure 20 also shows that the within rotation combinations are an average
107% higher than thex-metric scores for the two-way across combinations.
Docking Experiment lsometric Device M-metric Scores Two-way Combinations
Figure 20. The W-metric scores in the docking erperiment for oniy the immemè inptrr device. Al[ nvo-rvay degree offreedom combinations are shown.
The three-way cornparisons shown in Figure 21 show similar results, with the witbin
translation condition (X-Y-Z) and the within rotation condition (RX-RY-RZ) showing
significantiy (paired t test, p < 0.000 1, Bonferroni) higher W-metric scores than their across
rotation and translation counterparts. The within translation combination (X-Y-2) is 156% higher
than the average of the 18 diiferent three-way across combinations, and the within rotation
combination (RX-RY-RZ) is L22% higher.
Docking Experiment lsometric Device M-metric Scores 0.6 Three-way Combinations
Figure 21. Tlre W-tnetric scores in the docking erperiment for only the issometric input device. Ali tltree-wq degree offieedont combinations are sltown.
However, for the four-way (Figure 22). and five-way (Figure 23) combinations, the
magnitude of the differences between combinations is too small to warrant further analysis. The
singIe six-way combination is shown in Figure 24 for completeness.
0.6 . Docking Experiment lsometric Device Mmetric Scores
Four-way Combinations
Figure 17. The m-rnezric scores in the docking mperinlent for oniy the isontetric input device. Ali fotir-ivay degree offieedom combinations are sltown.
0.6 Docking Experiment lsometric Device M-metric Scores
Five-way Combinations
Figrre 13. Tlie W-rnetric scores in the docking aperimerrt for oniy the isometric inprrt device. Ail five-rvay degree offieedom combinarions are shorvn-
Docking Experiment lsometric Oevice M-metric Scores 0.6 . Six-way Combination
Figure 24. The nC-metric scores in the clocking erperiment for only the isometric inprit device. The sir-way degree offieedoni cornbinarion tF shoivrr.
For the second input device, the isotonic W-rnetric scores portray a somewhat diffèrent
picture than the isometric scores, indicating differences between the devices. For the isotonic
input device two-way combinations shown in Figure 25, the three highest scores again belong to
the within translation degree of freedom, averaging 40% higher than the average across score.
However, the within rotation degrees of Freedom do not show the same high values as their
isornetric counterparts, but instead are comparable to the bvo-way between translation and
rotation scores. ïhree-way cornparisons for the isotonic device in the docking experiment are
given in Figure 26, which shows the within translation group (X-Y-Z to have the highestw-
metric scores. The remaining four-way and five-way combinations are shown in Figure 27 and
Figure 28 respectively, appear constant across al1 combinations with no obvious patterns. For
completeness the six-way combination is shown in Figure 29.
Docking Experiment lsotonic Device M.metric Scores Two-way Combinations
Figure 15. fie %?-rrietric scores in the docking ~rperivtent for only ihe isotonic input device. Al1 nvo-ivay degree offeedom combinacions are stiown.
Docking Experiment lsotonic hv ice Mmetric Scores 0.6 Three-way Combinations
0.5 .
Figure 26. Zïte W-rnetrie scores in the dochfng expen-ment for only the isotonie input device. ALI tlrree-tvay degree of f~edom combinations are show-
Oocking Experiment Isotonic Device Mnietric Scores 0.6 - Four-way Combinations
0.5 -
Figure 27. The ?X-netric scores in the docking erperimenrfir only the isotonie input device. Al1 four-rvay degree offieedont combinarions are shoivn.
Docking Experiment lsotonic Device M-metric Scores 0.6 Five-way Combinations
Figure 28, The W-niettic scores in the docking erperintentbr only the isotonic input dalce. Al1 five-wvay degree offreedorn combinations ore sliown.
Docking Experiment lsotonic Device M-metric Scores 0.6 . Six-way Combination
XYZRXRY RZ
Figure 29. The W-merric scores in the docking aperiment for oniy the isoronic input device. ï3e sk-rvay degree offreedom combinarion is shorvn.
Figure 30 shows changes in W-metric scores over time/session, broken down by input
device and number of comparisons. OnIy a representative subset ofW-metric scores is shown, to
Save space. Al1 W-metric scores increase over session. For the two-way combination case, X-RX
and RX-RY have been selected as representative of an across translation-rotation pairing and a
within rotation pairing respectively. Across al1 the two-way comparisons, the highest W-memc
scores always belonged to the within rotation isometric rate conditions. The isotonic scores for
both the within and across conditions were always lower. The lowestm-metric scores for the two-
way cornparisons always belonged to isometric rate across translation and rotation pairings.
Docking M-metric Score vs Time Across 2 Degrees of Freedorn for X-RX and RX-RY
0.6
L -0- lsotonic Position X-RX a c r m -0- Isornetric Rate X-RX -across + lsotonic Position RXdY -within -ç- Isometric Rate RX-RY -within
0.0 O 1 2 3 4 5 6
Session
Figure 30. How the ?#-mefric scores changes over rime in the doch?ng aperiment, A ser of represenrarive benveert trunslution and rorurion degree ofjieedom (X-Rv and a wifhin rotariun Jegree ofIreedotn (M-RY) scores, for both the isornetric and isotonic input devices, are shown.
The representative three-way pairings depicted in Figure 3 1 by Y-2-RY and RX-RY-RZ
show the sarne consistent pattern. Isometric within scores were the highest, followed by isotonic
within W-metric scores, with the lowest scores belonging to the isomemc across groups. For the
four. five, and six-way combinations (Figure 32), isotonic position W-metric scores were in fact
larger than their isomemc rate counterparts, though in al1 cases the values were small (isotonic
scores were on average 32% higher than the corresponding isornetric scores).
-+ lsotonic Position Y-2-RY -across + lsornetrk Rate Y-Z-RY -across + lsotonic Position RX-RY-RZ -within + Isornetric Rate RX-RY-RZ -within T
Docking M-metric Score vs Tirne Across 3 Degrees of Freedom for Y-2-RY and RX-RY-RZ
0.6 ,
O 1 2 3 4 5 6 Session
Figwre 3 1. How the W-metrie scores changes over tinte in the doeking experiment. A set of rrpresetrtutive benveeri rrat~lution und rotation dryrer offirrrloni (Y-2-RY) and a within rotation degree offeedonr (RY-RY-RZ) for both the isometric and isotonie input devices are shown,
O 1 2 3 4 5 6
Session
Docking M-metric Score vs Time Across 6 Degrees of Freedom for X-Y-Z-RX-RY-RZ
0.6
Figwe 32. The m-tnetric scores over rime in the docking experitwtt across all6 degrees of fieedom.
0.5 -
Figure 33-Figure 35 portray the reIationship between M-rnetric scores and task
completion times for both isometnc and isotonic devices co1IectiveIy. Three wo-way
cornparisons are gnphed; a within translation pairing (X-Y in Figure 33), a between translation
and rotation pairing (X-RZ in Figure 341, and a within rotation pairing (RX-RY in Figure 35). Zn
these tigures, raw W-meaic scores are shown along the vertical aUs, and the task completion
tirnes are dong the horizontal axis. Linear regression analysis of the three graphs resulted in slope
estimates of -0.006 (X-Y in Figure 33, percent of variance accounted for, R' = 4.62%), -0.004 (X-
RZ in Figure 34, percent of variance accounted for, Et' =420%), and -0.005 (RX-RY in Figure
35, percent of variance accounted for, R' = 2.8 1%). These low R' scores indicate that task
completion time is a poor predictor of R-metnc scores. The W-metric is quantiS.ing a different
aspect of performance than the traditional rask compIetion time rneasure.
-C- Isotonic Position X-YZ-RX-RY-CU + Isornetric Rate X-Y-Z-RX-RY-RZ
The Relationship Between M-metric and Task Completion Time 1.0 . For the Docking Experiment X-Y M-metric Comparison
0.0 - - - O 5 10 15 20 25 30 35 40
Tark Completion Time (seconds)
Figure 33. The relationship benveen the nvo dependent variables task-completion tirne and the W-tnetric for the K Y cornbinarion for the docking erperiment. The solid line represents the linear regression fit benveen the nvo variables.
The Relationship Between (H-metric and Task Completion Time For the Oocking Experiment X-RZ M-metric Comparison
1.0 -
O 5 1 0 15 20 25 30 35 40 Task Completion lime (seconds)
Figure 34. The relationsi@ benveen the nvo dependent variables task-completion time and the W-metricfor the X-RZ comparkon for the docking experiment. The solid line represents the linear regression jît benveen the hvo variables.
The Relationship Between t~(metric and Task Cornpletion Time For the Docking Experiment RX-RY (H-metric Cornparison
5 10 15 20 25 30 35 40 Ta& Completion lime (seconds)
Figure 35. The relationship benveen the nvo dependent variables rask-conipletion timr and the W-merric for the RY-RY cornpanSon for the docking e.rpennment. The solid line represents the linear regressionjit benveen ihe nvo variables.
3.8 Discussion
There was no statistically significant task cortipletion tirne difference between the
isornemc and isotonic input devices. This result is identical to that found by Zhai in a comparable
experimrnt using the same input devices and number of subjects, but for only one session inçtead
of tive ("Experiment #1" in (Zhai 1995), Chapter 2).
The lack of significant task performance differences between task completion times could
lead to the conclusion that for the docking tasks examined there were no performance differences
behveen the two devices. f i s conctusion does not hold in terms ofa trajectory based analysis
such as the W-rnetnc. This point is extremely important- yet easy to overlook- c.f. Masliah &
Milgram's 2000 (Masliah and Milgram 2000) CHI paper where the two input devices were
lurnped together for most graphs, resulting in somewhat incomplete conclusions.
in the experirnent the translation degrees of fieedom were highIy coupled for both the
isornetric and isotonic conditions, while the rotation degrees of freedom showed coupling only for
the isornetnc condition, in the other words, for the isomemc condition subjects switched control
between the translation and rotation degrees of freedom, but they did not generally translate and
rotate at the sarne time. For the isotonic condition, on the other hand, subjects would a s l a t e
without rotating, at the same tirne, but did not generally rotate without translating. This is
illustrated in Figure 26 where error reduction in the rotation degrees of freedom is coupIed with
error reduction in the translation X degree of freedorn.
Unlike the task cornpletion times in Figure 19, the W-metric scores depicted in Figure 30-
Figure 32 show rnuch less evidence of approaching a lirnit. For exarnple, the average increases in
W-rnetric scores between sessions across both input devices for the RX-RY-RZ comparison are
0.057 (1'' to session), 0.0 18 (2""o 3*),0.024 (3* to 4 9 , and 0.023 (4" to 5"). The change
From the first to second session is the largest, and fiorn the second session on W-rnetric scores
increases at a constant rate rather than asymptotically like the task completion times. if%-rnetric
scores continue to change at a faster rate than task cornpletion tirnes, it may thus be possible to
use W-metric scores as a more sensitive rneasure of manual control expertise.
Using the purely isornetric input device, subjects tended to allocate control within
rotation and translation groups sepantely. Previous research fiom the motor control literature has
showed that novices control subsets of their total available degrees of fieedom (Vereijken et al.
1992). In addition, research from the psychology literature (Imai and Garner 1965), has identified
a perceptual preference to categorise stimuli into rotation and translation groups. However, this is
the first time, to the author's knowledge, that quantitative evidence has dernonstrated an action
preference to alternate between rotation and translation manipulations. This is exactly the type of
analysis that is extremely difficult to do without the W-metric.
An isotonic position controller imposes fewer restrictions on an operator's movements,
since muscle groups are allowed to move in a manner similar to how they are used in real wodd
manipulation. This may rnean that an isotonic position controller is a more "naturai" means of
interactinç with a M a l environment, and should thus result in a more even distribution of
control across available degrees of freedorn. in an experiment involving two degrees of
mslation and one degree of rotation, Wang et al. found that subjects were able to translate and
rotate simultaneousty (Wang et al. 1998). The higherW-rnetric scores with the isotonic position
controller for the across rotation and translation conditions, as compared to the isornetric rate
across conditions appear to support this conclusion.
If an isornemc rate controller is mdeed a "less natual" interaction rnethod, this couid
mean that the isornetric rate device should be comparably more difficult. A more complicated
interaction rnethod therefore should thus result in an uneven dismiution of controI. in Fi,we 30,
in the 2-way comparison graph, the difference between the X-RX condition (an across translation
and rotation grotip) and the RX-RY condition (a within rotation group) for the isometric rate is
very large. nius, for more cornpiicated interaction devices, it is arguably more important for
subjects to reduce the complexity of the task by controlling only a subset ofthe total 6 degrecs of
Freedom at a time. Switching control between subsets of the total available degrees of freedom
appears to be the method subjects used even after 1000 trials,
One of the goals of this expenment was to ay to understand what happens to the
allocation of control with extended practice, based on the assumption that novices will exhibit
separated and inefficient control early in the experiment. The hypothesised mode1 was that one of
two opposing possibilities may occur: subjects will either continue to allocate control
concurrently and efticiently within subsets or increasingly allocate control across al1 degrees of
Freedom. Rather than an eithedor hypothesis, it now appears that both cases occur. That is,
subjects continue to allocate control between rotation and translation subsets but at the same time
show some increase in heir ability to simultaneously control al1 the degrees of fieedom.
These observations have implications for Bernstein's theory of how motor control skills
develop. It appears that under conditions where subjects are left to their own devices as to how to
learn a new rnotor skiII, that is, they receive no training as to how to do the task, they continue to
have preferences for how they allocate their control. Degrecs of freedom that were coupled early
on continue to rernain strongly coupled, and that coupling in fact gets suonger with practice. Tt is
theorised that with specific instructions or training this effect could be countered or strengthened
as desired.
Whiie there is a temptation CO claim that equal allocation of control across al1 degrees of
Geedom is "better" than unequai control, this may or may not be the case, depending on the task,
the environment, and the users. For example, if one imagines a task where the trajectory taken is
irrelevant to performance, and the cognitive Ioad of simultaneoudy manipuiating multiple
variables is hi@, then unequa1 allocation of control wouId probably be the best strategy. Either
way, in order to make such judgements, a framework for measunng the alfocation of control, such
as the 7X-memc, is a necessary tool,
in a 6 degree of freedom Wtual docking task, operators do not aIlocate theü controI
equally across al1 availabte degrees of freedom. Instead, operators aIIocate controI arnong subsets,
by controlling rotation and translation degrees of fieedom separately and switching contro1
behveen those subsets. in addition, the type of input device used has an effect on the strategy used
by operators to allocate control. A more "natural" type of input device should allow operators to
exercise a more even distnïution of control across the avaiIable degrees of freedom. On the other
hmd, an "unnatural" input device might force operators to control only subsets of the total
number of degrees of freedom at a time. Some simultaneous allocation of control does exist
across al1 6 degrees of fieedom, and the amount of this allocation appears to be a tùnction of the
type of device used.
Task completion tirnes across al1 subjects fiom session 4 to session 5 dropped an average
of only 0.40 seconds (from 5.37 to 4.87 seconds), compared to a mean 5.38 second drop fiom the
1st to the 2nd session. Therefore, the taskcompletion times show evidence of subjects
approaching a minimum time floor. With additional sessions, any further time reductions would
probably be very small in magnitude.
Conversely, however. the%-metric scores depicted in Figure 30 show much less
evidence of approaching a limit. If%-metric scores continue to change at a faster rate than task
completion times, it may be possible to use W-metnc scores as a more sensitive measure of
manual control expertise.
4 The %-metric for Tracking Tasks
The M-mehic for tracking tasks is based upon the same principles as the W-rneüic for
docking tasks, that allocation of control is a function of both the simultaneity and the eficiency
of control across the available degrees of Freedom. A tracking task is defined here as a task where
both the time and space components of the trajectory of the working point are specified by the
task. Figure 36 illustrates this distinction by presenting a shaded subset of Figure 3. in docking
tasks the target's location does not change, therefore computing the W-meûic for docking tasks
does not depend upon the target's trajectory since none exists. In order to maintain the attributes
of "task dependent" and "trajectory based", calculating the W-meûic for tracking tasks involves
computing the change in error due to both cursor movement and target movement.
Time Domain Externaiiy Paced Se KPaced (The Matching) (Time Minimising)
Targe t Doc!cing . menu selection . peg-inhole tasks
Tncmg . drawing . rnarking menus
Figtrre 36. Taronomy of manital conrrol ta&, emphasis on trucking rasks. Tracking tasks defne borh rite rrqtrired trajeciory in space and the pace at tvltich the trajectory is to be fallowed
When tracking tasks have been studied in controlled experimental settings, a sum of sines
function (Poulton 1974) has traditionaiIy been used to drive the target's motion for each degree of
freedom (Zhai 1995; Zhai and Senders 1997a). Such a forcing function is "sufficientIy
unpredictable to the experimental subjects" (Zhai 1995) and provides
independent motion on each degree of fieedorn. Performance in tracking experirnents is usually
measured by calcuIating the root mean square error between the cursor and the target for the
duration of the task. For experirnents that are concemed strictly with accuracy as a rneasure of
performance, using independent forcing functions for each degree of fieedom is a perfectly
appropriate methodoIogy. However, having independent forcing functions rneans that the target
may move by a large arnount in one degree of fieedom and a smaller arnount in another. For
studies concerned with equal allocation of control it is necessary to have forcing functions which
drive the target to move equal arnounts for each degree of freedom, which is not possible with
independent functions. In addition to desaibing the rnethodology for cornputing the X-metric for
tracking tasks, the traditional sum of sines forcing function is discussed and a new "modified"
sum of sines forcing function is introduced which is suitable For allocation of control studies.
4.1 Simultaneity o f Control
For docking tasks the position of the target is constant, so the area under the error
reduction hc t ion equals the distance moved by the cursor towards the target. However, for
dynarnic tracking tasks, since the target is continuously changing position, a simple graph of the
change in error does not necessarily equal the distance moved by the cursor towards the target.
For example, if the cursor is following the target exactly, then the change in error of the cursor's
movernent wiIl have a constant zero value, which obviously does not reflect the user's control
efforts. In other words, even though there rnay be a lot of movement, the change in error
reduction tunçtion for cursor movement is not sufficient to show what is going on.
A graph of the change in cursor position is not sufficient either, since sûictly asking if
there is movement or not, like a measure of integrality (Jacob et al. 1994), is not a task dependent
rneasure. That is, a graph of the change in cursor position does not distinguish between movement
contributing towards reaching the goal and movement that is moving away Erom the goal. The
objective is thus to have a metric which is task dependent and distinguishes between different
types of movements. For the purpose of the X-rnetric, there are two only types of movement,
those which reduce the amount of error (error is the distance between the cursor and the target),
and those which increase the amount of error.
The solution proposed is to treat al1 movernent as either error reducing or error creating,
whether the motion is due to cursor movement or target movement. Consider for exarnple the two
cases shown in Figure 37. in case A, the cursor is lagging contmuousIy behind the target by a
constant arnount during a tracking task, but otherwise is tracking correctly. in case B, the cursor
is leading the target by a constant amount during a tracking task, but otherwise is tracking
correctly. The amount and direction of motion, and the change in error for both cases is the same.
(in this genenc case, lagging is no betier or worse than Ieading, which may or may not be true for
a real world task.) In both case A and case B, the cursor and target have each moved 3 units in the
same direction but the change in error fiom TI to T: is zero. That is, 3 units of "error" have been
reduced by cursor movement and 3 units of "error" have been created by target movement in each
case.
â' .- S I
rn E B UJ C
P Y
x
Figure 3 7. Case A shows rhe ctrrsor lagging behind the target. Case B shows the cursor leading in fiont of the rarget. T represenrs time and slroivs the position of borh the ctirsor and rlre targer und rinie T, and c.. The numbers at the righr nerr io the brackets indicate "rinits of errer':
First, defining some of the tems:
equals the difference between the target's position and the cursor's position.
Error reduction (error reduced or decreasing) is movement Chat reduces the absolute value of
the error. There are two types of error reduction: error reduction due to motion of the cursor
and error reduction due to motion of the target.
Error creation (error created or increasing) is movement that increases the absolute value of
the error. There are two types of error creation: error creation due to cursor movement and
error creation due to target motion.
Sumrnated error reduced equals the error reduced by the cursor plus the error reduced by the
target.
Summated error created equals the error created by the cursor plus the error created by the
target-
The previous definirions are subject to the following basic constraints:
Total distance travelled by the cursor equals the error reduced by the cursor plus the error
created by the cursor.
Total distance tnve1led by the target equals the error reduced by the targer plus the erroc
created by the target.
0 Total distance travelled equaIs the summated error created plus the summated error reduced.
and one nile:
Error reduction is "açsigned" to cursor movement first.
The rule is explained as fol~ows, In Figure 37 there are hvo scenarios for values of the
functions ERT(t) (Error Reduction due to Target Movernent), ERC(t) (Error Reduction due to
Curçor movement), ECT(t) (Error Creation due to Target Movement), and ECC(t) (Error Creation
due to C m o r Movement) that sti1I satis@ al1 oftfie constraints, as is shown in Table 6. In the lefi
side column, the error reduction has been assigned to the target. Again, both scenarios satisfy all
three constraints but only right side column foIIows the rule of k t assigning error reduction to
cursor movement. Error reduced is assigned to the cursor first because, as in Figure 37, it makes
more sense to claim that the operator is tracking the target rather thm the other way around.
Table 6. livo sceriarios for assigning error reduction for die e~atnple in Figure 37.
The simrrltaneity of controi for tracking tasks is calculated by first computing the error
redriction fùnction for the cursor and target separatery, and for each degree of fkeedom sqarately.
The cursor and target error reduction hct ions are added together to create the summated error
reduction fùnction.
error reduction assigned to target
ERT(t) = 3
ERC(t) = O
ECT(t)= O
ECC(t) = 3
error reduction assigned to cursor
ERT{t) = O
ERC(t) = 3
ECT(t) = 3
ECC(t) = O
The s i . steps to compute simultaneity of control component illustrated in Figure 38 are:
Compute the change in error for each time step for the target and cursor movement
separately. Each degree of fieedorn is computed separately. Figure 38 shows the change in
error for the "X" degree of freedom. The change in enor is computed for the entire duration
of the trial or task.
Error can either increase (cursor moves farther from the target, target moves farther from
cursor) or decrease (cursor moves closer to the target, target moves closer to the target), or
remain unchanged (cursor and target do not rnove, or cursor and target move by the same
amount). Computing the W-metric involves using on1y error decreasing data. Error increasing
values are zeroed out.
Sumrnated enor reduced is computed for each step by adding together the error reduced by
cursor movement and the error reduced by target movement.
The summated enor reduction cuve is normalised so that the area under the curve equals 1.
Normalisation is accompIished by dividing al1 values fiorn step 3 by the total area under the
curve (which is equal to the summated error reduced by both the cursor and target
movement).
Steps 1-4 are repeated for rach degree a€ ficedom.
When placed on the sarne graph, the area of overlap across different normalised summated
error reduction curves represents the amount of simultaneity for the corresponding degrees of
freedom. Since the normaIised area under each curve is equal to I (step J), the area of overlap
between mu1tipIe curves can take on any value between O and 1.
More formally, NSERi(t) (where i = 12, . . . n are uie degrees of freedom being analysed,
and t is tirne, and SERi is the Sumrnated Error Reduced), is defined as:
-d(ERC,(r) + ERc(r ) ) 1 NSER, ( t ) = *-
dt SER,
The area of overlap between the c w e s is thus defied as the amount of simultaneity of
control. Simultaneity of controI (SOC) is computed according to:
T
SOC = ~ M ~ ~ ( N S E R , ( r ) , NSER,(~),-..NSER. (t))dr whcre Min renims mmimum value over al1 O
NSERi(t)'s as a function of t, and T = total duration of the task. The minimum function (Min)
tieflnes the contour of the curve to be integrated, for computation of the area of overlap.
1, Compte the DOF " X cursor movement change in error over time Ci
O target movement separately for the 2
2 Consider only DOF "X" data for which cursor movernent error is reduced. 8 .-
Ci O
target rnovement 3
QL L
CHANGE 2 IN ERROR
Time
3 SU^ error DOF "x" reduction due to 8 A
\ total movement
cursor and target = movement. " '8 u .=
al 0 3 s Ee J CHANGE a
IN ERROR
Time
4. Normalize area Area under
under the error DOF curve = 1
reduction curve.
Normalized Surnrnated Error
Reduction
Time
Repeat steps 1-4
t C
for each DOF.
Norrnalized Surnmated Error
Reduction
Time
Area under 6 . Cornpute the a m of overlap between the
DOF cuwe = 1
normalized error reduction curves.
Norrnalized Surnrnated Error
Reduction
Time
intersection between the DOFs.
Figure 38. How simidtaneisf is calctifated by way of a nonnaiised error redtrctiort graph for tracking rash
4.2 Efficiency of Control
The efficiency of control is based on Zhai & Milgrarns's inefficiency measure (Zhai and
Milgram 1998). As in computation of efficiency for docking tasks, efficiency for each degree of
fieedom is computed separately. However, unlike in the=-metric for docking it is not
appropriate to use a ratio of the optima1 trajectory over the actual trajectory because the actual
trajectory is not constrained to be some minimum. (if the operator does nothing, then the actual
trajectory Q O thereby giving an undefined eficiency ratio of optimal/actual,) Instead the enor
rcduced by the cursor is compared to the error reduced by the target. The efficiency cornponent of
the X-metric is defined as the foIlowing:
Efficiency Ratio = Total Error Reduced by the Cursor/(Total Enor Reduced by the
Cursor + Total Error Reduced by the Target)
where tord refers to error reduced over the entire mal by either the target or the cursor.
4 3 Summary of the W-metric for Tracking Tasks
Once again, a bounded norrnalised interval of O to 1 is returned as a measure of how
connol has been allocated among different degrees of freedom during a task. A value closer to 1
indicates "efficient" and essentialIy synchronous control across degrees of fieedom, while a value
closer to O indicates a switching of control between the degrees of fieedom or a relatively
inefficient control or both. Raw error scores do not take into account the amount of movement in
the task; thcrefore the amount of error reduced and created is used instead. Both the trajectory of
the cursor and the tmjectory of the target are analysed in terrns of error created and reduced to
produce a metric that is task dependent.
The two components of the W-metric have been defined with this in mind, such that the
%-metric = SOC x (Efiiciency Ratio).
The simultaneity and efEciency components are muttiplied together to maintain a O to I
interval. Averaging the two components would also remit in a range between O and 1, but in such
a case situations involving one degree of tkeedom at a time control (simultaneity =O) would not
give W-mctric scores of O.
The W-metric for tracking tasks shares many of the sarne features as the W-metric for
docking tasks:
measures the allocation of control
is equal to the product of simultaneity and efficiency where
'r simultaneity is equal to the overiapping area under the nomalised summated error
reduction curve
'r efficiency is the ratio = TotaI Error Reduced by the CursorI(Tota1 Enor Reduced by the
Cursor + Total Error Reduced by the Target)
retums a value between O and 1, where values closer to O mean a separation of control or
inefficient control and values closer to 1 mean simultaneous and efficient control
is cornputed for any number of degrees of freedorn (2 or more) and subsets of the total
available degrees of freedom
4.4 The Traditional Forcing Function
The "traditional" forcing function used by Zhai consisted of the sum of twency sine waves
with different predefined amplitudes and wavelengths but with random initial phases.
Mathematically, the forcing function for the X degree of freedom for time t (in seconds) used in
Zhai's expenments (Zhai 1995) was
19
~ ( t ) = i lp -' sin(?@o ' t + #,= (i)) i=O
A different amplitude constant, B, was used for the rotation degrees of freedom, such that
for RY the forcing function in the Zhai experirnents was:
1'1
Rr(t) = B ~ - ' sin(21&~p't + #, (i)) i=O
where 4, and 4, were cornputer generated pseudo-random nurnbers ranging uniformly
between O and l x , and the constants were set as given in Table 7.
Table 7. Traditional foreingfimtion coristanrs ilsed by Zhai (Ba i 1995).
appropriately dit'ficult- not too hard and not too easy. The number of sine waves summed
constant
A
P
b
B
together, twenty, was chosen so that the forcing function would seem complex and to move
value
3.5
1.25
0.008
d3.5
nndomIy. A sample trajectory generated by this forcing h c t i o n for a 40-second tracking triai is
The values for the constants were chosen so that the forcing function would be
shown in Figure 39.
Traditional Sum of Sines Forcing Function
10 20 30 40
Time (seconds)
Figure 39. Position of the screen rarget as generated by rhe traditional sum of sinesfircing fiinetion. One graphie mit = 1.4 cm (Zhai 1995). The traditional forcingfinctions for three degrees offieedom are s h o w as used by Zhai 1995.
The absolute value of the rate of change in position over tirne (Le. the absolute value of
the fust derivative of the forcing function) for the forcing functions in Figure 39 are shown in
Figure JO. What Figure 40 shows is that at any point in time each degree of fieedom changes its
position at a different rate, independentIy of the other degree of iÏeedom. Using a dEerent
traditional sum of sines forcing function for each degree of fixedom resdts in a target that does
not move at the same rate for each degree of fieedom. Because the movements of each degree of
freedom are not equal, subjects tracking this surn of sine forced target are not compelled to
allocate their control equally across degrees of freedom to perform well. Tt would therefore be
difficult to assess how subjects allocated their control across degrees of fieedom in such cases for
which the task does not require such an allocation. In other words, although the "traditional"
forcing h c t i o n is perfectly suitable for most dynamic tracking experirnents. for the purpose of
assessing aIlocation of control it was deemed inadequate, thus compelling the design of a new
forcing function.
One way of generating the same amount of motion for each degree of freedom would be
to use the exact same forcing fict ion for each degree of freedom, instead of a different forcing
hc t ion for each. Unfortunately this would result a very un-interesting trajectory because the
target would effectively rnove only along a diagonal and only rotate about a single (though
arbitrary) z ~ i s . For this reason the traditional sum of sines forcing h c t i o n approach was deemed
inadequate for the present allocation of control study and a new "modified" forcing function was
developed.
Traditional Sum of Sines Forcing Function c absolute value of the fwt derivative of the forcing function O .- ~5 0.15 ,
a - x - Y - 2
Time (seconds)
Figure 40- The absolute value of thefirsr derivative of the forcingficnctionsfrom Figtrre 39. Each degree ofJreedom changes ifs position at a different rare.
4.5 The Modiied Forcing Function
The purpose behind the creation of the modified forcing fimctions was to produce a
forcing fimction with the same basic characteristics as the traditional forcing fimction (Zhai 1995)
but which, in addition, has identical absolute values of thefirst derivativefor eack degree of
fieedonz. in other words, if the first derivative of the forcing h c t i o n for degree of fieedom X is
0.5, then the first derivative of the forcing hc t ion for the other five degrees of fieedom may
equal only 0.5 or -0.5.
One approach that was tried and rejected was to have identical traditional forcing
hnctions for each degree of freedom, perhaps diffenng only in the sign (+ or -). Mathematically
such an approach howvever does have identical absolute values for the first derivative across al1
the degrees of fieedom. Unfortunately using identical forcing hctions (or fimctions that differ
only by one sign change) results in a target that moves only dong a single vector and rotates
about only a single ~ x i s for the entire task, which is rather boring stimuli fiom the subject's point
of view.
/ - similac forcing I function
traditional forcing
I b Time
Figtire 41. fllrtstratiorr of the diference benveen the traditional and modijied forcingfirnciions. nie modi/ed forcingjünction is a mirror reflection of the traditional forcing function accomplislied via a sign change at tlie srvitch point. Switcli points are selected so that the target's trajectory appears relatively sniootli to the stibject.
instead the approach used in the modified forcing h c t i o n has sign changes occurring at
multiple points during each trial. Sign changes occur only when the fmt derivative of the hrcing
fimchon is close to zero (at the asymptotes) so that the trajectory of the target appears smooth to
the opentor. The point where a sign change is introduced is refened to here as a "switch point".
Figure 41 illustrates how a sign change at a switch point results in a modified forcing fünction
that Iocally is a mirror reflection of the tnditional forcing hction. CaIculations for the modified
forcing h c t i o n for al1 the degrees of fieedom are based upon a single traditional forcing
fünction. Switch points occur at identical points in time for al1 degrees of fteedom. The onty
difference between the different degrees of Freedom is the sign of the switch, which is assigned
randornly. Additional constnints are imposed so that the total number of switch points per trial is
Iimited and that the switch points do not occur too close together.
The modified forcing function is a modification of the traditional surn of sines forcing
hnction. First a genenc mm of sines forcing function is cornputed:
19
g ( t ) = A ~ " sin(?~&~~'t + 4, (i)) i=O
The modified forcing function is
where R(t) has the value of either +I or -1. R(t) is a binomial random elernent that
switches the direction of the movernent by changing sign. 1, is the arnount of time that has passed
since the last switch in direction.
So the mod@ed(t) is a recursive fiinction in that it rnust keep track of the history of the
hct ion. R(t) also has the following constraints:
when a new R(t) is calculated, it has an equal chance of being set to +l or -1
a new R(t) is calculated if and only if at least 3.5 seconds have passed since the last switch or
dg(t) < E , whtxe E equals 0.025 For the cranslntion degree of it is the start of a new mai, a d - dt
freedom and 0.025 *BIA for the rotation degree of Freedom.
Sa al1 6 degree of freedom are derived From one generic sum of sines forcing function, but are
computed with different R(t) values.
An example set of translation degree of freedom generated by rnodified forcing functions
is depicted in Figure 42. The trajectories in Figure 42 are not obviously different than the
traditional sum of sines forcing function in Figure 40, in that the trajectories are difficult for
subjects to predict. However the modified forcing functions have the additional characteristic of
having identical absoiute value of the function's f i t derivative as s h o w in Figure 43.
Modified Sum of Sines Forcing Function
10 20 30 40
Time (seconds)
Figtrre 32. Position of the screen [urger as generared by the mod~~edfircingfinction. The ntodified forcing/iinction for three degree of freedom is shown.
Modified Sum of Sines Forcing Function absolute value of the first derivative of the forcing function
Time (seconds)
Figure 43. Only one line is visible 6ecurcse ail three translation degree ofieedom have the same absolrite value of the firsr derivative for the mod$ed srim of sines forcing function.
A spectral analysis (magnitude versus fiequency plot) of the rnodified forcing fitnction
was conducted to provide evidence that the modified forcing function satisfies the sarne specml
criteria as the traditional forcing function. The power spectral densitj for the traditional forcing
h c t i o n (for a 1000 second sample) is shown m Figure 44. InFigure 44 there are twenty diffetent
spïkes corresponding to the twenty different sine waves that are summed together to create the
forcing hction. The twenty different spikes occur at 0.009,0.011,0.014,0.018,0.022,0.027,
0.033,0.033,0.054,0.067,0.054,0.105,0.13 1,0.164, 0,205,0.256,0.320,0.300,0.500, and
0.635 Hz,
The porver spectral density for the modified forcing ficnction show in Figwe 45 contains
the same spectral signature as the traditional forcing function, No Frequencies are missing and no
new wavelengths have been added. The on1y difference behveen the power spectral density
graphs behveen the naditional and rnodified forcing functions is that the power spectral densiry
for the modified Function contains slightly more noise, in that the individual Frequencies are not
as well defined.
Power Spectral Density- Traditional Forcing Function
Figure 44. Power spectral density for the tradi~ional forcingfiinction.
Power Spectral Density- Modified Forcing Function
O.0Ot 0.010 0.100
Log(Frequency (*fi))
Figrrre 45- Porver spectral demiry for rhe modified forcingfincrion.
5 The Dynamic T racking Experiment
In a pure docking task the operator does not have to follow a required trajectory; any
trajectory that acco~nplishes the dockinggoal is acceptable. in the expenment reported in
Chapter 3 subjects were not instnicted how to do the task, so the docking experiment reflected
what people naturally chose to do without any training. It remains to be seen whether, in a
dynamic tracking task, where simultaneous control of al1 6 degrees of freedom is required,
opentors \vil1 continue to choose to allocate control to subsets of degrees of Eeedom or instead
change snategies to control al1 degrees of freedom together. A follow-up expenment is therefore
necessary to test the validity of the docking expenmental conclusions. The results from a tracking
experiment should shed light as to what operators are capable of doing versus how they prefer to
allocate their control.
A six degree of Freedom tracking task was implemented using the same pladorm as Zhai
(Zhai 1995; Zhai and Senders 1997a; Zhai and Senders 199%). Performance under similar
conditions had aIready been published but no allocation of control differences had been identified
previously:
tirne-on-target had produced a "coordination constant with results contrary to
expectations" (Zhai and Senders 1997a) (the "coordination constant" actually
becarne smaller with practice)
The d-vnamic tracking experiment results were expected to be similar to the results found
in the docking experiment. That is, subjects were expected to control the rotation and translation
subsets of al1 the degrees of freedom separately and switch control between those subsets.
However, given that the tracking task requires simultaneous movement in al1 degrees of keedom
the difference in the W-metric between the within groups and between groups was not expected to
be as large as in the docking experiment. The isotonic input device, as the mos! "natural" input
device, was expected to show a more uniforrn allocation of control across al1 six degrees of
freedom. The isometric input device was expected to continue to show a higher degree of
separation between the rotation and translation degrees of kedom.
Sirnilar to the docking task, the following predictions were made:
1. Operators \vil1 continue to allocate their control behveen the translation and rotation degrees
of Freedorn, and only their control will i m p r o v e , ~ d
2. Allocation of control across al1 6 degrees of fieedorn \vil1 continue to become more uniform
over tirne.
Note that, in Iight of what was learned tiom the docking experiment, both hypothesis were
predicted to be supporteciIn other words, al1 possible subsets of the available degrees of fieedom
were expected to show continuous increases over tirne. The degree of increase was expected to be
linear, with little evidence of the W-rnetric scores approaching a ceiling value.
5.2 Subjects
Ten right-handed volunteers fiom the University of Toronto community were recruited as
subjects. One subject was rejected for failing to discern a binocular disparity of at Ieast 50
seconds orarc at JO cm, as tested using the RandotB Stereotest (Stereo ûptical Co., inc.,
Chicago. IL). A second subject was rejected for being unable to complete the tracking tasks. The
rernaining 2 male and 6 fernale subjects ranged in age fiorn 22 to 35, and were paid $55 CND
upon completion of the experiment. While rnost of the subjects had extensive experience
intencting with computers, none of the subjects had previous experience with any 6 degree of
fieedorn computer input devices. Some of the subjects had seen 3D movies in theatres before,
however none of the subjects had any working experience with stereoscopic displays.
5.3 Eaperimeatal Platform
The hardware setup used for the tracking experiment was identicaI to the setup used for
the docking experiment (section 3.3). The experiment was conducted on a Silicon Gtaphics
Indigon' workstation with a 20 inch colour monitor, running MITS (Manipulation in Three
Space) sotiware, developed by Zhai (Zhai 1995), to create a through-the-window virtual
environment. MAX8 Iiquid crystal glasses (MAX Ltd, Toronto, Canada) operating at 120 Hz
were used to provide stereoscopic viewing. For the isometric condition, subjects used a
SpacebaN@ (Mode1 "rr2003) rnanufactured by Labtec hc. (Vancouver, WA), operating in rate
control mode. For the isotonic condition, subjects used the Fingerbail (Zhai 1995; Zhai et al.
1996) porvered by a Rock of Büds@ (Ascension TechnoIogy Corp., Burlington, VT), operathg
in position control mode. The MlTS software sampled subjects' data at 15 Hz, The experiment
was conducted in a darkened room and subjects were encouraged to adjust the position and height
of their chair so that they would feel comfort;ibIe.
5.4 Task
Dynamic tracking tasks are the most constrained type of task in the manual control
taxonomy shown in Figure 3 and Figure 36, in that both the trajectory of the working point and
the pace at which the trajectory is to be followed are subject to pre-defhed conditions. The three-
dimensional virtual tracking task used in this experiment is identical to MITS tracking software
developed by ïhai ( f ia i 1995), exceptas explained in section 4.5. The wirefiame tetrahedron
target used was identical to the target used in the docking experiment, except that there were no
markers on the corners. The cursor manipulated by the subjects made use of the semi-
transparency effect to convey depth information (Zhai 1996; Zhai et al. 1994). Subjects were told
to capture the target within their semi-transparent "silKi cursor, which was just slightly larger
than the target. In addition to tracking position they also had to align the cursor with the target
orientation. A tracking mal Iasted for 40 seconds, which is Iong enough to produce stationary
data (see Appendix A: Stationarity), but not so Iong as to tire out the subject. Subjects were told
that they could take breaks in behveen trials as desired. The cursor and target trajectories were
sampled at lSHz . giving N=600 tracking steps per trial. The subjects initiated each trial by
pressing the space bar on a keyboard. A modiîied forcing function (described in section 4.5) was
used to drive the target motion with the constants given in Table 8.
Table 8. Table of constanfs iaed in the rnodified forcingfirnction for the dynamic tracking e~peritnent.
The traditional forcing h c h o n generates values bounded in magnitude by the amplitude
constants A, B and p. For example, the sum of two sine waves where A = 3.5 and p = 1.25 can
take a maximum value of 6.3 (Afp4 *çin(@/2) +A?-' *sin(@/2) = 4*2°* 1 + 4*2-'*l) or a
minimum vaIue of -6.3. The rnodified forcing function however may take on any value and is not
bounded by the values of its constants. For a through-the-window VR setup, the values of the
amplitude constants for the traditional forcing function are usually sdected so that the target
movement stays within the window viewing area (Zhai 1995)- Since the modified forcing
function is not lirnited by the value of the constants, an additional constraint was added, such that
when the target approached the sdges ofthe viewing area the next RCt) took a value that would
cause the target to move back towards the centre.
For al1 mals, the initial position of the cursor and target was the centre of the screen.
FinaIly, subjects initiated each trial by pressing the spacebar raiher than the FI key (as was used
in (Zhai 1995)). As the Iargest key on the keybuard, the spacebar is easier to find and can in fact
easily be pressed without looking at the keyboard even for those who can not touch-type.
5.5 Procedure
After the Randoc@ Stereotest, a short questionnaire was used as a screener to identify
subjects' experience with stereoscopic viewing and 6 degree of Freedurn controI devices. The
questionnaire also incIuded questions from the Edinburgh inventory (OIdfield 1971) to assess
handedness. Subjects were then introduced CO their control device and asked to rnmipuIate the
cunor up/down, feftlright, idout, and then to rotate about those corresponding axes in a targetless
environment. A cardboard modei of an axis system was used to illustrate the axes of rotation.
This introduction to the control device took Iess than two minutes. Subjects were then aven a
single tracking rial as a trrtiningle.qIanation of the task. For ail mals, subjects used onIy their
dominant hand.
5.6 Design
The experiment was a 2 x 5 x 60 between subjects design. ï h e independent variables
were as folIows:
Input Device: isornetric rate, isotonic position
Session- 1, 2, ... 5
Trial: 1,3, ... 60
The above conditions with 8 subjects represent a total of 2400 uiaIs, collected over 40
hours of expenmentation. A stratified random method was used to assign subjects to either the
isometric rate or isotonic position conditions, such that each group was composed of I male and 3
females. The number of trials, 60 pet session, was chosen so that each session wouId last about an
hour. Subjects completed one session per day on five consecutive days. Subjects were told to take
breaks as needed in between trials.
5.7 Results
Root mean square (RMS) error (Poulton 1974), an integrated measure identicai to the one
used by (Zhai 1995), was used to mess global tracking performance. As described in(&i 1995)
this was cornputed as:
where
The cracking error function e is a fuiction of k, the tracking instant (sampled points), and
N is the total number of sampled points. Vcl, Vc2, Vc3, Vc4 are the four vertices of the user's
cursor tetrahedron, and Vtl, VU, Vt3, Vt4 are the four vertices of the rnoving target tetrahedron.
RMS error was used as the traditional performance measure.
The nw RMS data, session means (5 one hour sessions with 40 hais per session), and
session standard deviations for task completion times for the isometrïc spaceball device condition
are shown in Figure 46, and the isotonic fingerball device are shown in Figure 47. Both tracking
performance graphs show significantly (F(4,24) = 41.51, P e 0.0001) shorter task completion
times with extended practice, though the biggest improvement is between the first and second
sessions, Between the first two sessions isometnc RMS scores dropped from 7.1 to 4.9 (a 3 1%
improvement) and the isotonic RMS scores went from 3.5 to 2.6 (a 26% improvement). The
performance improvements fiom the fourth to the fifth session are much srnalier with the
isornetric times dropping fÏom 4.L to 3.7 (a 10% improvernent) and the isotonic times dropping
fiom 2.39 to 2.36 (a I % improvement). Session rneans and standard deviations for both devices
togerher are shown in Figure 48. The isotonic input device group had significantly (F(I,6) =
37.890 P =0,00 1) better RMS scores than the isometrïc group for al1 sessions.
RMS Performance Score for Subjects using the lsometric Device
O 50 1 O0 150 200 250 300
Trial Number
Figirre 46. Trachg performance over time for the four stibjecrs irsing the SpacebaZI (an kometric inpirr device). Raw data, session nteans (5 one-hour sessiom with 60 trials per session) and session standard d#ialion~ are sltoivn.
RMS Performance Score for Subjects using the lsotonic Device
O 50 I aa 150 200 250 300
Trial nurnber
Figirre 47. Tracking performance over rime for the four subjects urring the Fingerball (an isotonie inpirr device). Raw dara. smion meam and session standard deviarioris are slioivn.
Tracking Performances Over Time Isometric vs. lsotonic Input Device
(4 subjects per device)
+ Spaceball (isornetric) + Fingerball (iotonic)
O 50 1 O0 150 200 250 300
Trial Number
Figure 18. Trackingpeflorntarrce over rime for 60th the isomern-c and kutonic devices compared. Session means and standard deviarions are sho~vn.
Breaking down the W-meûic scores by input device type, Figure 49 shows the isometric
two-way comparisons. For the hvo-way cornpansons the within rotation and within translation
pairings had significantly (paired t test, p < 0.0001, Bonferroni) higherm-meûic scores than pair-
\.vise comparisons across pairs of rotation and translation degree of fieedom. The translation and
rotation combinations for the isomeûic condition were an average 62% and 65% higher than the
average across W-rnetric scores respectively.
Tracking Experiment lsometric Device M-metric Scores Two-way Corn parisons
Figure 39. Tlie hl-rnefric scores in the tracking aperiment /or on& the isometric input device. wirli nvo-way degree offreedom comparisons sltown.
The three-way comparisons for the isornetric device depicted in Figure 50 show similar
results, with the within translation condition (X-Y-Z) and the wiihin rotation condition (RX-RY-
RZ) showing significantIy higher (paired t test, p < 0.0001, Bonferroni) W-metric scores than the
across rotation and translation combinations (X-Y-RX, X-Y-RY, ..., 2-RY-RZ). The within
translation combination (X-Y-2) is 61% higher than the average of the 18 different three-way
across combinations, and the within rotation combination (RX-RY-RZ) is 67% higher. However,
for the four-way (Figure SI), and five-way (Figure 52) combinations the magnitude of the mean
differences between combinations is too small(< 20%) to warrant further anaIysis. The six way
combination is shown in Figure 53 for completeness.
Tracking Expriment lsomebic Device M-metric Scores 0.6 T hree-way Comparisons
Figrcre 50. The M-nierric scores itt the rracking erperitnenrfor only [lie isornetric inpur device, rvirh rhree-rvay degree offieedorn cornparisons sliown.
0.6 . Tracking Expriment lsometric Device M-metric Scores
Four-way Comparisons 0.5 -
Figrire 51. The iM-rnerric scores in the tracking erperiment for on& the isomeiric inpttt device, ivifh fotrr-way degree offeedom cornparisons shoivn.
0.6 . Tracking Experiment lsometric Device M-metric Scores
Five-way Comparisons
Figure 51. î l e M-mevic scores in the tracking aperimenl for only the isometric input device, rvitli five-rvay degree O ffreedoni cornparisons slrown.
Tracking Experiment lsometric Device M-metric Scores 0.6 Six-way Cornparison
Figure 53. fie M-metric scores in rite rracking erperimenf for oniy the isometric input device. wirh the sir-tvay degree offiedom conrparison shown.
As in the docking experiment, the isotonic W-metric scores portny a different picture
than the isometric 1X-metric scores. For the isotonic input device two-way combinations are
s h o w in Figure 54, the three highest scores berong this time to the within rotation degree of
Freedorn, though the difference in scores is not very large. The translation degree of freedorn Z-
metric scores are comparable CO the two-way between translation and rotation scores. Three-way
comparisons for the isotonic device in the tracking experiment are shown in Figure 55, which
shows the within rotation group (X-Y-Z to have the highest W-rnetric scores. The remaining four-
way (Figure %), five-way (Figure 57), and six-way (Figure 58) combinations show no significant
differences in 2%-rnetric scores between comparisons.
Tracking Expariment lsotonic Device M-metric Scores Two-way Comparisons
Figure 54. nie M-merric scores in the tracking aperiinenr for only the isoronic inpur device. rvith n v o - i v ~ degree offreedom comparisons shown.
0.6 - Tracking Experiment Isotonie üevice M-metric Scores
1 hree-way Comparisons
Figure 55. f ie hf-nietric scores in the tracking aperiment for only the isotonic input device. with rhree-)va): degree offieedotn coniparisons slioivn.
0.6 Tracking Experiment lsotonic üevice M-metric Scores
Four-way Comparisons 0.5
Figrire 56. The hf-rnetric scores in the t r a c h g experimenr for oniy rile isotonic input device, with four-ivay degree O ffieedom comparisons shownvn
0.6 . Tracking Experiment lsotonic Device Y metric Scores
Five-way Comparisons
XYZRXRY XYZRXRZ XY2RYR.Z XYRXRYRZ XiRXRYRZ YZRXRYRZ
Figure 57. The hl-nietric scores in the tracking rrperitnent for only the isotonie input device. with jve-ivay degree of freedom contparisons shoivn.
Tracking Experiment lsotonic Device M-metric Scores 0.6 . Six-way Cornparison
Figure 58. The M-menic scores in the tracking e.rperiment for only the isotonic input device. witii the sir-~vay degree offiedom comparison sho~vn.
Figure 39, Figure 60, and Figure 61 shows changes in %-rneaic scores over tirne/session,
broken down by input device and number of comparisons. As was seen for the RMS scores, the
%-metri scores show clear signs of approaching a limit with practice.
Tracking M-metric Score vs Time Across 2 Degrees of Freedom for X-RX and RX-RY
0.6 i
-0- lsotonic Position X-RX ' -3- Immetric Rate X-RX 0.5 4 t Isotonic Position RX-RY
O 1 2 3 4 5 6
Session
Figure 59. How the M-rnetric score changes over tinre in the trackitig mperi~netit. A benveen rranslarion attd rotation degree offreedom (Y-2-RY) and a ivithin rotarion degree offreedom (RY-RY-RZ) fir both the isometric and isotonic input devices are sitoivn.
Tracking M-metric Score vs Time Across 3 Degrees of Freedom for Y-Z-RY and RX-RY-RZ
0.6 , -@- isotonic Position Y-2-RY + lsometric Rate Y-Z-RY + lsotonic Position RX-RY-RZ -G- lsometric Rate RX-RY-RZ
O 1 2 3 4 5 6 Session
Figure 60. How [Ire W-tnetric score changes over rime in the tracking crperimenr. A benveen rrartslarion and rotarion degree offreedom (Y-2-RY) and a rvirliin rorarion degree offreedonr (RY-R Y-RZ) for borh rhe isomerric and isoronic inprir devices are siiown.
Tracking M-metric Score vs Time Across 6 Degrees of Freedom for X-Y-2-RX-RY-RZ
0.6 i I
0.5 1 -+ hotonic Position X-Y-2-RX-RY-RZ + lsometric Rate X-Y-Z-RX-RY-RZ
I
O 1 2 3 4 5 6 Session
Figure 61. The W-merrîc score over rime in [lie rracking erperiment for al1 6 degrees of freedom.
Figure 62-Figure 64 portray the relationship between W-metric scores and RMS error.
Tne same three nvo-way cornparisons are pphed ; a within translation pairing (X-Y in Figure
62), a behveen translation and rotation pairing (X-RZ in Figure 63), and a within rotation pairing
(RX-RY in Figure 64). Linear regression analysis of the three graphs resulted in slope estimates
of 4.008 (X-Y in Figure 62, percent of variance accounted Cor, R' = 9.70%), -0.326 (X-RZ in
Figure 63, percent of variance accounted for, R' = 43.3%), and 4.159 (RX-RY in Figure 64,
percent of variance accounted for, R' = 20.5%). These R' scores, while higher than the docking
R', are still low enough to indicate that task completion time is a poor predictor of?#-rnetric
scores. The W-mecric is quantirnng a different aspect of performance than the traditional task
completion time measure.
The Relationship Between M-metric and T ask Completion Tirne For the T racking Experiment X-Y M-metric Cornparison
1 .O
0.9 .
0.8 .
O.? .
"0.6 . - 20.5 .
0 0 . 4 .
0.3 -
0.2 .
0.1 .
0.0 - - - - - - -
O 5 1 O 1 S 20 25 RMS Enor
Figure 62. The relarionsliip benveen the nvo dependent variables mis error and tlzeW-tnetric for ,KY combination for rhe fracking erperimenr.
The Relationship Between M-metric and Task Completion Time For the Tracking Experiment X-RZ M-metric Comparison
Figure 63. Tlie relarionship benveen the nvo dependenr variables MIS error and them-metric for RY-R Y combinarion for the rracking erperimenr.
The Relationship Between M-metric and Task Completion Time For the Tracking Experiment RX-RY A((-metric Comparison
0.0 --- O 5 1 O 15 20 25
RMS Enor
Figure 64. The relationship benveen rire nvo dependent variables RMS error and the=-metric for X-RZ combination for the docking erperimenr.
5.8 Discussion
The FingerbaIl outperfonned the Spaceball in ternis of RMS scores. Zhai's work (Zhai
1993') did not include a FingerbalVSpaceball comparison, but included instead a test of the
Spaceball against an elastic controller. Zhai concluded that the elastic device (the EGG) was
advantageous over the Spaceball only in the initia1 stages of learning, with the advantage fading
away after about 1 hour of practice (Zhai 1995). The curent expenment demonstrates that
performance with the Fingerbali is better than with the Spaceball, even with extended practice.
Spaceball performance did not even approach the FingerbaIl's first session RMS scores until the
third session of pnctice.
Even though the tracking task is by subjective user accounts much harder than the
docking task, RMS performance scores did not irnprove by great amounts after the third hour of
practice. This is contrary to what one may initia1ly expect- that a harder task should show
continuous improvement from session to session, and an easier task should asymptote sooner.
From an experimental design point of view the fourth and fifth sessions could be omitted from
tùture studies.
In the tracking rxperiment subjects continued to allocate their control separately between
the translation and rotation degrees of freedom, as seen in the docking expenment. The
magnitude of the separation was smaller though. This difference in magnitude is most apparent
when comparing the W-metric scores for the isornetric device for the docking expenment in
Figure ZOand the X-metric scores for the isometric device for the tracking expenment in Figure
49.
Whereas the rotation degrees of tieedom were highly coupled in both the isometric and
isotonic conditions, the translation degree of freedom showed coupling only in the isornemc
condition, but also to a lesser degree. Consequently, for the isometric condition subjects switched
control between the translation and rotation degree of freedorn- they did not track orientation and
position at the same time or efficiently to a great degree. But the magnitude of difference is small.
In Figure 55, error reduction in the rotation degree of kedom is slightly coupled with error
reduction in the translation X degree of Eeedom. However no expianation is offered as to why.
Unlike in the docking e.xperiment, these W-metrïc scores show clear evidence of
approaching an asymptote (Figure 59-Figure 61). While the docking experiment consisted of the
sarne eight targets repeated 135 times (though in a randomised order), the forcing fimction for the
tracking session was unique for each session - repeating h m session to session only 5 times. In
the docking experiment subjects were repeating actions over and over again, while the tracking
experiment involved for each tria1 fo1Iowed essentially a unique and randorn trajecrory. This is
most likely the reason for the continuous improving W-metric scores in the docking experiment
and why the W-metric did not show the sarne linear increase in the tracking experiment. In the
docking experiment subjects were given the chance to practice the same experiment over and
over again, but the same \vas not mie for the tracking experiment.
It is hypothesised that, for manual control tasks that are practised over and over,
allocation of controI scores will be more sensitive to expertise than traditional performance
scores.
6 The Docking Experiment with Etderiy Subjects
One area of possible application of the W-metric is to neuroIogica1 assessrnent of motor
control. SevenI researchers in the biomedical and neuropsychologicaI communities have been
working on cornputerised tasks to advance the current methods used by physicians for evaluating
motor control damage. 1s there an opportunity for the W-metric to play a role?
6.1 Introduction: Ncurological assessrnent
Clinical evaluation of neurological motor function often is "dependent on the skilled but
subjective judgernent of a physician" (Kondraske et al. 1984). Such evaluations usually consist of
having patients move their arms in certain prescribed motions white the physician assesses
performance on an ordinal scale (e-g. 1 = nomal, 2 = mild abnormal ity, 3 = moderate
abnormality, 4 =severe abnormality, 5 = paralysis). Tests such as these are used, for exampIe, to
a c k the progression of Parkinson's Disease, which is characterised by increased movement
latency, slowing of movement execution, and diffrculties in execution of muIticomponent
movements (Hocherman and Aharon-Peretz 1994). The disadvantages of the current examination
technique are thac 1 ) the scale is not sensitive enough to small changes in specifk hctions, and
3) it does not provide a measure of the patient's "proportion of normal functiont'(Kondraske et al.
1984).
With the sdvent of relativeiy inexpensive cornputers, some researchers have focused on
using computetised mcking m k s as a quantitative and objective means of assessing neurologica1
damage (Andersen 1986; Hocherman and Aharon-Peretz 1994; Hufschmidt and Lucking 1995;
Kondnske et al, 1984: Watson et al, 1997). The potential advantages of assessing neuroIogica1
damage through computer interaction tasks could include:
standardisation
reproducibility
reliability (Kondnske et a1. 1984)
more cost effective (a possibitity based on the relativeiy low cost of computer equipment)
Other advantages of using computerised tests to assess neuroIogicaI motor damage listed
by (Kondraske et al. 1984) are
w ease of data acquisition, storage, anaIysis, and retrieval
stimuli c m easily be generated and manipulated (for example computer generated graphics
can be used to produce stimuli that can not be generated in the real world)
computer based exams do not necessarily require administration by a trained physician
easy to upgrade. rnodify, or expand the tests
What effect exactly does Parkinson's disease have on motor controI? Docurnented motor
related irnpairments due to Parkinson's disease include (Hocherman and ~ h a r o n - ~ e r e i 1994):
a increased movcment Iatency
slotving of movernent execution
a tremor
a difficulties in the execution of multi-component movements
Cornbined. these motor irnpairments reduce a person's coordination (Hocherman and Aharon-
Peretz 1994). To put it another way, regardless of what definition of coordination is used, the
characteristics of Parkinson's disease remit in zmoordinated behaviour.
Even though much research has been devoted to finding motor rasks that are sensitive
enough to detect subtle differences in performance, many fundamental questions remain
unanswered. For exarnpIe, as recently as 1998 "the question of whether tracbng in 2D is more
demanding than tracking in ID has yet to be unequivocalIy answered."(Watson and Jones 1998)
Watson and Jones 1997 (Watson et al. 1997) have hypothesised that more complex tracking tasks,
2 degrees of freedom versus 1 degree of fiedom tasks, "might provide additional valuable
information on certain sensary-motor disorden." Two supporthg reasons are given:
1. A nvo-dimensional environment is more similar to the m l world than a one-dimensional
environment, and it rnakes sense to study motor hction in as n a m l an environment as
possible, and thereby obtain the most vaiid resuIts.
2. A two degree of fieedom task is more likely to stress the sensory-motor abilities of a human,
and therefore is more likely to expose subtle characteristics of behaviour as compared to one
degree of fieedom tasks.
Watson and Jones have found that normal subjects' performance clearly degrades on
going fiorn a one degree of freedom to a two degree of fieedom task (Watson and Jones 1998).
In addition, Watson and Jones have found that two degree of freedom pursuit tracking tasks are
more sensitive to motor control deficits in Parkinson's patients than one degree of Geedom tasks
(Watson et al. 1997). On the other hand, Navon et al. have found "no evidence that duaI axis
tracking w i h the panmeters used in this study is more demanding than single mis tracking"
(Navon et al. 1984).
In a study with patients with Alzheimer's disease, Baddeley et al. have provided
expenmental data showing that, when tracking tasks are combined with memory tasks, patients
suffering from dementia caused by Alzheimer's show significantly wone performance than
normal subjects (Baddeley et al. 1986). The Central Executive is a component of Baddeley's 1986
working memory mode1 (Baddeley 1986) postulated to be responsible for the selection, initiation,
and termination of processing routines in the brain, Baddeley et al. have hypothesised that
patients with Alzheimer's "are particulariy impaired in the opention of the Central Executive, and
that this system is important for integrating the performance of two or more concurrent tasks."
These results have been replicated in studies with patients with Parkinson's disease who "were
less able than matched controls to coordinate successfully two concurrent tasks in that they
showed a clear decline in tracking performance during dual task conditions." (Dalrymple-Alford
et ai. 1994) By concurrent tasks, the previous study is referring to experiments where subjects
were asked to simuItaneously track a hvo degree of freedom target while reciting h m memory
numbers that were presented in sequences of increasising length.
6.2 Motivation
The uttirnate goal is to provide a useful measuring tool that c m easily be applied in a
standardised and reliabIe way. However, before the 7X-meaic c m possibly be used as a diagnostic
tool for assessing neurological damage, control data fiorn a "normal" population must ftrst be
collected. Since neurological diseases are more likely to afflict people as they grow older, the
control population should aIso be elderiy subjects.
ïhere is also the opportunity to take advantage of a confounding factor that cornes with
usïng eIderly subjects. The younger çubjects' performance m the first docking task rnight possibly
be a function of their computer experience or training Eorn years of exposure to computer games.
Compared to the younger subjects in the fmt docking experiment, many of whom were students
studying to be engineen, many older subjects comparably should be classified as strict novices in
regards to computer experience.
6.3 Eypothesis
The predictions for the elderly subjects performing the docking task were the following:
Task completion times will generally be much longer for the elderIy subjects.
Task completion time differences behveen the isometric and isotonic input devices will be
much greater for the elderly subjects, due to a presumed increase in the difficulty of coping
with a "less natural" (isometric) device.
Elderly subjects were expected to allocate their control in exactly the same pattern as the
younger subjects. That is, subjects were expected to control the rotation and translation
subsets of the total of degrees of freedom separately and switch control between those
subsets. (If a difference in allocation of control patterns were to be found it would be unclear
as to the reason, since effects of age and computer experience have been confounded in this
experiment,) The isotonic input device, as the most "natuni" input device, will show a more
uniform allocation of control across al1 six degrees of fieedom. The isomemc input device
will continue to show a higher degree of separation between the rotation and translation
degrees of fieedom.
AI1 possible subsets of the avaiIable degrees of freedom were expected to show
continuous increases over time. The level of increase was expected to be linear with little
evidence of the W-metric scores approaching a ceiling value. The hypotheses formally were
therefore:
1. Opentors will switch to allocate their control between the translation and rotation degrees of
freedom as the experirnent progresses, and only their control performance will improve,=d
2. hcreasingly uniform allocation of control across a11 6 degrees of fieedom wilI continue to
develop over time.
6.4 Subjects
Founeen right-handed parents o € students fiom the University of Toronto community
were recmited as subjects. The criterion for recnriting subjects was that they must be 55 or oIder,
and should have "good" vision. Good vision was not defined other than to Say that corrected
vision !vas considered satisfactory. Five çubjects were rejected for failing to discern a binocular
disparity of at least 50 seconds of arc at 40 cm, as tested using the RandotB Stereorest (Stereo
Optica1 Co., Inc., Chicago, IL). A sixth subject was rejected for being unable to complete the
docking tasks. The remaining 4 male and 4 female subjects ranged in age from 56 to 65 with a
mean age of 60 years. Subjects were paid $55 CND upon compIetion of the experiment. AH the
subjects had only basic computer experience, and none of the subjects had previous expenence
wvith any 6 degree of fteedom computer input device. Most of the subjects had seen 3D movies in
theatres before; however none of the subjects had any working experience with stereoscopic
displays.
6.5 Experimenial Platform
The hardware setup used for the cracking experiment was identical to the setup used for
the previous docking and tracking experirnents (section 3.3 and 5.3). The expenment was
conducted on a Silicon Graphics indigof"t workstation with a 20 inch colour monitor, running
MITS (Manipulation in Three Space) software, developed by Zhai (Zhai 1995), to create a
through-the-window virtual environment. MAX@ Iiquid crystal glasses (IMAX Ltd. Toronto.
Canada) operating at 120 Hz were used to allow stereoscopic viewing. For the isometric
condition, subjects used a SpaceballB (Model$2003) mmufachued by Labtec inc. (Vancouver,
WA), operacing in rate controI mode. For the isutonic condition, subjects used the FingerbaII
(Zhai 1995: Zhai et al. 1996) powered by a FIock of BirdsB (Ascension Techology Coq.,
Burlingron, Vï), operating in position control mode. The MlTS s o h a r e sampled subjects' data
at 15 Hz. The experiment !vas conducted in a darkened room and subjects were encouraged to
adjust the position and height of theù chair so that they would feel comfortable.
6.6 Task
The task used for the elderly subjects was identicai to that with the younger subjects, as
outiined in section 3 4 , with the onIy difference being in the period in between trials. Since the
text feedback at the end of each trial (showing the number of trials completed and the docking
time for the Iast completed triai) remained on screen for three seconds instead of only two
seconds, the minimum time between trials was now three seconds instead of two.
6.7 Procedure
Following the RandotB Stereotest subjects were administered a short demographic
questionnaire to collect subjects' information and experience with stereoscopic viewing and 6
degree of fieedom control devices, which was used for screening purposes. The questionnaire
a1so included questions From the Edinburgh inventory (Oldfield 1971) to assess handedness. For
al1 trials, subjects were asked to use only their dominant hand.
Subjects were then introduced to their control device and asked to manipulate the cursor
upldown, lewright, idout, and then to rotate about those corresponding a e s in a targetless
environment. A cardboard mode1 of an mis system was used to illustrate the axes of rotation.
However, whereas the younger subjects needed less than two minutes to understand how to use
their input device, the older subjects required between 5 and 15 minutes to fuIly gnsp
manipulation of 6 degrees of Freedom. Subjects were given a single docking trial as a
trainingiexplanation of the task.
6.8 Design
The original docking experiment design was too difficult for the elderly subjectç. In order
to simplifi the experiment two options were considered:
1. Reduce the complexity of the task. This could perhaps be accomplished by reducing the
number of degrees of freedorn needed to dock, reducing the amount of movement required to
dock, or reducing the accuracy of the dock needed to finish the task.
7. Reducing the totaI number of ûiaIs required pet- session. Although each trial would be
expected to take longer to complete, since there would be fewer trials, the total experiment
time should remain about the sarne.
Option $2, to use identical tasks but fewer trials, was chosen since this would abo allow
direct comparïsons between the etder and younger subjects. 120 trials per session, instead of 216,
were therefore chosen, so that each session wouId last about an hour.
The experiment followed a 2 x 5 x 120 between subjects design. The independent
variables were as follows:
Input Device: isomemc rate, isotonic position
Session: l7 2? ... 5
Trial: 1,2, ... 120
The above conditions with 8 subjects represented a total of 4800 trials, collected over 40
hours of e-xperirnentation. A stratified random method {vas used to assign subjects to either the
isornetric rate or isotonic position conditions, such that each group was composed of 2 males and
2 fernales. Subjects completed one session per day on five consecutk days. ï h e MITS s o b a r e
enforced a mandatory rest period of 90 seconds afler every 24 trials. Each block of 24 trials
consisted of 8 randomly shuffled target locations selected three times each.
ï h e raw data, session means (5 one hour sessions with 120 trials per session), and session
standard deviations for task completion times for the isometric device condition are shown in
Figure 65 and the isotonic device condition in Figure 66. Both docking performance graphs show
significantly F(J,2J) = 26.5 1, P < 0.0001 shoner msk completion times wïth extended practice,
although the biggest improvement is between the firçt and second sessions. Bettveen the first nvo
sessions isornen-ic tirnes dropped fkom 30.6 to 19.3 (an 11.3-second or 37% improvement) and
the isotonic times went From 19.7 to 14.1 (a 5.5-second or 28% improvement). The performance
improvement From the fourth to the fifth session is rnuch smaIler with the isometric times
dropping from 13.7 to 13 .O (0.7-second or 5% improvement) and the isotonic tirnes dropping
From 8.8 to 7.6 (1.7 second or 14% improvement) seconds. Session means and standard
deviations for both devices together are shown in Figure 67 for cornparison. OvenII the isotonic
input device has a 6 second sharter average docking time across aii sessions, and this difference is
significant F(1,6) = 6.644 P =0.042.
O ! I O 200 400 600
Trial Number
Figure 65. Docking performance over rime for the four elderlv subjects using the Spaceball (an isometric input device). Raiv data, session rneans (5 one hour sessions ivith 120 trials per session) and sessionstandard deviarions are shoivn.
Docking Performance over Time
E n lsotonic Position Device - Elderly Subjects
200 400
Trial Number
Figure 66. Docking pet$ormance over timefor the four efderfv subjects uing the FingerbaII (an i5otonic input device). Rarv data, session means and session standard de~~acions are shown.
Docking Performance Over Time lsometric vs. lsotonic Input Device
(4 subjects per device)- Elderly Subjects
+ Spaceball (isometric device) + FingerbaIl (isotonic device)
300
Trial Number
Figttre 67. Docking performance over rime for both &lie isonrerric and isoronic devices compared for dderiy stibjecrs. Session means and standard deviarions are sltown.
The W-memc scores were computed for each input device separately and the results are
first presented for the isometric input device. Figure 68 shows the isometric two-way
combinations, and again the within translation and within rotation combinations had significantly
(paired t test, p < 0.0001, Bonferroni) higherw-metric scores than pair-wise combinations across
rotation and translation degrees of freedom, The within translation combinations were on average
160% higher than the average for the across combinations, whiIe the within roation combinations
were on average 103% higher than the average for the across combinations. The three-way
combinations depicted in Figure 69 show similar resuh, wïth the within translation condition (X-
Y-2) and the within rotation condition (RX-RY-RZ) showing significantly (paired t test, p <
0.000 1, Bonferroni) higher W-metric scores than their across rotation and translation counterparts
(X-Y-RX, X-Y-RY, ..., 2-RY-RZ), 158% and 103% higher respectively. However, for the four-
way (Figure 70), and five-way (Figure 71) combinations, no significant differences in X-meûic
scores existed for any combination. The six way combination is shown in Figure 72 for
comp Ieteness.
Docking Experiment lsometric Device M-metric Scores Two-way Comparisons - Elderly Subjecîs
Figrrre 68. The W-nietric scores in the docking erperiment with elderiy mbjects for on[v the isometric inpur device. Al1 NO-ivay degree of freedom combinations are slzoivn.
Oocking Experiment lsometric Device Y-metrit Scores T hree-way 0.6 Comparisons - Elderly Subjects
Figrire 69. The W-nretric scores in the docking experiment for only the kometric input device- Al1 rfiree-way degree offiecdom combinations are shown.
0.6 - Docking Experiment Isometric Device Y-metric Scores Four-way
Comparisons - Elderiy Subjects
0.5 .
Figure 70. î l e Wrnerric scores in the docking erperiment wifh elderly subjects for on/y the isonretric input device. -411 four-way degree of freedom combinarions are sliown.
0.6 Docking Experiment lsometric Device Mnietric Scores Five-
way Comparisons - Eiderly Subjects
Figure 71. The %-metric scores in the docking qer iment witii elderly subjects for on@ the komerric input device. Allfive-way degree offieedom combinations are shown.
Docking Experiment lsometric Device M-metric Scores Six-way 0.6 - Comparison - Elderly Subjects
Figtrre 72. f ie %Y-merric scores in the docking erperi~rtetir with elderly srrbjecrs for only the isonrerric inpirr device. f ie siwvuy degree of freedom combination is siiown.
However, the isotonic %Y-menic scores portray a very different picture than the isometric
%Y-metric scores. For the isotonic input device two-way combinations shown inFigure 73, the two
highest scores beiong to the within translation degree of freedom. On the other hand, the within
rotation degree of Freedom subsets do not show the same high scores as their isometric
counterpcirts. The rotation degree of freedom W-metric scores are comparable to the two-way
benveen translation and rotation subset. Three-way combinations for the isotonic device in the
docking experiment are shown in Figure 74, which shows the within anslation group (X-Y-Z) to
have the highest W-metric scores. The remaining four-way (Figure 75), five-way (Figure 76), and
six-way (Figure 77) combinations depict no significant differences in %-memc scores between
combinations.
Docking Experiment fsotonic Device U-metrk Scores Two-way Comparisons - Elderly Subjects
Figure 73. Tiie W-rnetrie scores in tire docking aperiment with elderly subjects for only the isotonie input deviee. Al1 nvo-tvq degree ofjeedom combinations are sltown.
Docking Experiment lsotonic Oevke M-melric Scores Three-way 0.6 - Comparisons - Elderly Subjects
0.5 .
Figure 74. î l e m-metric scores in tire docking erperiment with elderly strbjectsfor only the isotonie input device. A11 three-woq: degree of freedoom combinafions ore shown,
Oocking Experiment lsotonic Device M-metric Scores Four-way 0.6 Comparisons - Elderly SubJects
0.5 .
Figtire 7.5. The W-nrerric scores in the docking erpeninent ivifh elderIy sirbjecrsfir only the isotonie inptrf device. =Ill four-way degree offreedont combinarions are shotvn.
0.6 Docking Experiment lsotonic Device M-rnetric Scores Five-way
Comparisons - Elderly Subjects
0.5
Figtire 76. The 9X-metrie scores in the docking erperimenr wifh elderly nrbjecrs for on@ die isotonic inptrt h i c e . Allfive-ivay degree offreedom combinations are shorvn.
Docking Experiment lsotonic Device M-metric Scores Six-way 0.6 Comparison - Elderiy Subjects
Figtire 77. The W-metric scores in the docking txperïnrent with elderly subjecrs for only the kotonic inptir device. iire sir-way degree of freedoni cor,ibinariort is sltown.
Figure 78 shows changes in W-metric scores over timdsession, broken d o m by input
device and number of combinations. Only a subset of representative %Y-metric scores are shown,
to Save space. Al1 W-metric scores increase over sessions. For the nvo-way combination case, X-
RY and RX-RY have been selected as representative of an across translation-rotation pairing and
a within rotation pairing respectively. Across aII the two-way combinations, the highest W-metric
scores consistently belong to the within rotation isometric rate conditions. The isotonic scores for
both the within and across conditions were altvays lower. The lowest W-metnc scores, for the
nvo-way combinations consistently belong to isometnc rate across translation and rotation
painngs.
Docking M-metric Score vs Time Across 2 Degrees of Freedorn for X-FU( and RX-RY
Elderly Subjects 0.6 ,
+ lrotonic Position X-RX -acrorf 4- lsometric Rate X-RX -across + lsotonic Posltlon RX.RY -within + Isornetn'c Rate RX-RY -within
0.0 O 1 2 3 4 5 6
Session
Figure 75. How the W-metric score cltattges over time in the docking experiment with elderly srtbjecrs. A benverri rruttshiiori urid rotation degree oJfieerlotri (X-iLV uttd u witliin rotution degree O ffieedom fRKR Y) for borh rhe isometric and isotonic input devices are shown.
The three-way pairings depicted in Figure 79 by Y-Z-RY and RX-RY-RZ show this same
pattern. Isomemc within scores were the highest, CoIlowed by isotonic W-metric scores, with the
lowest scores belonging to the isometric across groups. For the four, five, and six-way (Figurego)
combinations, isotonic positionm-metnc scores were in fact larger than their isometric rate
counterparts, though in al1 cases the values, and thus the differences, were srnall. In addition the
R-metric scores over time do not show the same IeveI of asymptoting as evident in the task
completion times.
Docking M-metric Score vs Time Across 3 Degrees of Freedom for Y-2-RY and RX-RY-RZ
Elderly Subjects 0.6 , 1
O 1 2 3 4 5 6 Session
0.5 -
Figure 79. Hoiv the W-»tetrie score changes over tirne in the docking mperimenr wirh elderiy sirbjecrs. rl brnveen rrarrrlarion and rotation degree offreedom (Y-2-RY) and a witltin rotation degree of'freetiom (RY-RY-RZ) for botlt rltr isometric and isotor~ic input devices are s h o w
-0- lsotonic Position Y-Z-RY -acmss -2- lsometric Rate Y-2-RY -across t Isotonic Position RX-RYdZ -within + lsometric Rate RX-RY-FLZ -within
0.4 1 T
Docking M-metric Score vs Time Across 6 Degrees of Freedom for X-Y-2-RX-RY-RZ
0.6 1 Elderly Subjects
O 1 2 3 4 5 6
Session
Figure 80. How [lie %-niefric score changes over rime i~t rile docking e~periment ivith elderiy sttbjecrs fir al1 6 degrees offieedom.Resitltsf;o~n borh the isometric and isotonic input device conditions are show.
Figure 8 \-Figure 83 examine the rdationship between W-metric scores and task
compIetion tirnes. Tnree hvo-way combinations are gnphed; a within transIation p a i ~ g (X-Y in
Figure 8 I), a between translation and rotation painng (X-RZ in Figure 82), and a within rotation
pairing (ILY-RY in Figure 83). Linear regression analysis of the three graphs resuited in dope
estirnates of -0.003 (X-Y in Figure 81, percent of variance accounted for, R' = 6.62%), -0.003 (X-
RZ in Figure 82, percent of variance accounted for, R' = 17.5%), and -0.002 (RX-RY in Figure
83. percent of variance accounted for, R' = 4.50%). These R' scores, sirnilar to the R' scores
Crom the docking experirnent with younger subjects, indicate that taskcompletion time is a poor
predictor of*-rnetric scores. The R-metric is quantikg a different aspect of performance than
the traditional task completion time m e m .
The Relationship Between M-metnc and Task Completion Time For the Docking Experiment X-Y M-metric Comparison
Elderiy Subjects
- :
5 10 15 20 25 30 35 40 Task Completion fime (seconds)
Figtre SI. 771e relationslzip benveen the nvo dependent varinbies rask-completion time and the W-nietric for rhe ,Y- Y combination for the docking erperiment with eideriy sttbjects.
The Relationship Between M-metric and Task Completion Time For the Docking Experiment X-RZ M-metric Comparison
Elderly Subjects
0.0
O 5 10 15 20 25 30 35 40 Task Completion rime (seconds)
Figure 82. The reiationshlp benveen the two dependent variables task-completion rime and the 7X-metric for rhe X-RZ combinarion for the docking erperimenr with eideriy subjects.
the Relationship Betwsen ~nietr ic and Task Completion Time For the Docking Experiment RX-RY M-metric Cornparison
Elderly Subjects - .
-- -- ---W. ~ ~ U A -+
5 1 O 15 20 25 30 35 40 Task Completion Time (seconds)
Figure 83. TIte rdalionship benveen the nvo dependent variables task-completion rime und rite W-nrerric for the &Y-R Y conibination for the docking erperimen with elderly subjects.
Figure 84 compares the performance of ihe older subjects with the younger subjects. The
eIder subjects' performance scores with the SpacebaII never achieve the performance levels of the
younger subjects. However the performance scores of the older subjects with the FingerbaII w ih
pnctice do approach the younger subjects' initial performance Ievels.
Docking Performance Over Tirne Between Device and Subject Cornparisons
+ Spaœball -0- Fingerball -t Spaœball - Elderty Subjecîs -3- Fingerball - Eideriy Subjecîs
Trial Number
Figure 81. Docking perfortnance over iime sliorving botk rhe yoiinger and older sribject by input (levice condition.
6.10 Discussion
Unlike the task completion times in Figure 67, the W-metric scores depicted in Figure 78
through Figure 80 show much Iess evidence ofapproaching a limit. For exarnple, the average
increase in W-memc scores across both input devices for the RX-RY-RZ combination are 0.029
(1" to session), 0.029 (znd to 3d), 0.01 1 (3"' to 4"), and 0.022 (4' to 5'). The change from the
tint to second session is the largest, and from the second session on W-metric scores increases at
an alrnost constant n t e nther than asymptoticalty Iike the task completion times. This non-
asymptoting W-metnc is identical to the W-metric score seen in the original docking expenment
with younger subjects. The hypothesis that it is possible to use the W-metrk scores as a more
sensitive measure of manual control expertise appears to be holding me. Figure 81-Figure 83
provide additional evidence that the W-meüic is an appropriate performance metnc.
Whereas the translation degrees of ûeedom were highly coupied for both the isometric
and isotonic conditions, the rotation degree of freedom showed coupling only in the isometric
condition. This suggests that for the isometnc condition the subjects tended to switch control
behveen only translational and only rotational controI; that is, they did not generally translate and
rotate at the same tirne- However, under the isotonic condition the subjects would translate
without rotating some of the time, they wouId not rotate without also translating during the rest of
the time.
No differences in the pafferns of the alocation of control between the younger and oIder
subjects were obsewed. Therefore, neither age nor level of computer experience is believed to
have any effect on people's allocation of control across multiple degrees of fkeedom in 3D
environrnents. Therefore, if this experiment were to be conducted with patients with neurological
damage, it is believed that any differences in the patterns of the allocation of control may be
amibuted to the neurological disease. The next step wou1d involve identifjmg whether in fact
such a pattern difference exists.
Using a variant of the type of experiments discussed in this dissertation and applying it to
a real world problem has certain appeal. Unfominately, before a successful application could be
achieved there would first be a host of hurdIes to overcorne, including:
Patients suffering fiom neurological disease often are also suffering From additional
complications, leaving serious doubt as to whether or not they could adhere to the
rigours of a complex motor control trisk.
One of the complications includes epilepsy and the hardware used in this experiment,
specifically the W B gIasses, because of their inherent flickenng could potentially
instigate seinires in susceptible patients.
O Neurological disease is most Iikely to strike as people get older. However, in the
docking experiment with eldedy subjects a total of 6 of the 14 "normal" participants
recruited (42%) were rejected for failing the RandotB Stereotest. The rejection rate
would probably be higher in populations ~vith neurological damage than in healthy
populations.
7 Conclusions
Many complex hurnan-computer interaction tasks, including computer-aided design,
scientific data visualisation, computer graphics animation, teieoperation, virtual reality, and 3D
video games require 6 degrees of freedom control in 3D space. To be effective, these computer
applications potentially require the user to simultaneowly and eficiently control multiple degrees
of freedom, requinng a very different type of interaction than the discrete, singIe key-press
interactions of word processing and spreadsheet applications. But what is the appropriate
terminology that describes exactly the type of human-computer interaction throughout this
dissertation?
Consider the following statements and definitions from the literature:
'The well timed and well balanced functioning together of sevenl muscles in a single
movement." b u s , H. as cited in (Broer 1973)
'The combining of simple movements without unnecessary tension and in proper sequence to
make a smooth complex movement." (Broer 1973)
"...the way in which two or more distinct elements are brought together to form a new
complex, in which temporal or spatial characteristics of the originaI elements are munialIy
constrained." (Wallace 1989, pg. 286)
O "...a repeatable spatiotemporal pattern of movement in relation to a behavioral act or goal."
(Wallace 1989, pg. 4 17)
r "...is optimal because it is the shortest and is also most coordinated in the sense that x and y
move simultaneously at the same relative pace." (Zhai 1995) p. 108
*'...the two degrees of keedom are completely un-CO-ordinated, because x and y are not
moved at the same rime ..."( Zhai 1995) p. 108
'&The CO-ordination of a movement is the process of mastering redundant degrees of Geedom
of the moving organ, in other words its conversion to a controllabIe system."(Bernstein 1967)
Statements about simultaneity, the timing of events, proper sequencing, the
spatiotemporal pattern of movement, multi-components moving as one, or the smoothness of a
trajectory are realIy talking about coordination. However there are no basic units of coordination,
and the term coordination means different things to different people working in
different domains. The fundamental reason for inconclusive or misleading statements in the
litenture is not deceitfulness or a lack of thoroughess, but rather the lack of an adequate
measuring tool for quantifjmg coordinahon. This is not to say that metrics for measuring
coordination have not been developed, only that they are not complete.
The primary contribution of this dissertation is the development of the %-metric as a
proposed measurement of coordination, where coordination is defmed here as the allocation of
conuol across multiple degrees of fieedom. "Controliing a degree of fieedom" has been defined
as reducing the distance between the c m o r and the goal. The W-metric measwes the simultaneity
and efficiency of control of a trajectory for both docking and tracking tasks, and is applicable for
any number (two or more) ofdegrees of freedom. The W-metric, through its use of normalisation,
is not constnined to having al1 the degrees of fieedom measured in the same units. Therefore,
using the %-metric rotation and translation degrees of freedorn c m be analysed together.
7.1 The Original Motivation
initially the ultimate goal was to develop a quantifiable measure of human coordination.
It would be presumptuous to declare the M-rnetric as the measure of coordination; rather instead
it is more appropriate to view the Z-metric as a proposed definition of coordination. No one
definition is appropriate for al1 scenacios and the analysis toot used should match the time and
space consmints of the task. In addition, depending upon which aspects are most important, there
are the time, space, and frequency components of the operator's trajectory that should be
considered. Thex-metric emphasises the time and space components of a trajectory, with the
corresponding measures of simultaneity and efficiency of control.
Formai control experiments were conducted for three reasons:
L) to provide some validation to the metric as an applied tool for analysing data,
2) to demonstrate the usefulness of the W-metric by providing new insights using a
previously studied experimental platform,
3) and to gather data on human-cornputer interaction coordination performance with 6
degree of fieedom input devices.
7.2 Experimental Conclusions Summary
The usefulness of the W-metric has been demonstrated in a longitudinal docking
expenment and in a longitudinal tracking experiment. The 7#-metric could potentially be usehl in
the assesment of neurological damage and a data coIIecting study using elderly subjects was
conducted. A summary of the experimental conclusions is presented in Table 9.
Table 9. Srrmntary of hypothesises and erperimental conclmions.
Hypotheses
Novice opentors will find it difficult to dlocate their control equally across six degrees ~f tieedom and will instead switch control benveen the translation and rotation degrees of Freedom.
1. Operators will continue to ailocate their control benveen the translation and rotation degees of Freedom, and onIy their contro1 performance will improve, or
2. Allocation of control across al1 6 degrees of Freedom will graduaIly become more uniform over time.
The W-metric is more sensitive than task completion time or RMS error as a measure of expertise.
Elderly subjects and cornputer novices exhibit the same allocation of control as younger, expenenced computer users in 6 degee of Eeedom docking tasks.
Expcrimental Conclusions
Input device dependent. The Spaceball, an isornetric device, showed very large differences in W-rneiric scores between the within and across combinations in both the docking and tracking experiments. The FingerbaII, an isotonic device, showed much srnaller differences in the dockinç task and no switching of control in the tracking task.
Results indicate that both hypotheses are actually tnie. Operators improve their ability to switch control between subsets and they irnprove their ability to allocate their control equally across al1 the available degrees of Freedom.
Perhps. Appears to be true for docking tasks where the same docking locations are repeated a large nurnber of times. Does not appear to be tnie for tracking tasks of a non-repeating forcing function.
True- While there is a large cornpletion hme performance difference elderly subjects exhibit the sarne alIocation of control behaviour in 6 degree of fieedom tasks as younger subjects.
in the docking experiment subjects demonstrated a preference to control the rotation and
translation degrees of Freedorn sepantely and to switch control between the two groups.
Controlling a subset of the avaiIabIe degrees of tieedom in order to reduce the complexity oPa
task fits within Bernstein's mode1 of rnotor controI development. The choice of which subsets,
namely translation and rotation, show that the perceptual preference identified by imai, S- and W.
R. Garner (Imai and Garner 1965) extends into the action domain. While the d o c h g experiment
did not specify how subjects were to perforrn the tasks, these resuIts are representative of what
people do when rhey have their choice.
The docking expriment also demonsmted a qualitative difierence in trajectory
behaviour benveen the Spaceball and the Fingerball. Zhai's research had already demonstrated
that the Fingerball offers supenor perfomance to the Spaceball, eçpecially for tasks including
rnuch rotation manipulation. The reason as to why this is so is hypothesised to be because the
Fingerball alIows users to better atloçate their control.
The tracking experiment provided insight that the degree to which people are: hlly able to
a1Iacate their contrai rqually across al1 degrees of fieedom if they are specifically required to do
so is still dependent upon the input device. A tracking task is a more consained than docking
motor controi mk, where both the tirne and space components ofa trajectory are specilied, Even
for a more constrained task operators have limitations in their ability to alIocate their control
equally.
8 Limitations of the W-metric, and Future Work
8.1 Limitations of the R-melric
the 3H-metnc is fundamentalIy a definition for "aIIocation of control", a phrase
inkaduced in this dissertation. The W-memc has been tested through conmved tasks in order to
make generalities about human compter interaction tasks. All of the following limitations must
be kept in mind when applying thex-metric to real worId data-
The %-rnetric is used to analyse data at the output Ievel and nat at the control level. Al1 3n-
metric caIcuIations are conducted at the working point level, where the actual mator control
actions being conducted by human operator's hand rnay be very different in behaviour.
Conclusions concerning the working point do not necessarily extend to the operator's muscle
movements.
The nurnencal values of aliocation of control obtained are a tùnction of the coordinate systern
seiected. If the coordinate system is changed (transhrmed or rotated) then the computedm-
metric scores will also change. The coordinate systern selected in this thesis is not arbitrary,
however; it was selected to match the naturai language of up/down, Iefdright, idout.
Nevertheless. it would not be proper to claim at this tirne that there is not a more appropriate
axis systern.
6 Computing the efficiency of conrro1 component of the W-merric for docking is based on the
assumption that the shortest path is the "optimal" p a h If this assumption can not be safely
made, then equaI allocation of contrai (an %-meaic score of 1) may not be the optima1 score.
For performance rneasures, assurning that the shortest task completion time for a docking task
is the best is a safe assumption, in particular when subjects are insûucted to perform "as
quickly as possibIe", Assuming that the shortest trajectory is best may not aIways be correct..
r Computing the simultaneity of contro1 requires normalisation of the error reduction function-
For docking tasks the error reduction function cannat be normalised until the entire task is
completed. Cf the error reduction function cannot be nonnalised, then it is not possille to
compare the allocation olcontrol between multipIe degrees of fkedom. This is also the
reason why it is not possible to compute an instantaneous W-metric score.
r The W-rnetrïc does not take into account the fcequency domain, o d y the time and space
dornains. Whether the allocation of control is switched only once during a taçk or is switched
several times a second is w t reflected in the Wmetric score. Incorporating the fiequency
dornain into a rneasure would be one step cIoser towards the develapment of a tnie
coordination metric.
8.2 Future Work
The W-metric is a trajectory based analysis that cornputes the alIocation of control across
multiple degrees of fteedorn within the constraints of its definition. The validity of the W-mecric
has been demonstrated through three formal experirnents within the field of human-computer
interaction. This allocation of control metric has potential for applications @th in and out of the
human-cornputer interaction field) where rndtiple degrees of freedom must be manipuIated
simultaneousIy and an evaluation of the quality of performance is necessary.
8 .2 1 Errending the W-merric into lhe Frequencv Domain
The %-metric as it stands measures the allocation of contro1 in the tirne and space
dornains but does not say anything about the Frequency of control. For example, the two
hypothetical trajectories iliustrated in Figure 85 have very different Frequencies of switching
contror between translation X and translation Y, even though they have identical %V-metric scores.
In this thesis that information has not been extracted frorn the expetimental data and it is
unknown how rnuch explanatory vaIue is contained within the fiequency information. How ofien
is c o n t d switched between different degrees of freedorn and how does the pattern of switching
change with extended practice?
Goal Position Goal Position
Start Position Start Position
Figure 83: Two Ii-vpotlierical irajecrories rvirh idenrical W-tnerric scores but different fieqtrencies.
What is the "correct" or "optimal" kequency of performance? The first step in extending
the?#-metric could iwolve measuring the fiequency ofshifting of control between the degrees of
freedorn. Tne next step would be to determine a correspondhg meaning for the different
frequencies. with perhaps multivariate ana1ysis of coherence functions as an appropriate approach
to take.
8.2.2 Tivo Hajtded Coordinario~i
Al1 the experiments in this thesis are one-handed computer input tasks; however many
reaI wor1d tasks that humans perfonn every day are in fact two-handed, Two hands are usually
used in an asymmehic fashion, with the non-dominant hand doing the Iarger or stabilizkg
movements and the dominant hand doing the fine manipulations. (Guiard 1987) As computer
interface technologies advance there are many hvo handed interactions chat could be
irnpIernented, such as scene manipuIation, where panning, zooming, and rotation are the degrees
of freedom. Such scene manipulations would be identicai to the manipulations that have been
demonstrated to be usehl for two-hded interactions with electronic rnaps (Hinckley et al.
1990). Pilot work on symrnetrica1 bimanual interaction using the W-metric (Balakrishnan and
HinckIey 2000) has indicated that the degree of parallelism between the two han& in a mcking
task is a h c t i o n of the difficulty of the task and the visua1 distance between the two mgets (Le.
whether they are both within the same view or not).
Studying of two handed interaction cou1d be just the tip of the coordination iceberg. For
m e complexity in simultaneous manipdation ofmuItiple degrees of fieedom, the W-metric could
in theory be applied to multi-person coordination or computer supported coIIaborative work For
tasks (such as steering a submarine) where one person can not possibly mck aU the amiable
degrees of Freedom at one time, perhaps nvo or more operators each controlling a subset of the
degrees of Freedom may exhibit better perfomance. AIternatively, there may be some tasks
where the nurnber of degrees of Freedom is simply too high for one person to handle and the task
must be divided among several operators. The W-metric could perhaps be used to evaluate how
the degrees of freedom should be divided among the operators and to report the relative
performance of different operators.
8.2.3 Evaluation o f Elastic and Mrlti-channel Input Devices
The input devices used in the experiments in this thesis for al1 six degrees of fieedom
were either strictly isometric (the Spaceball) or strictly isotonic (the Fingerball) input devices.
However, many input devices are multi-channe1 or "mixed resistance mode" devices, for which
different types of interaction modes fsuch as isotonic mouse, touchpad, or isometric joystick) are
rnerged together into a single device. How would an operator's allocation of control change based
on changes to the haptic quality of the input device? The new models of the Spaceball are no
longer strictly isornetric devices; rather they are slightiy elastic devices. What type of change of
performance is the result of the new elastic design? What type ofW-metric scores might be
expected in a six degree of Freedom tracking task if two of the degrees of Freedom are elastic, two
are isometric, and the last two are touchpad controlled? Theories as to the interaction between
allocation of control and input device haptics are needed to predict performance without having to
test every possible combination that can be manufactured.
There is also the potential to develop a standard that could be used to evaluate muli-
modal input devices once they do appear on the market.
8.2.4 Evalrrarion o f Transformed Ares
In the expenments conducted in this thesis, the mapping of control device input to cursor
movement is straightfonvard. In the isomemc condition if a subject puIls up on the Spaceball, for
example, then the cursor moves upward. In the isotonic condition if a subject lifts up the
Fingerball then the cursor moves upward. Rowever, not a11 input devices are designed or used in
environments with such a straightforward and direct mapping. A computer mouse, which is
normally placed flat on a desk, demonstrates one type oftransposed mapping. While right and Ieft
movements of the mouse do correspond to right and Ieft movements of the cursor, the mouse is
not lifted up and d o m relative to the desk for the cursor to move similady on the screen; rather
the mouse is moved fonvard and back. For most reai world teleoperation manipulations the
mapping is anything but s t r a i g h t f o d and can in fact change during the task. Miimally
invasive surgery is a worst case scenario, where not only can the end-effector's movement
rnapping relative to the input device change, but the scene view can be changed by movements of
the camera.
How important is the mapping between the control device input in the hand space to the
cursor input in the display space? Do al1 transformations work equally well or is there a subject
preference? What is the relationship between performance and axis transformations? How easily
are operators able to switch between different transformations? What about tasks where the
transformation is dynamic, changing during the task? A systematic approach studying axis
transformations could not only lead to further understanding of control action to performance but
could perhaps tùrther improve the W-mettic by identibng the "correct" axes of transformation to
evaluate performance.
8.1.5 The ?&narie as a Meantre of Ewerrise
Docking task completion times for both younger and elder subjects over time are shown
in Figure 81. Al1 groups of subjects for both isometric and isotonic input devices show an
asymptoting of performance, where performance is approaching an identifiable limit. This type of
behaviour, sometimes referred to as a "learning curve", is expected and is typicalty seen in
performance over time graphs. However, the corresponding W-metric curves depicting allocation
ofcontrol s h o w in Figure 30-Figure 3 1 and Figure 78-Figure 79 do not show any sign of
asymptoting and instead appear to be increasing Iinearly. This thesis has hypothesised that the W-
meu-ic could potentially be used as a more sensitive measure of expertise, that is, to continue
measunng performance improvement after other measures no longer reflect this.
For the docking task subjects were instructed to dock a cursor ont0 a target, where the
targec's location was one of only eight different possibilities, ïhese same eight locations were
then repeated in a random order hundreds of times. For the tracking experirnent, the trajectory of
the target did not repeat from trial to trial, rather only session to session. Each trial within a
session was a unique trajectory path that did not repeat until the next day, when the subject ran
the experiment again for a new session. If the expenment were to be rerun, it is proposed that
only eight (or even fewer) different trajectories be used, and to have subjects practice tracking
those mjectones over and over again.
Unanswered questions include: would tracking the same trajectones over and over again
show the same type of continuous mcrease in W-metric scores as seen in the docking
experiments? And as for the docking ta& at what point wilI the W-metric scores start to
asymptote? The W-metric is rnathematically bounded by 1, therefore at some point the allocation
of control scores seen in the docking experiment is going to have to asymptote, but how high cm
the scores go and how much practice would it take to get there?
8.1.6 Teleoperation- Minimallv Invasive Surgerv
Simple robotic tnovements are sotnerinies seen to be a sequential series of uni- directional motions tlrat lack the appearance of smooth coordination benveen multi-joints. (Cao et al. 1996)
Minirnally invasive surgery (also known as endoscopic or laparoscopic surgery) is
essentially a form of teleoperation. Human tissue and intemal organs that are normally directly
palpated by a surgeon's hands rnwt now be handled remotely through specially designed
manipulation tools. ïhese tools are inserted through relatively srnall incisions in the body
cornpared to the larger cut that rnust be made for standard "open" surgery. From the patient's
point of view, minimally invasive surgery means a shorter recuperation tirne. However, tom the
surgeon's point of view, rninimally invasive surgery means a much more dernanding and longer
operation.
From a human factors point of view, what is the difference between minirnally invasive
surgery and traditional open surgery? Obviously there are the additional constraints of limited
haptic feedback, lack of a direct view, the separation of handspace tiom workspace From visual
space (surgeons must observe their manipuIations on video rnonitors) and a restricted range of
motion. An additional finding tom task and motion anaIyses of novice and expert surgeons'
performance in training workshops was that "motions chat are normally executed in pmllel in
natural prehension must now be planned and executed in serial order." (Cao et al. 1996) For
example, the jaws of an endoscopic tool were observed not to open to grasp at the same time that
the tool was being transposed. in cornparison, when the human reaches for an object to grab it,
the hand's fingers open to take the shape of the desired object while in motion (MacKenzie and
iberall 1994). Cao et al. hypothesised that the executing of motions one at a time is a coping
rnechanim for the difficuIties involved in minimatly invasive surgery. Separating surgical
movements into their most basic components of reaching, grasping, pushing, pulling, and
releasing effectively reduces the number of degrees of freedom that surgeons must manipulate
simultaneously and thereby reduces their cognitive Ioad. The main difficulty for surgeons
conducting minimally invasive surgery appears to be the reduction of their coordination.
Minirnally invasive surgery is still in its infancy and as new technologies are developed
they will be introduced into the openting field. One possible way to evaluate whether or not a
new technology is indeed to progress is to quanti@ the amount of coordination improvement seen
in surgical manipulations. Optimal behatiour exists in the motions of surgeons conducting open
surgery, which is well estaidished in its technique, so a direct and appropriate benchmark exists.
The tasks in a minirnalty invasive environment are neither strictly docking nor tracking
task, but nther perhaps overlap more with the mcing and target acquisition tasks in the manuaI
control tavonomy of Figure 3. By extending the%-metric to include the tracing and target
acquisition the W-merric could potentially be used to analyse the trajectory of surgical tooIs.
8.1.7 Process Conrrol
Studying performance in a complex environment can help researchers understand the
type of saategy operators rnay be using (Yu et al. 1998). In process controt environments, for
example, operators are sometimes required to manipulate a multitude of different variables, such
as temperature, volume, pressure, and flow rates, towards a goal state in reaI time. Because of the
cornplexity inherent in modern process control plants. identical goaI States rnay be reached
through quaiitatively different strategies,
A virtual environment known as DURESS II (DUaI REservoir System Simulator) was
designed to be representative of indusma1 process control systems and has been used for
extensive longitudinal studies of operator behaviour (Bisante and Vicente 1994; Yu et al. 1998).
At one level of analysis DURESS II rnay be dsscrîbed as having four degrees of fieedom: the
temperature of two different tanks and the two flowntes associated with each tank. A start-up
procedure for the DURESS il system might consist of taking the system h m initial conditions
(Le. room temperature, no flow) to a particular production state (i.e. 50°, LOO Umin) quickly,
while staying within safety constraints. (Safery constraints wou1d inchde thùigs Iike not heating a
tank while it is empty.) Such a start-up procedure is sirnitar to a manuai control dockîng task, The
temperatures and flowrates of both tanks are variables that change over time, there is an initial
and goal state, and optimisation involves doing the task as quickly as possible. The changes in
temperature and flowrate variables produce a trajectory over time. AnaIysing different operators'
üajectories is a study of coordination. New insights could potentially arise by appiying the Hf-
metric to existing data, and to future process control studies. In addition, existing theories couid
be supported with quantifiable evidence rather than qualitative.
8.2.8 Assessrnent of hrettrolo.qrqrcal Damgce
Motor function can be ÜnpaÏred by neurologica1 damage, 0 t h seriousiy as illness
progresses. The most usehl application of computerised tests to assess nemlogical damage may
be in the ear1y detection of neurological diseases. Still much works needs to be done in
identifying quantitatively how the progression of a disease c m be expected to impair motor
function. Rigorous and systematic testing is needed to quantifi exactly how motor h c t i o n is
impaired by different types ofdiseases. The goal of this testing shouId be to develop theones that
predict the dificulty of different tasks and how vanous States of neurological damage might
impair performance. A theory that answers whether a one degree of ûeedom or a two degree
kedom task is more cognitively demanding wouId be a good place to start (see section 6.1). The
foilow-up questions quickly become apparent. WouId six degree of freedom tasks be more or less
sensitive to differences in performance than one or two degree of freedom tasks? How much
more or less sensitive, and why? Does the Executive Function decrement observed by (BaddeIey
et al. 1986) hoId tnie between degrees of freedorn within a tracking experiment?
Collaboration between human-cornputer interaction research and neurological research
should be beneficiai to both groups. Studying patients with neurological damage could possibly
iead tu new insights into how the brain functions in normal patients, thereby Ieading to new
iheories or designs of input devices for mmual conuol of computer tasks. Neurological research
could benefit greatly kom what is aIready known in the human factors Iiterature about baseIine
human performance and optima1 interface design. For exampIe, in Behbehani's experiment
analysed using phase plane analysis (Behbehani et aI. 1988) subjects had to align a vertical Iine
controlled by a joystick over a m e t Line in a one degree of freedom docking task. However, the
joystick was used in a position control mode as opposed to a rate-controlled mode that may have
yielded supenor performance for a self-centring device.
Parkinson's disease and strokes are more likely to affect the elderly. The dockuig
experiment with elderly subjects may be used as a baseline for subjects with neurological
damage. If the Executive Function deficit extends into motor contror function then that should
translate into a change in patients' allocation of controI in rnuIti-degree of freedorn tasks,
Therefore, patients with neuroIogica1 damage are expected to have significantly tower allocation
of control scores Cor higher combinations of degrees of kedom, AIlocation of control across
translation and rotation degees of freedom in such patients rnay be so Iow as to be essentially
non-existent in extreme cases. [fsuch a qualitative difference in allocation of control does exist
then the N-metnc shouId prove to be an extremely usehl tool.
However an investigation mto patients with neurological damage will hordly be
mightforward and, unfortunately, most likeIy be fiaught with difficulties. The main difficulty
may be that patients with neurologicai damage wilI simply be unable to accomplish the same type
of tasks as those used in the experiments discussed in this dissertation. Across al1 three
experiments discussed in this dissertation a total of 36 subjects were recruited, where 3 "normal"
subjects wcre unable to either dock the tetrahedron or even come close to tracking a target..
Another 9 subjects failed the binocular disparity cnteria for a combined 33% overall rejection
rate. Tnere is no reason to believe that patients with neurological damage would have a lower
rejection rate, and if anything, it is expected to be even higher than for healthy subjects. It rnay
therefore be necessary to come up with a more appropriate pool of computerised tasks. Also,
patients with neurological diseases rnay have additional complications that will be impossible to
elirninate, thereby confounding any results. One complication could be susceptibility to epileptic
seinires that could be triggered by the shutter glasses used in the experimental setup, a very real
possibility.
Nevertheless, even with al1 these difficulties, the assessrnent of patients with neurologica1
darnage has the potential to be the most usehl application of the W-rnetric because of the possible
benefits it could bnng as a rnedical tool for early detection and evaluation.
Appendix A: Stationarity
T'he purpose of using formal time series analysis methods on sequential data is to l e m
"something" about the nature of the system generating the data. For the present case, the systern
consists of a human operator interacting with a multiple degree of freedom input device. The
"something" being investigated is the nature of hurnan coordination. This section is part of an
exploration of time series analysis for the purpose of learning something about the nature of
human coordination.
The first step in ail time analysis approaches is to check for stationarity, because if the
data are stationary then many simplifjmg assumptions can be made.
The following definition of stationarity is taken tiom (Challis and Kitney 1991).
Stationarity, is defined as a quality of a process in which the statistical parameters fnrean and standard deviarion) of the process do not change witlr rime.
n i e rnost important property of a stationary process is that the auto-correlation function (acf)
depends on lag alone and does not change with the instant at which the f ict ion was
calculated.
A weakly starionary process has a constant mean and acf (and therefore variance)
A triciy stationary (or srrongiy starionary) process has al1 higher-order moments constant
including the variance and mean.
ïhe preceding defmition of stationarity is typical of what can be found in the Iiterature.
What is usuaIly not explained in the literature is that strongly stationary processes are never seen
in pnctice and are discussed only for their mathematical properties. Weakly stationary proccsses,
are sometimes observed in the reaI world and are usually m t m e d to be "cIose enough" to
stationarity in the strict sense (strong stationarity) to be treated as such. In addition, stationarity is
really a relative term, rather than an absolute one, as the definition above may lead one to beIieve.
h y process that "really" is stationary, can only be seen as stationary if the sampled data fkom the
process is very long compared to the lowest frequency component in the data. in other words, if
one coIlects data for onIy a short time, relative to the bandwidth of the data, then even a stationary
process wilI appear to be nonstationary. Finally, very little research
exists which discusses what effect deviations, large or small, fiom stationarity rnay have on
analysis techniques which require stationariv.
For the purpose of analysis, the stationarity property is a very important property to have
in one's data, since it leads to many simplifymg assumptions. Again, the fmt step in uing any
methodology for time series analysis is to check if one's data are stationary.
Tesring for Stationaritv
There are hvo general approaches to testing for stationarity, paramehic and
nonpararnetric. A review of the literature indicates that parametric approaches are those usually
used by researchers working in the time domain, such as economists, who are making certain
assumptions about the nature of their data. Nonparametric approaches are more commonly used
by researchers working in the frequency domain, such as electrical engineers, who often treat the
system as a "black box" and can not make any basic assumptions about the nature of the system.
Nonpanmetric tests are not based on the knowledge or assumption that the population is
norrnally distributed (Bethea and Rhinehart 199 1). By making no assumptions about the nature of
the data, nonparametric tests are more widely applicable than paramettic tests which oRen require
normality in the data. Although more widely applicable, the trade-off is that nonpararnetric tests
are also Iess powerhl than pararnetric tests. To arrive at the same statistical conclusion with the
same confidence level, nonparamemc tests generally require anywhere from 5% to 35% more
data than panmetric tests (Bethea and Rhinehart 1991).
f i e Riins Test lnonpurnmerric)
A rtin is defined as "a succession of one or more identical symbols, which are followed
and preceded by a different symbol or no symbol at all" (Gibbons L985). For example, for a series
of identical flips of a coin, where H represents heads and T for tails, such as
the long succession of H is a counted as a run of heads. Too few or too many runs is evidence of
dependency between the observahoris, and therefore, nonstationarity. A nms test is a counting of
the number of runs in a series, and c o m p a ~ g the nurnber found to what one would expect if the
observations were independent of one another.
The stationarity of data can be determined by ushg a runs test (Bendat and Piersol 1986)
as follows:
1. Divide the series into time intervals of equal lengths.
2. Compte a rnean value (or other, see below) for each interval.
3. Count the number of runs of mean values above and below the median value of the series.
3. Compare the number ofcounts foound to known probabilities ofruns for randorn data of the
same length.
Note that the runs test works equally weII on mean values, mean square values, variance,
standard deviation, or any other parameter estimate (Bendat and Piersol 1986). Known
probabilities of runs distributions can be found in (Bendat and Piersol 1986), (Bethea and
Rhinehart 199 L), and (Gibbons 1985).
However, the preceding references on the runs test al1 deal with applying the nins test to
ri single observation series- This is fine if one has onIy one sequence of data. What about
experiments where one can obtain multiple realisations of the same process? It does not seem
appropriate to simpiy select one of the series and apply a nuis test only to that series. The answer
proposed hem is to apply the nuis test to al1 the data available and then to compare the
distribution of mns found to the distribution of cuns for a stationary mdom series. For exampie,
assume that data fiom 100 realisations of the same process are coIlected, where nothing is known
about the fiequency components of the process generating the data. To test for stationarity, divide
each data sample Uito 18 equal sized segments (the number 18 htis been arbitratily chosen, any
even division may be chosen). Then, count the number of runs above and below the median value
(of the particular sample) in each data sarnple. In theory, the number of runs can range From 2 to
18 per sampk. A üuly random process wiIl expect 90 of the 100 sarnptes to have counts ofat
least 7 and not more than 14, where 7 and 14 are the 0.05% left and right tail cut-offs (fiom Table
L: Number of Runs Distribution (Gibbons 1985)).
Note that using 0.05% Ieft and right tail cut-off in the preceding example is a more
sringent requirement than using a 0.01% tai1 probability (which is in the opposite direction of the
probability values From a standard ANOVA test)- To illustrate this, imagine using a 0.000 1% cut-
off A nuis dimiution table wilI gïve corresponding nins count between 2 and 18, which covers
al1 the possfiilities. A 0.0001% criterion is not stringent enough and wiZI result in any data set
passing a test for stationarïty. For the purposes of the work here on human coordination, a 0.05%
tail cut-off is considered to be a sufficient cntenon.
Stationan'N of trac Lin,^ Data
Are the error data colIected using the MITS so&are (Zhai 1995) smtionary? To test for
stationary, one subject was run through 38 triais of a 40 second six degree-of-fieedom tracking
task. The tracking error for each degree of fieedom is computed as the difference between the
user's cursor position and the required target position. Data was sampled at 0.05 seconds during
the task. Using the methodology from (Bendat and Piersol 1986) runs above and below the
median were counted for 228 series (38 riiais .u 6 degrees of Freedom), for different size segments.
The results of the runs count for the 40 second trials divided into 16, 14, 12, and 10
segments (corresponding to segments of 2.5,2.9,3.3, and 4.0 seconds in length) are presented in
Figure 86. The 0.05% two tail cut-offs are shown for the different size segments. in order for a
process to be considered stationary, 90% of the number of runs distribution should be between the
leFt and right tails. The results indicate that segments of 3.3 seconds and greater may be
considered stationary, while segments shorter than 3.3 seconds are nonstationary.
Runs Test for 2.5 second Segments 40 second vackng data divded mm 18 segments
60
runs from 40 - 228 s e h of
C 40 second U
20 m c h g data are show n
O O 2 4 6 8 1 0 1 2 1 4
Runs Test for 2.9 second Segments JI] second irackiig dam d~iied iito 14 segments
60 ml m m 228 setes tmm of
& 20 40 second uackng dae are show n
O "'
O 2 4 6 8 10 12 14
n u e r of ruru
Runs Test for 3.3 second Segments 40 second lrackng data divded nt0 12 segmenis
NN fl0m 228 serés of
! 40 second 20 tracMg dam
", '401&J O O 2 4 6 0 1 0 1 2 1 4 are s h w n
n u e r of ~ n s
Runs Test for 4.0 second Segments 40 second trackmg data d~ided inlo 10 segments
60 40 ml runs fmm
- C 228 se& of
40 second 20 oacklng data
areshwn
O O 2 4 6 8 10 12 14
n u m r of runs
Figure 86. Runs distribution of tracking datafiom 228 series, divided into 2.5, 2.9, 3.3, and 4.0 second segments. The 0.05% tails are showvn for the different tests. In order for a process to be considered stationary, 90% of the number of runs shorrld 6e behveen the Ieft and right tails.
Results indicate rhar segments of 3.3 secon& and greater may be considered starionary, wirile segments shorter rhan 3.3 seconds are nonîtationary.
Paramerric Approaclres
According to (Bowerman and O'Connel1 2979) and (Box and Jenkins 1976), if a rime
senes is notsrarionary, then the sample auto-correlation tùnction will neither cut off nor die down
quickiy, but rather will die down ertremely slorvly. The next question is what exactly is
considered quick or slow? Unfortunately, there does not seem to be a quantifiable answer to this
question in the literature. Clearly, the rate at which a hc t ion dies d o m depends upon the
frequency of the signal compared to the sarnpIing rate. BasicalIy, paramehic approaches assume a
certain level of experience with the data, and with that experience one can then tell by looking
wherher data may be considered stahonary or non-stationary.
-1 - -30~2o- fOOtO--20-30-40
Time - seconds
Figiire 87. f ie auto-correIation firnction of the Y translation errorfiom a single 40 second tracking trial.
The auto-correlation hnction of the error from a tracking tria1 for one of the degrees of
keedom is shown in Figure 87. Does this auto-correlation funchon agree with the results FEom the
runs test? The runs test is essentially a test of independence; that is, are different observations
independent of one another or are they codated? Results fiom the runs test indicate that
observations 3.3 seconds and farther apart Eom each other may be considered independent. The
auto-correlation h c t i o n shown in Figure 87 drops to near zero correlation at Iags greater than
about 3 to 5 seconds. The auto-correlation does seem to agree with results of the nms test.
Concltuions as to the Stationan'N o f the Data
h conclusion of stationarity is reasonable when one considers the nature of the ûacking
process that is occurrïng. Weak stationarity exists if the mean and variance of the data remain
constant. In the MiTS task, the target's range of motion is restricted to the operator's field of
view. tf one assumes that the subject is at al1 times attempting to track the target with equal effort,
then it is reasonable to expect that the subject's error (and the variance of that error) wil1 remain
relatively constant. The only question remains is what is the minimum time period which must be
considered to achieve a "relatively constant" value. This question has been answered using the
Runs Test. Based on the results from the Runs Test, segments 0F3.3 seconds and larger of
tracking data from the MITS tracking task may be considered independent and stationary.
Segments smaller than around 3.3 seconds capture only the higher fiequency cornponents of the
error process of a human tracking in six degrees of freedom.
Appendix B. W-metric Docking Calculations Example
This appendix walks through the W-metric calculations for a docking task. The
theoretical explanation of the W-metric is discussed in 2. The W-metric for Docking Tasks The
W-rnetric is computed for a hypotheticaI2 degree of fieedorn docking task along degrees of
freedom "X' and "Y". The data and calculations shown in this appendiv match the example
shown in Figure 7. The original raw data for this example is shown in the 'Trajectory X" and
"Tnjectory Y" colurnns in Table 10. The trajectory information for degree of fieedorn X is
shoivn in Figure 88.
Table 1 O. Raw data and calarlarions.
Table 10. Raw data and caladafions continued.
i ime i rajectory I rajectory uocring uoc~ing mange mange t r o t X Y EmrX Emr Y in Error in Emr Reducthn Errar Emr Emr
X Y X Reduction Reduction Reduction X Y X& Y
The simultaneity of control is computed by first calculating the m o t information. To go
frorn tnjectory information to error information involves çubtracting the target position from the
cursor position. The resuIts in this exarnpk are labelted as "Docking Error X" in Table IO and
depicred in Figure 89. The docking error graph is a mirror image of the trajectory mformation.
Trajectory of Degree of F reedom X
- DOF "X
10 20 30 40 50 60
Time (units of t)
Figiire 88. Trajectory forJictional degree of freedom ",Y" graphed aiong space and rime. - - -- - . -
Docking Error for Oegree of Freedom X
D O F "X
O 10 20 30 40 50 60
fime (units of 1)
Figtrre 89. Distancefiom the goal position of "X" (targec position -ctrrsorposirion} calcdated from Figure 88.
The nexr step învolves computing the change in emr for X, which means caIcuIating the
change in X from TimeIIl to Time,. By the convention used in this dissertation, the enor reduced
is graphed as the positive values on the y-auis, as s h o w in Figure 90. The data is in Table 10
under the "Change in Error X' column. However the M-metric only makes use of the error
reduction data, so a l error increasing values are set equal to zero. The error reduction data only is
shom in Figure 91 and cm be found under the "Error Reduction X" colurnn in Table IO.
Change in Error for Degree of Freedom X
150
-100 1 Time (uniîs of t)
O O F "X
3
-
Figure 90. Change in error for Xper trnit of rime.
Error Reduction for Degree of Freedom X
O 10 20 30 40 50 60
Time (units of 1)
D O F "K
Figure 91. Error recitiction graplr for X Sanre as Figure 90 witlr error increasing valires zeraed OlrL
In order to compare across multiple degrees of Freedom, the error reduction scores must
be normalised. Normalisation is accomplished by Eîrst cornputing the area under the error
reduction curve by sumrning the error reduction X colurnn in Table 10, which in this example
gives O + 20 + 35 + . .,+8 + 5 + O = 1587 in units of x. The normalised error reduction X colurnn
in Table IO is computed by dividing the error reduction values by 2587. The same steps are done
for al1 additional degrees of freedom, in this case degee of freedorn Y shown in Figure 92. To
compute the simultaneity of control between X and Y, one must first compute the minimum of
the normalised error reduction curves for both X and Y, as shown in Figure 93. The simultaneity
of control is equal to the a m under this curve which is equal to the sum of the normalised error
reduction X & Y colurnn in Tible 10, which in this example is equal to 0.658.
Normalized Error Reduction for Degree of Freedom X & Y
- DOF "X
- DOF "Y"
10 20 30 40
Time (units of t)
Figure 92. Tlie area trnder rile error redtrction cttrve for X is normalised to 1. The same sreps are taken to comprrre rite normalised error rediraion ctrrve for Y .
Minimm Normalized Error Reduction of X & Y
O 10 20 30 40 50 60
Time (units of t)
Figrrre 93. Tlre minimm of the normalised error redttcrion curves ofXand Y are graphed. The area under rhis ctrrve t3 equal to the simultaneity of conrrol.
Efficiency of Control
The second part of the %Y-metric ïnvoIves calcuIating the efficiency of control. The length
of the optimal error reduction tünction trajectory is assumed to be the shortest path to the goal
position for degrees of tieedom X and Y are equal to 2350 and 2329 respectively (distance from
start position to goal position). The actual error reduction function trajectory is computed as the
sum of error reduction colurnns in Table 10, thus giving 2587 for X, and 2476 for Y.
CVeights are introduced because the optimal error reduction values for X and Y are not
cxactly equal. in this example the difference is minimal but one can image situation where the
weights could be more lüpsided. The weight for the X degree of Freedom equals
2350 2329 = 0.502, and for Y the weight equals = 0.498
(2350 + 2329) (2350 + 2329)
2350 2329 The efficiency of control therefore is equal to - * 0.502 + - * 0.498 = 0.924.
2587 2476
The W-metric Score
The final M-metric score is a product of the simultaneity and efficiency, thus
0.658 * 0.924 = 0.608 .
Appendix C: Algorithm for Computing the Wmetric for Tracking Tasks
The following algorithm is used for computing error reduction and error creation for
tracking tasks. It assumes that the data has been collected at discrete data points at time t. Pascal
notation has been used. First some definihons:
TargetPosition, = Position of target at time t
TargetPosition,, = Position of target at time t -1
CursorPosition, = Position of cursor at time t
CursorPosition,, = Position of cursor at time t -1
abs is the absolute value function
SameSigiCheck is a function that r e m s tnre if both numbers have the same sign and false if
the nvo numbers have different signs
PreviousEnor F TargetPosition,, - CunorP~sition,~, (error at time t-1)
CurrentError = TargetPosition, - CunorPosition, ; (error at time t)
DistCursor := C~rsorPosition,~ - CursorPosition, : (distance travelled by cursor)
DistTarget; = TargetPosition,, - CursorPosition, ; (distance travelled by target)
{leading case, where the cunor is Ieading the target}
{if error is in the same direction as direction travelled, and
cursor & target traveI in the same direction)
i f SameSignCheck(PreviousError, DistCursorl and SarneSignCheck (Dis tCursor, DistTarget ) and
SarneSignCheck(PreviousError,~rrentE~~or) then begin
if abs (DistCursorl >= abs (DiçtTarget) then begin
ErrorCreatedbyTarget := abs(DistTarget1;
ErrorReducedbyTarget := 0;
ErrorReducedbyCursor := ErrorCreatedbyTarget;
ErrorCreatedbyCursor := abs(DistCursor) - abs (DistTarget) ;
end
else begiri
ErrorReducedbyCursor := abs(DistCursor);
ErrorCreatedbyCursor := 0;
ErrorCreatedbyTarget := ErrorReducedbyCursor;
ErrorReducedbyTarget := abs(~istTarget1 - abs (DistCursor) ;
end ;
end :
{lagging case, where the cursor is lagging the target)
{if enor is in the same direction as direction travelled, and cunor & target travel in the
same direction)
if not(SameSignCheck(PreviousError, DistCursor)) and SameSignCheck(DistCursor, DistTarget) and
SarneSign~heck(PreviousError,CurrentError) then begin
ErrorReducedbyCursor : = abs (Dis tCursor) ;
ErrorCreatedbyCursor := 0;
ErrorReducedbyTarget := 0;
ErrorCreatedbyTarget := abs(DistTarget1 ;
end ;
{same direction, overshoot & overtaken case)
{if error is in the same direction as direction travelled, and cursor & target travel in the
same direction)
if SameSignCheck(DistCurçor, DistTarget) and
not(ÇarneSignCheck(PreviousErrorICurrentError)) then begin
if abs (DistCursor) >= abs (DistTarget) then begin
{overshoot
ErrorReducedbyTarget := 0;
ErrorCreatedbyCursor := abs(CurrentError1;
ErrorReducedbyCursor := abs(DistCurçor1 - ErrorCrea tedbycursor ;
end
else begin
(overtaken}
ErrorReducedbyCursor := abs(DistCursor1;
ErrorCreatedbyCursor := 0;
ErrorReducedbyTarqet := abs(PreviousError);
ErrorCreatedbyTarget : = abs (Dis tTarget - ErrorReducedbyTarget;
end ;
end ;
{converging & diverging cases, cursor and target are both movhg towrds each other or
away from each other)
if not(SameSignCheck(DistCursor, DistTargetl) and SameSignCheck(PreviousError,CurrentError~ then begin
if abs (PreviousError) >= abs (CurrentErrorl then begin
(converging}
ErrorReducedbyCursor := abs(DistCursor);
ErrorReducedbyTarget := abs(DistTarget1;
ErrorCreatedbyCursor := 0;
ErrorCreatedbyTarget := O;
end
else begin
{diverging)
ErrorReducedbyCursor := 0;
ErrorReducedbyTarget := O;
ErrorCreatedbyCursor := abs(DistCursor);
ErrorCreatedbyTarget := abs(DistTarget1 ;
end ;
end ;
(wong direction cases, cursor is not being controlled, cursor is not being moved so that
error is being reduced)
if not(SameSignCheck(DiçtCursor, DistTarget)) and
not(SameSignCheck(PreviousError,CurrentError 1 then begin
if abs ( D i s tCursor1 >= abs (PreviousError) then begin
ErrorCreatedbyTarget := abs(DistTarget1;
ErrorReducedbyCursor := abs(PreviousError);
ErrorCreatedbyCursor := abs(DistCursor) - ErrorReducedbyCursor;
end
else begin
ErrorReducedbyCursor := abs(DistCursor) ;
ErrorCreatedbyCursor := 0;
ErrorReducedhyTarget := abs(abs(distTarget1 - CurrentError! ;
end;
end ;
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Index
across group
defined ..................... - .............. . ~.......... 48
Bernstein .... 19,20,21,22,39,61, 119, 171, 150
behveen group
defined ............................... . ............... 48
coordinate system ................................ i i , 123
cross-correlation ............--...-.-........... 15, 16, 17, 23
docking
defined ...........,............................ 8, 25, 63 docking expenment-ii, iii, 48.49, 50,s 1,52,
53,54,55, 56,58,59,78, 79.80, 87.94,
95,99, 102, 106, 107, 108, 109,110, 1 1 1,
112, 113, 114, 115, 116, 117, il8, 121,
122,128,130
docking task
defined ..................................... ,.. 8 . 25
efficiency .... ii. 18,23,?5,30,3 1,3S, 33,63, 70,7L, 120, 123,143'
endoscopic ................-.---.--.--.--...... 128
Engineering Data Compendium ..... xviii, 150
Ergopoint 3D ........................ ,., .... ... 1, 3, 152 Executive Function ......................... 130
forcing function . . similar .................................... 74, 75, 76
traditional ................ 72, 73, 74, 76, 77, 80
haptic ........................................... 126, 128 human cornputer interaction ....... 9, 1 19, 123,
124, 130
human factors ......... ii, wiii, 9, 128, 130, 151
inefficiency ............ 18, 19, 23, 3 1, 33, 38, 70 input device ... ii , iii, 1,2,3,4,5,6,7, 16, 17, 18, 19,40,41,43,45,46,47,48.49,50,
51,52,53,54,55,56,59,60,62,78,79,
82,83,84,85,86,87,88, 89.90,91,92,
100, 101, 102,103, 104, 105, 106, 107,
108,109, 110,111, 112, 113, 114, 117,
120, 122,126, 127, 130, 132
input device
isometric.5,40,46,48,49,50,5 1,60,78,
83,85,86,87, 100, 103, 105, 106, 107,
108
isotonie ... 5, 16,40,43,36,47,51,52,53,
54 55,56,59,78,82,84,87,88,89,
90,91,92.100, 103, 104, 108, 109,
110,111, 112,113, 111, 127
resistance ......... fes1sfance..............................fes1sfance..............................fes1sfance..............................fes1sfance..............................fes1sfance.............................. fes1sfance..............................fes1sfance..............................fes1sfance..............................fes1sfance..............................fes1sfance..............................fes1sfance.............................. fes1sfance..............................fes1sfance.............................. ---- 5,6
integdity .............. 17, 18, 24, 33, 37, 38, 64
isumetric3,4,5,6, 16,36, JO, 41,45,46,47,
48,39,50,51, 54,55,56,57,59,60,78,
79,81,82,83,84,85,86,87,91,92.95,
100, 101, 102, 103, 105, 106, 107, 108,
111,112,113,114,117,121,126,127
isotonic.3,4,5,6, 16, 40, 41,42,43,45,46,
47,51,52,53, 54> 55,56,57, 59,60,78,
79, 81.82, 84, 87, 88,89,90,91,92,95,
100, 101, 102, 103, 104, 105, 108, 109,
110, 11 1, 112, 113, 114, 117, 121, 126,
127
................................ phase plane analysis 130
............................................... prehension 128
.................................... process control 1, 129
proprioceptive ........................................... 5
Randot Stereotest ... 40, 45,79,81, 100, 101,
I l8
reductionism ........................................ 22
resistance continuum ....................... 6, 41,42
mn test ..................................... 133, 134, 137
rnanual control7,8,9,39.60,62,63,80,96,
I 17, 129, 130
trtvonomy ...................................... 80, 129
..................... minimally invasive surgery 128
MITS- Manipulation in Three Space.. xix, 3,
JI 41,42,43.79,80, 101, 102, 134. 138
M-mehic A, iii, xix, 24,25,26,29,30,31,
32,33. 37,38,39,40,48.49,50,51,52,
53,54,55,56,57,58,59,60,61,62,63,
64,66,67,70,78,79,85,86,87,88,89,
90,91,92,93,94,95,97,99, 100, 105,
106,107, 108, 109,I IO, 11 1, 112,113,
114,115, 116, 117, 120, 121, 123,124,
125, 126, 127, 129, 130, 131, 139, 142,
145,146
moue .................................. 2, 3, 6, 126, 151
simultaneity..ii, 1,24,25,28.29,30,32,33,
63,66,67,69,70,71, 119, 120, 123, 140,
143,144,145
stationarity ....................... 132, 133, 134, 138
................. sum of sines 11, 63, 72, 73, 75, 76
........................ teleoperation 7, 119, 126, 128
.................... time-on-target 9, 10, 23, 78, 156
tracking experimentii, 63,73,78,79,80,85,
86,87, 88,89,90,91,92,93,94,95,96,
101,121,122,127,130
tracking task
................................................... defmed 63
transfer function ...................................... 5, 6
working point .......... 7,9,21,25,63,80, 123
- - .................................................. oscillation 14
