A stochastic sequential model for man-machine tracking systems

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 18, NO. 2, MARCH/APRIL 1988 316

1)

2)

3)

All the parameters of the robot, i.e., moments of inertia, lengths, coordinates of the centers of gravity of the segments, and surface shapes of all the segments must be a priori known. The local tangent (or normal) must be measured and trans- formed to the inertial coordinate system. Computation of matrices J - I , dXB/dO and d/dO (TT (dXB/dB)) is quite involved and may require large banks of associative memory or powerful neural nets.

In summary the required sensory and computational machinery may be exorbitant.

These difficulties as well as the presence of noise in all the measurements may make the above approach quite impractical for the time being. Simpler techniques that do not depend on the contact forces or the dynamics of the robot-surface interaction, and primarily use kinematical information are preferable for shape determination. Nevertheless one must recognize that ad- dition of computational tools, whether kinematic, dynamic, or both, could enhance the performance of systems that primarily rely on sensor data for shape perception.

ACKNOWLEDGMENT The author is indebted to Professor H. C. KO, Chairman of the

Department of Electrical Engineering, The Ohio State University for his sustained support and encouragement of this work. A short version of this paper was presented at the Nasa Workshop on Telerobotics at Jet Propulsion Laboratory, Pasadena, Jan. 20-22,1987.

REFERENCES

G. Gordon, Ed., Active Touch: The Mechanism of Recognition of Objects by Manipulation. Oxford, UK: Pergamon Press, 1978. D. E. Whitney, “Resolved motion rate control of manipulator and human prostheses,” IEEE Trans. Man-Mach. Syst., vol. 10, no. 2, pp.

M. H. Raibert and J. J. Craig, “Hybrid position/force control of manipulators,” J. Dynamic Syst. Measurement Contr., vol. 102, pp. 126-133, 1981. R. P. Paul, B. Shimano, and G. E. Mayer, “Differential kinematic control equations for simple manipulators,” IEEE Trans. Syst. Man Cybern., vol. 11, no. 6, pp. 456-460, 1981. S. Hackwood and G. Beni, ‘‘Sensor and high precision robotics research,” in Proc. 1st Int. Symp. Robotic Res., M. Brady and R. Paul, Eds. Cambridge, MA: MIT Press, pp. 529-545. L. D. Harmon, “Automated tactile sensing,” Int. J . Robotics Res., vol. 1, no. 2, pp. 3-32, 1982. R. Bajcsy, “What can we learn from one finger experiments,” 1st Int. Symp. Robotic Res., M. Brady and R. Paul, Eds. Cambridge, MA: MIT Press, pp. 509-527. 0. Faugeras and M. Hebert, “The representation, recognition, and locating of 3-D objects,” Int. J. Contr., vol. 5, no. 3, pp, 27-52, 1986. R. C. K. Lee, Optimal Estimation, Identification, and Control, Research Monograph, no. 28, Cambridge, MA: MIT Press, 1964. H. Hemami, and R. E. Goddard, “Recognition of geometric shape by a robot system,” J. Robotic Syst., vol. 4, no. 2, pp. 237-257, April 1987. H. Hemami, “Shape determinism by tactile sensing,” Proc. Nut. Sci. Foundation Workshop on Mach. Dynamics, A. H. Soni, Ed. Denver, CO, Aug. 10-13,1986. J. Y . Han, Stability, Contact Force and Adaptive Trajectory Control of Natural and Robotic Systems, Ph.D. Dissertation, Ohio State University, Mar. 1986. H. J. Buchner, M. J. Hines, and H. Hemami, “A mechanism for touch control of a sagittal five-link hand-finger,” IEEE Trans. Syst. Mun Cybern., vol. SMC-15, no. 1, pp. 69-77, 1985. C. Wongchaisuwat, H. Hemami, and H. I. Buchner, “Control of sliding and rolling at natural joints,” ASME Trans- J. Biomech. Eng., vol.

D. B. Brown, “On-line exploration of an unknown surface by a three-link planar robot,” M. S. Thesis, Ohio State University, June 1986, Report

H. Hemami, “A feedback on-off model of biped dynamics.” IEEE Trans. Syst. Man Cybern., vol. 10, pp. 376-383, 1980.

47-53,1969.

106, pp. 368-379, NOV. 1984.

NO. TH-86-”-142.

A Stochastic Sequential Model for Man-Machine Tracking Systems

D. E. GREENE, R. E. BARR, C. FULCHER, L. HWANG, AND s. G. K. RAo

Abstract -A sequential model, which provides probabilistic descriptions of perception and control effects during manual control tracking, is further developed, analyzed, and applied. The sequential model is extended to represent anticipation and delay in tracking. The strategy parameters are shown to have independent effects and to be uniquely defined. The sequential model is shown to provide at least a partial separation of perception and control effects. Evidence is given of a duality between the perception variables and the control variables. The sequential model parameters are identified in an experimental application and related to the tracking attributes of accuracy, consistency and degree of anticipation or delay.

I. INTRODUCTION A sequential model for manually controlled, man-machine

tracking systems was introduced and developed in [1]-[6]. In the sequential model, the controller sequentially estimates, predicts and controls. The controller strategy optimally determines the system response. Randomness in perception and randomness in control are represented by probability models. These randomness effects enter the initial conditions and the coefficients, respectively, of the differential equation that defines the tracking response.

In the sequential model it is assumed that the human controller-controlled plant has basic overall properties: an invariance expressed by the crossover model [7]. Further, it is assumed that the human controller responds to discrete samples of the input as in sampled-data models [8]. Finally, it is assumed that the human controller operates in an optimal manner, although sequentially, as in the optimal control model 191.

In spite of its simplicity, the sequential model provides, in a common man-machine application, a statistical description that is at least comparable to that of the technically complex optimal control model [3]. The sequential tracking algorithms, because they merely sum elementary functions, are ideally suited for simulation studies. In applications of the sequential model, the internal dynamics of the tracking system need not be explicitly known. The hierarchial nth order structure of the sequential model allows the orders of tracking systems to be compared.

The second-order sequential model is the lowest-order model that represents manual control tracking in an antiaircraft artillery (AAA) application [2]. The controller, in effect, makes useful estimates of input position and velocity. The second-order model is used in the present research.

In this correspondence the sequential model is further developed, analyzed, and applied. The sequential model is extended to represent anticipation and delay in tracking, the strategy concept is examined, a separation of perception and control effects is explored and the model parameters are identified and related to performance.

Manuscript received August 27, 1986; revised June 22, 1987, and December 20, 1987. This work supported by the USAF School of Aerospace Medicine under Contracts SCEEE-ARB/ 82-72, F33615-83-K-0604, and SCEEE- ARB/84-38.

D. E. Greene is with the Department of Electrical and Computer Engineer- ing, University of Texas at Austin, Austin, TX 78712.

R. E. Barr, C. Fulcher, L. Hwang, and S. G. K. Rao are with the Depart- ment of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712.

IEEE Log Number 8819528.

0018-9472/88/0300-0316$01.00 01988 IEEE


@-- I I I

I I L - _ _

Perception Control Var i ab 1 e s Variables

\ ,

_-___- - - -

Fig. 1. Random perception and control variables in the second-order sequential model.

11. SEQUENTIAL MODEL Following a review of the second-order sequential model, the

model is extended to represent anticipation and delay in tracking.

A. Second-Order Sequential Model In the second-order sequential model, the controller sequen-

tially estimates input position and velocity (according to probability density functions for i,, estimate of position, and i: , estimate of velocity), predicts the input by a linear function and effects systematic control (according to probability density functions for &, strategy to reduce projected error, and p2, strategy to reduce projected error rate). The random processes i , and i: are denoted the perception variables and the random processes b1 and p2 are denoted the control variables. The random perception and control variables in the second-order sequential model are illustrated in Fig. 1.

The second-order sequential model is now formally defined. The input i ( t ) is assumed to be piecewise differentiable. The controller predicts the input at times t , ( k = O , l , e . . ) by

where i e ( t k ) and i:( t ,) are estimates, made through observation or inference, of the input position and velocity. The estimates i , ( t , ) and i: ( t , ) are assumed to be random variables with means i ( t k ) and i ’ ( t k ) and variances u:(tk) and u;(t,), respectively.

The controller effects qntrol to reduce the error relative to the predicted input, 8 , ( t ) = i k ( t ) - m ( t ) where m ( t ) is the system output. The control process is defined by

Parameters (aj) are constants that minimize the cost function

for given strategy (4) with & > 0 and p2 2 0. The parameters ( aJ ) are uniquely determined by

(4)

a,=&. ( 5 )

1/2 a1=(/3,’++281)

(These relationships may be found from aJ/au, = 0, aJ/aa2 = 0 with a, and its derivatives defined by (2). Note that the strategy subscripts are interchanged from those in [3].) The parameters

( p j ) at times t , are assumed to be random variables. They reflect the importance given by the controller to the reduction of projected error and projected error rate. The upper limit in the cost function corresponds to idealized infinite-time prediction of target motion.

The control objective, specified by the strategy, is optimally mapped to the coefficients in differential equation (2). This differential equation, with its random initial conditions and random coefficients, is the central element of the sequential model.

In the tracking process defined by (1)-(5), the controller follows in a probabilistic sense a sequence of tangents to the system input, producing the system output

m ( t ) = i ; , ( t ) - c k ( t ) ( 6 )

( 7)

with a system error

e ( t ) = i ( t ) - m ( t ) = i ( t ) - i ^ , ( t ) + a k ( t )

on each subinterval (t,, t, + l).

form Differential equation (2) can be written in the vector-matrix

2 L ( t ) = A B , ( t ) t > t k ( 8)

with random initial conditions 8,(t ,) , where

0 1 A = ( -a2 - a J y

and

The solution to (8) is

0, ( t ) = @( r - r,) 2, ( t , ) t 2 t , ( 9)

where @ ( t - t , ) is the state transition matrix

with

and 1/2

Yl = :( s,’ + 2/31]

y2 = :( - /3; + 2 / 3 y 2 .

The solution to the sequence of differential equations (8) (k = 0,1,. . a,), given by (9), is applicable for generally defined random variables and sampling intervals. The system output and system error are given by (6) and (7).

If the strategy and sampling interval AT = t k + l - t , are constant, the system error at times t k + l ( k = 0,l; . .,) is

e ( t ,+1 ) = a , m ( t o ) + b , m ’ ( t o ) k

+ C [ ck-jie(tj) + d , - j i ~ ( t j ) ] + i ( t k + l ) (10) j - 0

318 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 18, NO. 2, MARCH/APRIL 1988

where

a , = - + , [ ( k + l ) A T ]

b , ~ - + ~ [ ( k + l ) A T ]

c, = cpl[(. +1)ATI - @1(nAT) d , = +2[( n +l )AT] - +2( nAT) - AT+l( nAT).

0 Y 1

(This result uses @,(AT) = cD(nAT) [3].) The mean of the system error from (10) is

0

E { e ( t , + 1 ) ) = a , E { m ( t o ) I + b , E { m ’ ( t o ) } k

Y 1 + Y: - c 1 + c [C , - , i ( t , )+dk- l i ’ ( f , ) ] + i ( t , + 1 ) . (11) J ’ O

0 If the random variables are independent, the variance of the

var { 4 t, + 1) 1 = a: var { ( to) 1 + b: var { m’( to) 1

Y 1 system error is Fig 2 Transformation TI maps the interiors of the regions A and B one-to-

one and onto the intenors of regions A’ and B’, respectively

k + [ c~- ,u?( t,) + d;_,$( t , ) ] . (12) error for the partial time-shift modification for constant strategy

is given by (10) with i , and i: shifted in time by T . J ’ O

B. Extension to Represent Anticipation and Delay 111. ANALYSIS The sequential model is extended to represent anticipation and

delay in tracking. This is accomplished through a time shift T in the predicted input

Mathematical properties of the sequential model are examined. The topics are the following: uniqueness of control strategy parameters, finite-time prediction, separation of perception and control effects, and relationship with an associated discrete state

;,( t ) = i,( t , + T ) + i:( tk + T ) ( t - t k ) t 2 t , (13) space model.

and a time shift in the initial conditions

?,( t , ) = i,( t , + T ) - m( t , + T )

&( t , ) = i:( t , + T ) - m’( t , + T ) .

A time shift T > 0 corresponds to anticipation, while T < 0 corresponds to delay in tracking.

A partial time-shift modification is defined by (13) with a time shift in the initial conditions

(14)

e,( t , ) = i,( t , + T ) - m( t , )

e;( t , ) = i:( tk + T ) - m’( t , ) .

In this modification the controller tracks a time-advanced ( T > 0) or a time-delayed ( T < 0) input.

The tracking algorithms for the full and partial time-shift modifications for constant sampling interval AT are defined by (7), (13) and from (9)

(15)

2, ( tk + 1) = @ ( AT) 2, ( t , ) (16) with

B k ( t k ) = i : ( t k + t ) - i : ( t k - l + t ) 1 i , ( t , + T ) - i r ( t k - l + t ) - i : ( t k - l + ~ ) ( A T + T )

+ B k - l ( t , + T ) (17)

i and

i i , ( t , + T ) - i,( t , - l + T ) - i:( t k P l + T)AT

+ 4 - 1 ( t , ) 3 (18)

B k ( t k ) = i i : ( t , + T ) - i : ( t k - l + T )

respectively. An expression for system error comparable to (lo), although

complex, can be found for the full time-shift modification. Each term m , m‘, i , and i: is shifted in time by T and each coefficient ak, b,, c, and d , is additionally a function of r . The system

A. Uniqueness of Control Strategy Parameters A perturbation approach and an approach based upon the

inverse function theorem [lo] are used to establish the existence of unique identifiable control strategy parameters.

The perturbation approach is given in [l l] . For each ( yl, y 2 ) pair, defined in (9), there corresponds a unique (&, p2) pair. This is so because if p1 is perturbed, a perturbation of p2 cannot be found which would cancel the B1 perturbation in both yl and y2. Similarly, if yl is perturbed, a perturbation of y2 cannot be found which would cancel the yl perturbation in both +1( t ) and + 2 ( t ) , defined in (9). Therefore, /I1 and /I2 have independent effects and given the functions + l ( t ) and $ ~ ~ ( t ) , there corresponds a unique control strategy pair ( /I1, b2).

The approach based upon the inverse function theorem illustrates how the control strategy parameters B1 and b2 are mapped to the functions + l ( t ) and +2( t ) . Let Tl and T2 be the transformations in (9) where TI: (&, /I2) + ( y ! , y 2 ) and T2: (yl , y 2 ) -, ( + l r +2). Transformation Tl maps the intenors of the regions A and B in Fig. 2 one-to-one and onto the interiors of the regions A’ and B’, respectively. This follows from the inverse function theorem since the Jacobian of the transformation Tl ,

82 2( - 824 +4/3?)”’ ’ JTi =

is nonzero for p2 > 0 with p1 and b2 bounded. The Jacobian of the composite transformation T = T2 ( Tl), JT = JT,JT2, is nonzero for p2 > 0 with b1 and b2 bounded and 0 < t < 00 [6]. Thus, for a given sequential model response prescribed by + l ( t ) and + 2 ( t ) , there corresponds a unique control strategy pair ( & , p2).

B. Finite- Time Prediction Finite-time prediction corresponds to a finite upper limit in the

cost function (3). The upper limit is denoted by t , + d where d is a constant. For finite-time prediction the cost function is

J = J( d , a1 9 a2 9 81 9 82). (20)


Necessary conditions for J to have a minimum are

It is difficult to analytically examine the relationships implied by (21) and (22). Only for a first-order sequential model has it been proven that a1 is uniquely determined by d and ,B1 [12]. How- ever, it is shown using numerical methods that ai and a2 are uniquely determined for various values of d for characteristic values of P1 and p2 [12]. Additionally, al + (S,” +2P1)1 /2 and a2 4 fil as d 00 in agreement with (4) and (5). The convergence is quite rapid: for d=1.5 s the values are within 1.2 percent of their limiting values.

The sequential model is extended by the use of finite-time prediction. Additionally, the convergence of al and az for characteristic values of p1 and p2 supports the use of the infinite upper limit in the cost function with its mathematical simplifica- tion.

C. Separation of Perception and Control Effects Perception effects enter the initial conditions and control ef-

fects enter the coefficients in differential equation (2). A separation of these effects, as inferred by the sequential model, is explored through a perturbation analysis. In this analysis the specific forms for the density functions for

the perception and control variables need not be known. It is assumed only that these variables take on values near their mean values.

The tracking error perturbations (perturbed tracking errors minus the mean tracking errors) caused by small changes in the perception and control variables are examined over the interval (0, A T ) for a unit step input with m(0) = m’(0) = 0.

When the perception and control variables are singularly perturbed from their mean values, the tracking error perturbations ep to the lowest orders are

(25)

t Ai:, e p ( t ) = [ e - y l ‘ y , - 1 sin y2 t

1 e - y 1 ( Y2 Y l ) [ siny2t t cosy2t e p ( t ) = - - --- --

Y2 4 Yl Y2

-

and

(27) t

tcosy2t Ap2 (28) 1 e p ( t ) = - - P2 ( -+ - Y2 Yl) [ -- siny2t

Y2 4 Yl Y2

for small changes in i , , i:, & and p2, respectively, [12]. The tracking error perturbations to the lowest orders in t are

ep ( t ) = tu1 A i , , (29)

e p ( t ) = - t2y lAi : , (30)

e p ( 0 = -AB1 2 (31) - 12

and

respectively. The function sinyzt is a dominant component in ep for

perturbations in i, and P,, but not for perturbations in i: and &. This follows since for small AT the terms in brackets in (25)-(28) tend to cancel.

Each perturbed perception and control variable produces a distinctive time response. While perturbations in i , and P1 produce similar frequency effects (with the presence of the frequency y 2 ) , they produce different time effects (linear versus quadratic).

E. An Associated Discrete State Space Model The relationship between the sequential model and an associ-

ated discrete state space model is examined. Let AT = t , + - tk 4 0 in (2). The equation becomes

e”( t ) + ale’( t ) + aze( t ) = i ” ( t ) . ( 3 3 )

If i ( t ) is set equal to i^,( t ) , then e( t ) can be identified with f?k ( t ) . To simplify the discussion, assume that t f , = 0 and m(0) =

m’(0- ) = 0. The transfer function correspondmg to (33) is

4 ( s > S2

i , ( s ) -=

s2 + als + a2 from which

si , (O) + i : (O)

E , ( s ) = sz + als + a2

Two applications of the initial-value theorem yield

e,(O+) = i , (O)

O;(O+) = i : (O) - alie(0) .

(34)

(35)

Thus, the initial conditions consistent with the transfer function are

(37) ‘ k ( ‘: ) = i e ( t k ) - m( t k )

S; ( t: ) = i:( t , ) - m’( t i ) - alie( tk ) .

A discrete state space model using these initial conditions is developed in [ l l ] .

The transfer function in (34) does not directly represent the sequential model; rather, it may be considered the starting point for the development of a new time domain model. The transfer function in (34) additionally represents a unity feedback control system with open-loop transfer function G ( s ) =al/, + a z / s 2 .

The initial conditions in (37) differ from those m (2) for the sequential model. Thus, the responses of the two models can be expected to be different. Whereas the sequential model has a continuous and differentiable output, the discrete state space model for a step input has a discontinuity in the derivative of the output.

IV. SIMULATION The sequential model, with computer-generated random per-

ception and control variables, is used to simulate an AAA man-machine tracking system. The sequential model response is examined in the time and frequency domains. Time-shift effects are studied.

The AAA man-machine system is described in [ l ] , [ 3 ] . In the simulations the initial conditions, variance models for the esti-


mates of position and velocity, model parameters and target trajectories are either the same or closely related to those in the AAA application [3].

The initial conditions for the system output are

E { m( t o ) } = E { m(O)} = i(0)

E { m’( t o ) } = E { m’(O)} = O (38)

var{ . z < t o > } = v, var{ m’( t o ) } = q.

Time to is set equal to T, (the reaction time of the controller during initial target acquisition) in the AAA simulations and is set equal to 7 (a constant time shift throughout the trial) in the time shift study.

As in [3], the variances for the estimates of position and velocity are given by

where 8, and c, are constants. These representations indicate that estimates of position become less precise as velocity increases and estimates of velocity become less precise as accelera- tion increases.

Equation (12), with variances given by (39) and (40), provides an approximation for the variance of system error. Within (12) for small AT, the effects of 6, and co can not be distinguished; only one of these parameters can be identified [ll]. Alternately, the constant variance component in (12), denoted V, , which results from 8, and co can be identified.

The model parameters in Table I are those in [3]. The bar indicates mean value. Constant effects are not examined in the AAA simulations and 6, and co are set equal to zero.

The model parameters in Table I1 exhibit long-term tracking effects (T, = V, = = 0, AT = 0.12 s). These parameters are used in the time-shift study and are also used to test the identification algorithms.

The target trajectories (in degrees) are

i l ( t ) = tan-,( +), x - v t

i2 ( t ) = 40sinO.lt -2Osin0.3t (42)

and

i3( t) = 40sinO.lt -2Osin0.3t +10sin0.6t. (43)

Trajectory 1 is the azimuth angle component of the flyby trajectory in [3]. (xo, R, and V are constants.) Trajectories 1, 2, and 3 are defined in increasing order of complexity.

The random variables ie ( tk ) , i : ( tk ) , & ( t k ) and & ( t k ) are assumed to be independent for all k. Each random vanable, for convenience denoted by x, is assumed to have a density of the form

f ( x ) = d x l IX-%l<nrJx) (44)

where g( x) is a normal density with mean and variance parameters 1, and u,’ and n is a positive integer. Thus, each random variable is approximately normal with extreme values excluded.

The random variables i , ( tk ) and i : ( t k ) have densities given by (44) with means i ( t k ) and i ’ ( t k ) and vanances given by (39) and (40), respectively. The random variables 8, ( t , ) and p2 ( t k ) have densities given by (44) with constant means given in Table I and

TABLE I PARAMETERS IN SIMULATIONS (FROM AAA APPLICATION)

B1 =12.5 s-* s, = 1 . 0 s-1

AT = 0.12 s T, = 0.44 s

8, = 0.052 s c1 = 0.485 s 6 = 0.25 deg’

= 1.5 deg’ s - ~

TABLE I1 PARAMETERS IN SIMULATIONS (LONG-TERM EFFECTS)

= 9 . 0 s - ~ p2 = 2.0 s-1

8, = 0.20 deg 6, = 0.05 s c, = 0.30 s

constant variances adjusted so that only positive values of the random variables are possible [12].

The simulated tracking error responses are given in Fig. 3 for singular randomness in i,, i:, B1 and p2 (only one variable in turn is allowed to be random) on Trajectory 1 for the parameters in Table I. Based upon a comparison of perturbations from the mean tracking error, the i, effects dominate the other effects, in particular, the i: effects. The 8, effects dominate the effects. These randomness effects, in combination, are characteristic of those in human tracking data [12].

The amplitude spectra of the tracking error perturbations (simulated tracking errors minus mean tracking errors) are given in Fig. 4 for singular randomness in i,, i : , /3, and b2 on Trajectory 1 for the parameters in Table I. The tracking error perturbations are prescribed every hT/4 s.

The amplitude spectra for randomness in i, and 8, have maximums near yz =:(- 8: +2/11)1/2 = 0.390 E. The amplitude spectra for randomness in i: and p2 have maximums near the origin. These results are in agreement with the perturbation analysis. Similarities in the amplitude spectra give evidence of a duality between the perception variable pairs ( i , , i : ) and the control variable pairs (jl, a).

The simulated mean tracking error responses are given in Fig. 5 for various values of time shift 7 for the full and partial time-shift modifications for the parameters in Table 11. For both modifications, anticipation ( T > 0) skews the response upward, while delay ( T < 0) skews the response downward. Such skewness is later found in the experimental data. The full time-shift modification is more sensitive to small changes in 7 than the partial time-shift modification.

V. IDENTIFICATION The sequential model parameters are identified using two

least-square identification algorithms that functionally are the same [ll]. The first algorithm finds the mean values &,j2 and the time-shift 7 that minimize

N Ge= c [ W , ) - e ( t , ) I 2 (45)

k - 0

where AT = t k + l - t, is constant, e‘ is the ensemble average of empirical tracking error, and e is the mean tracking error defined by (7), (13), (16) and (17) or (18)-with_ randomness suppressed. Given the identified parameters &, 8’ and 7 , the second algorithm finds 8, (or K), 6, and z1 which minimize

N Gs= c [ W , ) - 4 t , ) I 2 (46)

k - 0


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I

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0. 360

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0.400 7

I 0. IC0

0 . 2 4 0

0 . 1 1 0

0. 111)

0 . 0 6 a - m v o.oc0

L 0

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-0. I 1 0

-0. i c o

- 0 . 2 4 0

0.0 5 . 0 10.0 11.0 20.0 25.0 '30.0 '35.0 40.0 45.0 S0.0 0 . 0 S.0 10.0 1 5 . 0 20.0 2 S . O 3 0 . 0 35.0 40.0 4 S . O 5 0 . 0

Tine (sec) Time (sec)

(4 (4 Fig. 3. Simulated tracking error responses for singular randomness on Trajectory 1 in: (a) i,; (b) i:; (c) &; and (d)

where 5 is the standard deviation of the empirical tracking error and s is the standard deviation of tracking error defined by (7), (13), (16) and (17) or (18) through multiple trials with computer- generated random perception and control variables. If 17) e AT and the variances of & and & are small, then (12) may be used to approximate s2, hence s.

The sequential model is used to generate empirical tracking error from which the model parameters are subsequently identified by the least-square algorithms and then compared with their known values. The prescribed parameters are given in Table 11.

The identified parameters are given in Table I11 for 20 simulation trials and in Table IV for 50 simulation trials on Trajectories

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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 18, NO. 2, MARCH/APRIL 1988

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(4 (b) Fig. 4. Amplitude spectra of tracking error perturbations for singular randomness on Trajectory 1 in: (a) i,O and i:O; and

(b) 810 and 820.

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(a) (b) Fig. 5. Mean. tracking error on Trajectoxy 1 for: (a) full time-shift modification (T = 0, &0.001 s); and (b) partial time-shift

modification ( T = 0, 0.01 s).


TABLE 111 IDENTIFIED MODEL PARAMETERS (20 TRIALS)

Trajectory 1 2 3

p, s-2 8.7910 8.7750 8.5941 p2 s-1 0.0002 0.0013 1.2036 6, deg 0.1867 0.1233 0.1850 61 S 0.0547 0.0538 0.0516 €1 S 0.3354 0.3622 0.3082

TABLE IV IDENTIFIED MODEL PARAMETERS (50 TRIALS)

Trajectory 1 2 3

p, s-2 8.9583 9.0124 9.0894 p2 s-1 1.4970 2,1851 2.2127 6, deg 0.1987 0.1894 0.2049 61 S 0.0521 0.0497 0.0498 €1 S 0.3073 0.3294 0.3091

TABLE V IDENTIFIED MODEL PARAMETERS FULL TIME SHIFT MODIFICATION

Subject 1 Subject 2 Trajectory Trajectory

1 2 3 1 2 3

s, s-2 8.390 9.121 10.65 7.101 9.547 10.245 p* s-1 O.O+ O.O+ O.O+ O.O+ 5.185 O.O+ T 0.001 s 0.167 -0.668 -1.43 1.176 0.834 0.521

TABLE VI IDENTIFIED MODEL PARAMETERS PARTIAL TIME SHIFT MODIFICATION

Subject 1 Subject 2

Trajectory Trajectory 1 2 3 1 2 3

El s-2 8.389 9.338 10.694 7.086 9.326 10.234 P2 s-l O.O+ 2.169 O.O+ O.O+ 4.990 O.O+ T 0.001 s 0.726 -2.526 -6.111 5.756 5.333 2.173

TABLE VI1 IDENTTFIED MODEL PARAMETERS ( T E 0)

Subject 1 Subject 2

Trajectory Trajectory 1 2 3 1 2 3

6, s O.O+ O.O+ 0.0358 0.0277 0.0157 0.0334 c1 s 0.2684 0.2196 0.2806 0.1095 0.1697 0.2517 V, deg’ 0.0226 0.0249 0.0476 0.0012 0.0032 0.0022

1-3. Twenty trials are required to-accurately identify the model parameters with the exception of p2. Fifty trials are required to accurately identify all five of the model parameters. The recovery of accurate model parameters verifies the identification algorithms and gives further evidence of the existence of unique identifiable model parameters.

VI. EWERIMENT

A manual control tracking experiment is carried out. The sequential model parameters are identified from the tracking data and are related to performance.

In the experiment the controller manually positions a control stick so as to cause a simulated weapon system, with K / s plant dynamics, to track a horizontally moving target on a display scope. Two skilled adult subjects track the target trajectories defined by (41)-(43). A complete description of the experiment is given in [13].

The sequential model parameters are identified by the least- square algorithms from the tracking error of 20 experimental trials over the time interval 5 to 45 s. The identified parameters correspond to tracking behavior that follows initial acquisition of the target. The initial conditions for the sequential model are given by (38) with to = T and V, = &‘ = 0. f i e sampling period AT is 0.12 s.

The identified parameters &, a,, and T are given in Tables V and VI for the .full and partial time-shift modifications, respectively. The identified parameters a,, E, and V , , based upon the assumption that T = 0, are given in Table VII. The latter parameters approximate those for both the full and partial time-shift modifications. (This is so because I T ) <<AT and-because a,, E , and V,, change little for small changes in 8, and 8, as supported by Tables I11 and IV. The assumption that T = 0, allows the use of (12) to approximate the standard deviation of tracking error.)

The experimental and full time-shift sequential model tracking responses are given in Figs. 6 and 7 on Trajectories 1 and 3 (the least and most complex trajectories), respectively, for the parameters in Tables V and VII. (Error and standard deviation of error are in degrees.) The sequential model provides very good representations. An exception is the standard deviation of tracking error for Subject 1 on Trajectory 1. The odd symmetry of the experimental response about the midtrial point, rather than an expected even symmetry, reflects a nonunifonnity in tracking behavior.

The identified values of time shift T in Tables V and VI suggest that

‘Tpartial = “1Tf”ll

where partial and full refer to the partial and full time-shift modifications and a, is defined by (4). The relationship is in agreement with the observation in the simulation study that the full time-shift modification is more sensitive to small changes in T

than the partial time-shift modification. . The full time-shift modification with a time shift in the input

and output, provides a more realistic description than the partial time-shift modification. It is shown in [6] that the full time-shift modification has closer agreement with the experimental data in five of six cases (two subjects and three trajectories) than the partial time-shift modification.

The identified parameters in Tables V-VI1 can be related to performance; in particular, to the tracking attributes of accuracy, consistency and degree of anticipation or delay.

The larger 8, (strategy to reduce projected error), the smaller the magnitude of the tracking error; hence, the more accurate the tracking. If 8, is large, then p2 (strategy to reduce projected error rate) would likely be small as this represents a contrasting strategy.

The smaller the parameters a,, c1 and V,, the smaller the magnitude of the standard deviation of the tracking error; hence, the more consistent the tracking. The parameters 6, and el are related to the controller’s ability to observe or infer position and velocity, respectively.

The presence of a. nonzero time shift T would indicate anticipation or delay in tracking. Large delay ( T << 0) would indicate less effective tracking. It is interesting to note from Fig. 5 that the magnitude of the tracking error would be smallest if the target was anticipated ( T > 0) prior to the midtrial point and not anticipated ( 7 < 0) after the midtrial point.

With regard to the tracking attributes, Subject 1 can be considered more accurate, but less consistent than Subject 2 (note that

324 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 1 8 , NO. 2, MARCH/APRIL 1988

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parameter V , for Subject 1 greatly dominates that for Subject 2). The degree of anticipation for both subjects decreases as the trajectories become more complex. Subject 1 anticipates target motion on Trajectory 1, but has delayed tracking on Trajectories 2 and 3. Subject 2 anticipates target motion on all trajectories.

VII. CONCLUSION The descriptive capability of the sequential model is broadened

by the extension to represent anticipation and delay in tracking. The strategy concept is supported by the analysis in which it is shown that the strategy parameters have independent effects and that for the given model response they are uniquely defined. The

extension of the sequential model to include finite-time prediction of target motion allows a wider class of model responses.

The sequential model is only indirectly related to transfer function models. The associated, transfer function based, discrete state space model has initial conditions that differ from those of the sequential model. Whereas the sequential model has a continuous and differentiable output, the discrete state space model for a step input has a discontinuity in the derivative of the output. One could argue that a living controller would act to produce a continuous and differentiable output.

The sequentid model provides at least a partial separation of perception and control effects as these effects enter the


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initial conditions and the coefficients, respectively, of the differential equation that defines the tracking response. Ad- ditionally, a separation of these effects is a consequence of the assumed independence of the random processes. The perception and control variables produce distinctive time and frequency responses. There is evidence of a duality between the perception variable pairs ( i e , i i ) and the control variable pairs

In the verification of the least-square identification algorithms in which the sequential model is used to generate random data from which the model parameters are subsequently identified, it is shown that a large number of simulation trials is required to

(PbP2).

accurately identify all model parameters. The requirement for a large number of trials underscores the difficulty of identifying parameters from human tracking data.

The sequential model parameters can be related to the tracking attributes of accuracy, consistency and degree of anticipation or delay. In the experimental application, the subjects are shown to have varied tracking qualities as reflected in the sequential model parameters.

In summary, the sequential model provides broad probabilistic descriptions of perception and control effects during manual control tracking. These descriptions are easily programmable and they are supported by experiments.


Perception and control effects can be further examined through analytical, simulation and experimental studies. The probability models can be refined to reflect dependence of the perception and control processes and dependence upon the trajectory. The sampling interval AT can additionally be identified and related to physiological processes. The extent to which a separation of perception and control effects is realistic can be examined.

sequential program-execution transcripts further revealed that most pas- sageviewing episodes were short, were error free, accessed a single document, and included a look at the document’s keyword index. Two thirds of the errors that did occur involved a mismatch of available keywords and user search terms. Usage monitoring therefore suggests improvements that stress printing and viewing from a shared database, reference reading online, and iterative search refinement.

ACKNOWLEDGMENT INTRODUCTION The authors would like to thank Dr. Bryce Hartman, Dr.

Richard Albanese and Dr. Sherwood Samn at the USAF School of Aerospace Medicine for their guidance and support.

A . The Full-text online documentation has been a part of user service

at the National Magnetic Fusion Energy Computer (NMFECC) REFERENCES

D. E. Greene, “A mathematical theory for sequential input adaptive systems with applications to man-machine tracking systems,” IEEE Trans. Syst. Man Cybern., vol. SMC-8, pp. 498-507, June 1978. -, “A class of sequential input adaptive systems,” USAF Tech., Rep. SAM-TR-79-38,1979. -, “Stochastic sequential input adaptive system theory,” IEEE Truns. Syst. Man Cybern., vol. SMC-10, pp. 197-202, April 1980. D. E. Greene, R. E. Barr, C. Fulcher, L. Hwang, and S. G. K. Rao, “Statistical descriptors of pilot perception and control,” Res. Rep. for USAF School of Aerospace Medicine, Brooks Air Force Base, San Antonio, Texas, Oct. 1983. -, “Statistical models for nonpredictive tracking behavior as indica- tors of tolerance to stress,” Res. Rep. for USAF School of Aerospace Medicine, Brooks Air Force Base, San Antonio, TX, Apr. 1985. D. E. Greene, R. E. Barr, and C. Fulcher, “Estimation of human operator effective lag,” Res. Rep. for USAF School of Aerospace Medi- cine, Brooks Air Force Base, San Antonio, TX, Apr. 1985. D. T. McRuer, D. Graham, E. S. Krendel, and W. Reisener, Jr., “Hu- man pilot dynamics in compensatory systems, theory, models and experiments with controller element and forcing function variations,” USAF Tech. Rep. AFFDL-TR-65-15,1965. G. A. Bekey, “The human operator as a sampled-data system,” IRE Trans. Human Fact. Electron., vol. HFE3, pp. 43-51, Sept. 1962. D. L. Kleinman, S. Baron and W. H. Levinson, “A control theoretic approach to manned-vehicle systepls analysis,” IEEE Truns. Automat. Contr., vol. AC-16, pp. 824-832, Dec. 1971. W. Rudin, Principles of Mathematical Analysis. New York: McGraw- Hill. 1964. C. Fulcher, “Parameter identification in man-machine systems using a stochastic sequential model,” Master’s Thesis, The University of Texas at Austin, 1984. S. G. K. Rao, “An analysis of man-machine systems using a stochastic sequential model,” Master’s Thesis, The University of Texas at Austin, 1983. L. Hwang, ‘‘An experimental study of man-machine systems using a stochastic sequential model,” Master’s Thesis, The University of Texas at Austin, 1983.

The Impact Of Usage Monitoring on the Evolution of an Online-Documentation System: A Case Study

T. R. GIRILL, CLEMENT H. LUK, MEMBER, IEEE, AND SALLY NORTON

Abstruct - W s paper reports an analytical case study in which improvements in the usefulness of online-documentation retrieval and delivery software, as well as design conshints on the software’s evolution, arose from extensive usage monitoring. A decade of cumulative, overall usage statistics revealed that increases both in online passage viewing and in on-demand document printing accoml#uried growth in the user community served, with viewing consistentiy rising faster than printing. Detailed,

Manuscript received April 4, 1987; revised November 3, 1987. This work supported in part under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract W-7405-ENG-48.

The authors are with the National Magnetic Fusion Energy Computer Center, Lawrence Livermore National Laboratory, University of California, Livermore, CA 94550.

IEEE Log Number 8718925.

since 1976. We are now developing a more elaborate “automated consultant” program, to retrieve relevant text passages in response to user queries. How features of the earlier software should evolve into those of the new tool to meet user needs for information poses a problem in iterative design.

In their classic survey of “Monitoring and Evaluation of Online Information System Usage,” Penniman and Dominick complained that

While lip service is always given to “user-centered” systems, the user to whom the system was oriented existed primarily in the designer’s mind and tended to be more systems-oriented than the actual user group [17, p. 18).

Execution monitoring of an existing program is a very general and powerful technique that can overcome such complaints [8], [HI. This paper illustrates, through an analytic case study of our documentation system, how careful monitoring can yield not only evaluations of current software (cf [6]) but timely design constraints otherwise unavailable for developing the next genera- tion of information-delivery programs. This approach has im- proved the quality and focused the growth of our computer-aided consulting with each design cycle.

B. Solution Technique NMFECC‘s document-delivery software, called DOCUMENT

[SI, monitors system users in two broad ways: 1) it keeps cumulative usage statistics; and 2) it keeps complete, unobtrusive trans- action logs of every session. Our study draws on several years of the usage statistics, and concentrates on a one-month sample of the transcript logs. We selected for analysis the 966 DOCU- MENT sessions run on our CRAY X-MP during January 1986 as typical of recent activity (because no disruptive events, such as a mainframe replacement, occurred near that month).

This empirical data enabled us to explore three issues crucial for system evolution.

Amount of use-To what extent do users take advantage of online passage retrieval when given the choice of several ways to consult documentation? Kind of use-What role does online access to explanatory passages play in meeting users’ specific needs for information about resources and utility programs st a supercomputer center? Burden of use-What difficulties occur most and thwart most seriously the effective use of current passage-delivery software by professional scientists and engineers?

The online-documentation system whose performance we review here has several features that make it especially promising for a case study of the benefits of usage monitoring.

System Environment: DOCUMENT already serves a comrnun- ity of 4500 geographically dispersed post-graduate researchers in energy science and plasma physics. Not an ad hoc test group, this is the same community for which our new retrieval tools will be designed. Yet its members see themselves as computational physicists, not professional database searchers. Furthermore, most

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A stochastic sequential model for man-machine tracking systems