40. SBAI - Simpósio Brasileiro de Automação Inteligente, São Paulo, SP, 08-10 de Setembro de 1999

MOOELLlNG, SIMULATION ANO IMPLEMENTATION OF AANTHROPOMORPHIC MANIPULATOR

JoãoMaurício Rosário HelderAnibalHermini Marcos Antonio Porta SaramagoLAR - Laboratory of Automation and Robotics

Mech anical Design Department - Faculty of Mechanical EngineeringUniversity of Campinas

Campinas, CP 6122, 13083-970, SP.E-mail : rosario@dpm.fem.unicamp.br

Abstract: The technological evolution of ortheses andprostheses addressed the development of multid isciplinaryresearch works in the Automation and Robotics area, mainly inthe task of arms and artificial legs project. In this work, beingtaken in cons ideration anatomical, physiologic aspccts andcinesiologic of superior and inferior members of the humanbody, lhe kinematics model simil ar to the natural mechanismwas developed, which is the base so much of the project ofartificial system, as welJ as in the parameteri sation of neuralmyoclcctric con trol. Starting from lhe methodology of lhegenerated kinematics model , computational programs waselaborated with the purpose of rep roducing and man áger lhespace displacement of the articulate system. To validate thedeveloped algorithm , the proto type of the finger articulatesystem was elaborated in which was implemented and testedpart of the developed methodology.

Keywords: Robolics, Proslh eses, Biomechanic, Aulomalion

1 INTRODUCTIONThe development of prostheses and ortheses, demand thedevclopment of a kinematics model , which expresses themember 's movement in terms of dependent degrees offreedorn. The development of these Models constitutes a greatchallenge , becaus e, in spite of the great number ofmathematical modelling and simulation techniques todayavailable, they don 't present wanted efficiency when applied inclinicai tasks . .

Several characteristics obse rved in biological systemsintroduce a high complexity degree, due to the dynamiccomplex model to be multi-variable, presenting high nonIinearity degree and redundancy and a strong joining degreeamong articulations, hindering the determination of parameters.

The elaboration of intell igent prostheses, should be done bycomparative analogy with lhe anthropomorphic naturalcomplex considering aspects related with the structure,transmission, activation and control of the natural or artificialactuators, starting from myoelectric estimulation the one whichmanagement an generation of set trajectory algorithm based onthe phy sical mathematician model of the articulate humansystem.

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2 THE HUMAN ARTICULATION SYSTEMIn comparison to the artificial systems, the scapular wais tarticulation presents load capacity, precis ion, and much largerspeed than any existent artifici al manipul ator at the presen ttime. Those character istics are the result of the conjugation ofmultiple biological processes applied in the muscular structureby the nervous complex.

The observation of some of these phenomenon can converge touseful conclu sions for the improvement of prostheses robo tics.

The human arm displacement in the plane sagi tal isconsequence of the shoulder and elbow articulations action .Considering that the muscles are unidirection al actuators, inagreement with the muscular groups worked in a samedirec tion, the tlexion or extension movement is had startingfrom a respective electric command imposed by the nervou ssystem. The shoulder is a more complex articulation than theelbow, due to existence of two biomechanics sub-structures(waists slip away-urneral and slip away thoracic).

In the human scapular waist , the movement of the shoulder canbe considered as a combination of the joint movements on bothsides of the clavicle , The shoulder tlexion-extension iscomposed of the c1avicular extension and of the tlexion-extension umeral and the shoulder abduction-adduction iscomposed of the c1avicul ar abduction-adduction and the umeralabduction-adduction.

The observation of the anatomical structures involved in aclionof the two articulations shows that the human arm is a muchmore sophisticated system than them developed prostheses tiethe present moment.

(I)

(2)

where

Figure 2 - Utilised Reference System

Ai. i+' = AI, 2· A2. 3. ... A i. i+'

(a)

(b)

""",,. ,..,.:-.:..-- --

". ;.' :" J. .:

....-

40. SBAI - Simpósio Brasileiro de Automação Inteligente, São Paulo, SP, 08-10 de Setembro de 1999

.. translalion vector of an origin the other, where Ai. i+1 is resullingof lhe matrix product global between the several homogeneoustransformation matrixes related with rotations or successivetranslations oflhe different articulations (equation 2).

Any rotation in the space can be decomposed in a group ofelementary rotations along lhe axes X, Y and Z. Theelementary rotation matrix used in the transformalion equationis associated with the elementary rotation of the correspondingreferential in relalion to its previous one . This mathemalicalprocedure can be extended for every extension of the mode\.

(c)(3)

Like this being, the orientation matrix of an interest point canbe obtained for (2).

i..._

(d)

Figure 1 - PeIvic and ScapuIar Waist of the human body

3 MODELlNG MATHEMATICSAn ArlicuIate System can be represented mathematicallythrough n mobile bodies C, (i =1, 2,..., n) and of a fixed bodyCo, tied by n articulations, forming a chain structure, and lhesejoints can be rotational or prismatic.

To represent the severaI bodies reIative situation of the chain,is fastened to each eIement Ci a referent ial R. We can relate acertain referential Ri+1 (0;+1> Xi+1> Yi+1> Zi+' ) with previous one Ri(o, x., Yi, z.), as weIl as the co-ordinates system of origin of thebase (figure 1) lhrough of equation (1) where Ai, ;.. , representthe rotation homogeneous transformation matrix and Li the

Consequently the complete positioning of a rigid body in thespace, can be obtained easily through the equation (1) thatsupplies its vectorial position, and the equation (3) representsthe associated orientation matrix starting from theimplementalion of the melhod of Euler or of the angles RPY(Row, Pitch, YaIl) to the three rotation directions associated tothe corresponding co-ordinates axes.

The systematic presented previously, was applied in the studyof the scapular and pelvic articulations of the human bodywaists (figureI). Using robotics concepts, a Kinematics SystemModeI was developed to Articulate Anthropomorphic, beingconsidered lhe articuIations and its respective angular limits.

The figure 3 and 4 presents the Articulate System kinematicsstructure showing the ScapuIar Waist and lhe Pelvic Waist. Inthe model proposed in this work are defined the variablesdescribed beIow that use the methodology describedpreviously.

In the generated model kinematics structure (figures 3 and 4)two joints corresponding to lhe movement of the shouIder-eIbow and forearm are included and of the hand. The first wasnamed shouIder intems joint (task of the joint interns of thehuman arm clavicle) and second of shouIder external joint(substitutes olher joints in the complex shouIder-arm as theglenohumeraI joint and the acromion-clavicular joint).

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40. SBAI - Simpósio Brasileiro de Automação Inteligente, São Paulo.:SP, 08-10 de Setembro de 1999

The whole system is interlinked for articulations, in a chainstructure, giving a total of fifty nine rotational articulations foreach hemisphere, 82 co-ordinates systems attached inimportant points of the articulate structure.

4.1 Computational Simulation of Complete KinematicsModel

To apply the concept of the rotation and translationhomogeneous transformations, after the referential distribution,the different degrees of freedom of the articulate system aredefined through of its co-ordinates systems. This way theposition and orientation of the points of the structure can besystematicaIly defined.

The matrix notation used will stilI alIow the development ofnumeric models for resolution of the kinematics inverseproblem.

The system inertial characteristics as weIl as the effortsdeveloped in the task of the articulations actuation can be takenin consideration in a dynamic study of the complex.

Like this being, any object in the work space of the arm can berelated, and starting from this to establish a control law basedon the kinematics model that wilI relate the position and spaceorientation of the extremities of the manipulator's constituentelements .

4 EXPERIMENTAL IMPLEMENTATION

Starting from the articulate variables is possible to determinethe vectorial position and the orientation rnatrix of the systemin relation to the inertial referential fixed in the base located inthe geometric centre ofthe human body (Enclose 1).

To simplify the computational program making, the symmetryproperty of lhe left and right hemispheres was used, tends asfor modelling methodology the establishrnent of the parameterson the left side, facilitating like this the determination of theparameters on the right side. Some of the simulation results areintroduced in the EncIose 2.

The elbow joint in the model was substituted by a simplerotation representing flexion-extension, In the forearm a jointwas incIuded to o simulate the forearm rotation developedbetween the radio and the ulna . The part of the relative modellhe scapular waist extends of the cIavicle interns joint to thehand fingers and lhe part that considers the pelvic waist aregoing from the bone of the femur to the foot fingers .

,9",0

Figure 3 - Kinematics Structure of the Arms and Legs,

(a)Referential Local System (b) Rotational Articulations

Figure 4 - Kinematics Structure of the Hands and Feet.

Figure 5 - Blocks Diagram of the Trajectory Control

4.2 Experimental Prototype of a FingerFor the real system simulation, was developed in laboratory afinger's prototype. (Figure 6). The joint actuation ís madethrough lhe use of motors CC and to each one an encoder wascoupled. The transmission system is made by cables, whichcarry out similar function the one of the tendons of a naturalsystem.

This prototype presents four degrees of freedom and in themwere developed the direct and inverse kinematics model using

:fiO O

:

O

:

O

. . ,., .- .' - . ,

(b)Rotational Articulations(a) Referential Local System

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In this work was proposed a rnodelling melhodology ofBiomechanic Systems using autornation and robotics concepts,being elaborated a series of programs, which were tested a partof them in a plane manipulator, similar to an indicative fingerof a human hand, developed in lhe Laboratory of IntegratedAutomation and Robotics of FEM - UNICANP.

As for next stages be reached, will be developed lhe dynamicstudy of the efforts and exercised torques so that becomesinitially possible the an intelligent controller's implementalionto the finger, extending the implementation Jater on to thecomplete modeJ of the human articulate systern, seeking themak ing of proslheses commanded by the own patient's nervoussystem . starting from the signs read myoelectric of lheelectrodes implanted in the amputated neural terminations.

6 GRATEFULNESSWe thanked CNPq a special way that for lhe support andcollaboration, they did possible lhe accomplishment of thiswork.

7 REFERENCESBekey A., Tomovic R., Zeljkovic L, 1990, Control architecture

goes the Belgrade/USC hand, in Dextrous Robot Hands.S. T. Venkatararnan and T. Iberall, Eds., pp. 136-149.

Jacobsen c.,Everson. E.K., Knutti E.F., Johnson T.T., BiggersK.B., 1986, Design of lhe Ulah/MIT dextrous hand. InProc. IEEE Int. Conf. Robot. Automat., pp. 152-153 .

Lenarcic J., Umek A., 1994,Simple Model of Human ArmReachable Workspace. IEEE TRANSACTIONS ONSYSTEMS, MAN, AND CYBERNETICS, VOL. 24, inthe 8.

Y. C. Tsai e A. H. Soni , 1981, Accessible Region andSynthesis of Robot Arms, ASME J. Mechanical Design,voI.103, pp. 803-811.

Tsuneo Yoshikawa, Manipulability of Robotic Mechanisms,1985, The Int. J. Robotics Research, vol. 4, pp. 3-9.

K. YoucefToumi e H. Asada, 1987, The Design of Open-LoopManipulator Arms with Deeoupled and Configuration-Invariant Inertia Tensors, ASME J. Dynamic Systern,Meas., Contr., vo1.109, pp. 268-275.

(5)

(4)

(6)where i = 3

.óX = Jl!.8

40. SBAI- Simpósio Brasileiro de Automação Inteligente, São Paulo, SP, 08-10 de Setembro de 1999

Jaco biano for the inversion, that is to say, is known about lhe 5 RESULTS ANALYSIS AND FUTURE WORKSdirect geometric model , that a transformation of the jointsspace for the Cartesian space is given, for small displacemcnts,for:

When one wants to obtain the angular values corresponding toa certain articulate syslem configuration, lhe used relationshipis:

Figure 6 -Prototype developed

Therefore, the final expression that supplies the value of thevariables articulate is supplied for :

Ali lhe information of the variables described until then arefundamental in lhe implemenlation of trajectory generation,whose mesh of corresponding control is described in the figure5, and the used rnethodology can be applied in lhe completesystem described previously. An example of simulation isintroduced in the Enclose 3.

Y. Lasach et ai, 1992, on the evaluation of a multifunctionalprosthesis, 7th Word Congress of the Int. Soe, OfProsthesis And ortheses, Chicago, pp .185.

It is intended in a future work lo use metallic leagues of formmemory such a Iike NITINOL for the actuation of lhearticulations, and this metal, starting from lhe establishment of'áflow of controllable electric current in them, alter its physicalproperties, contracting and being stretched out when colds,generating like this an order of similar movement the one of amuscular system excited. .

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40. SBAI - Simpósio Brasileiro de Automação Inteligente, São Paulo, SP, 08-10 de Setembro de 1999

Enclose 1. Homogeneous Transformation Matrix (Rotation)ofthe Superior and Inferior Members (Left Side)

Enclose 2. Example of Simulation

67)

Ax= .4226183Ay=OAz =-.9063078

Sx =OSy=1Sz=O

Ox( 67 ' -'"Nx =-.9063078Ny=ONz =-.4226183

tet(l)= otet (2 )= otet(3) = otet(4)= olel(5)= otet(6)= 155ter (7)= Olel(8)= O_leI (9)= O

't.Ox(O) =O Oy(O) =O - Oz(O)=OOx( 1 ) = O Oy( 1 ) = O Oz( 1 ) = OOx( 2 ) = 5 Oy( 2 ) = O Oz( 2 ) = OOx( 3 ) = 5 Oy( 3 ) = 3 Oz( 3 ) = OOx( 4 ) = 5 Oy( 4 ) = 3 Oz(4 ) = 60Ox( 5 ) =-67 Oy( 5 ) = 3 Oz( 5 ) = 60Ox( 6 ) =-67 Oy( 6 ) = 158 Oz( 6 ) = 60Ox( 7 ) = 5 Oy( 7 ) = 158 Oz( 7 ) = 60Ox( 8 ) = 5 Oy( 8)= 198 Oz( 8 ) = 60Ox( 9 ) = 5 Oy( 9) = 198 Oz( 9 ) =-8Ox( 10 ) = 5 Oy( 10) = 158 Oz( 10 ) =-8Ox( 11) = 5 Oy( 11) = 158 Oz( 11 ) =-294Ox( 12) = -37.26183 Oy( 12) = 158 Oz( 12) = - 203.3692Ox( 13) = -99.80935 Oy( 13 ) = 158 Oz( 13 ) = - 69.23567Ox( 14 ) = -101.9224 Oy( 14) = 158 Oz( 14) : - 64 .70413Ox( 15) = -104.0355 Oy( 15 ) = 158 Oz( 15 ) =- 60.17259Ox( 16 ) = -106.1486 Oy( 16) = 158 Oz( 16) =- 55 .64105

) = -108.2617 2x!.,..!7.$=.' '1i1l, &., mil... , M ' " .. ....,g.>; ''':

Ox(l7 ) = -108,2617 Oy( 17) = 158 Oz(l7) =-51.10951. : ..'Nx= -.9063078 Sx = O Ax= .4226183Ny=O Sy=O Ay =0Nz = -.4226183 Sz = O Az=-.9063078

[

C.. -5.. O]Rz(IO); 5.. C.. O

O o 1

R,(ll)=[- S" o CIl

o s; C;,

o s., C"

o 5" C"

o SI' C;,

;"o S" C"

o 5" C;,

o S" C;.

R, (43);- 5.0 o C. l

R,(44);[ C; S;]- 5" o C"

. [C" o S"JlR, (45); O . 1 o-S" o c"

R,(46) ;-5" o C"

[

C" o 5,,]R,(47)= o 1 o

- 5" o C"

[c.. OS'']

R,(48); o 1 °-5" o C..

[

C" os",]R,(49); ° 1 o. -S", o c..

r00R,(5C1)= . _

ro. nOl/U(51)= ..

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40. SBAI - SimpósioBrasileirode Automação Inteligente, SãoPaulo,SP, 08-10de Setembro de 1999

Enclose 3. Some Results of Generation of Trajectories forthcfinger

c :c

h , ha

X. = 54.695614, Y. = 29.880350 X. = 55.729374, Y. = 30.691900Xb= 0.000000, Yb= 65.000000 X-= 0.541051 , Yb= 65.022095dx= 0.353044 , dv = 0.601196 dx= 0.025371 , dv = 1.002039

\ '\: .,' ... . : ...

C

ha

x.- 60.468324, Y. = 39.336526 X" - 63.985764 , Y. - 45.359267Xb= 1.441079, Yb= 66.553880 X-= 3.286147 , Yb= 68.609137dx- 0.229035 , dv 0.764164 dx- 0.242034 • dv - 0.753389

\ \" ...

'z\'\

;'/ c '} c

IhL a-.--X. = 69.609583, Y. = 55.007086 X. = 75.580062, Y. = 65.269742x.,= 7.144306, Yb= 72.981768 Xb= 11.984097 , Yb= 78.706754dx= 0.266917,dv= 0.724714 dx= 0.298184 , dv = 0.682398

cc

a b ac

x,= 78.739225, Y.=70.706828 X. = 81.546553, Y. = 75.541675X- = 14.745473, Yb= 82.099796 X-= 17.283402, Yb=85.301149dx= 0.316415 dv= 0.656080 dx- 0.333438 dy = 0.630805

cc

ba a

- -x.- 85.054793 , Y. = 81.587351 X" = 87.510049, Y. = 85.820506X- =20.541971 , Yb= 89.530643 X- = 22.868167, Yb= 92.634250dx- 0.355637 • dv ,.. ' 0.597094 dx - 0.371688 • dv 0.572315

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