MOOELLlNG, SIMULATION ANO IMPLEMENTATION OF A ANTHROPOMORPHIC MANIPULATOR

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1 40. SBAI - Simpósio Brsileiro de Automção Inteligente, São Pulo, SP, de Setembro de 1999 MOOELLlNG, SIMULATION ANO IMPLEMENTATION OF A ANTHROPOMORPHIC MANIPULATOR João Muríio Rosário Helder Anibl Hermini Mros Antonio Port Srmgo LAR - Lbortory of Automtion nd Robotis Meh nil Design Deprtment -Fulty of Mehnil Engineering University of Cmpins Cmpins, CP 6122, , SP.E-mil : Abstrt: The tehnologil evolution of ortheses nd prostheses ddressed the development of multidisiplinry reserh works in the Automtion nd Robotis re, minly in the tsk of rms nd rtifiil legs projet. In this work, being tken in ons idertion ntomil, physiologi spts nd inesiologi of superior nd inferior members of the humn body, lhe kinemtis mod el simil r to the nturl mehnism ws develop ed, whih is the bse so muh of the projet of rtifiil system, s welj s in the prmeteri stion of neurl myoltri on trol. Strting from lhe methodology of lhe generted kinemtis model, omputtionl progrms ws elborted with the purpose of rep roduing nd mn áger lhe spe displement of the rti ulte system. To vlidte the developed lgorithm, the proto type of the finger rtiulte system ws elborted in whih ws implemented nd tested prt of the developed methodology. Keyw ords: Robolis, Proslh eses, Biomehni, Aulomlion 1 INTRODUCTION The developm ent of prostheses nd ortheses, demnd the devlopment of kinemtis model, whih expresses the member's movement in terms of dependent degrees of freedorn. The development of these Models onstitutes gret hllenge, beus e, in spite of the gret number of mthemtil modelling nd simultion tehniques tody vilble, they don 't present wnted effiieny when pplied in linii tsks.. Severl hrteristis obse rved in biologil systems introdue high omplexity degree, due to the dynmi omplex model to be multi-vrible, presenting high non Iinerity degree nd redundny nd strong joining degree mong rtiultions, hindering the determintion of prmeters. 2 THE HUMAN ARTICULATION SYSTEM In om prison to the rtifiil systems, the spulr wis t rtiultion presents lod pity, preis ion, nd muh lrger speed thn ny existent rtifii l mnipul tor t the present time. Those hrter istis re the result of the onjugtion of multiple biologil proesses pplied in the musulr struture by the nervous omplex. The observtion of some of these phenom enon n onverge to useful onlu sions for the improvement of prostheses robo tis. The humn rm displement in the plne sgi tl is onseq uene of the shoulder nd elbow rtiultions tion. Considering tht the musles re unidiretion l tutors, in greement with the musulr group s worked in sme dire tion, the tlexion or extension movement is hd strting from respetive eletri ommnd imposed by the nervou s system. The shoulder is more omplex rtiultion thn the elbow, due to existene of two biomehnis sub-strutures (wists slip wy-urnerl nd slip wy thori). In the humn spulr wist, the movement of the shoulder n be onsidered s ombintion of the joint movements on both sides of the lvile, The shoulder tlexion-extension is omposed of the 1viulr extension nd of the tlexionextension umer l nd the shoulder bdution-ddution is omposed of the 1viul r bdution-ddution nd the umerl bdution-ddution. The observtion of the ntomil strutures involved in lion of the two rtiultions shows tht the humn rm is muh more sophistited system thn them developed prostheses tie the present moment. The elbortion of intell igent prostheses, should be done by omprtive nlogy with lhe nthropomorphi nturl omplex onsidering spets relted with the struture, trnsmission, tivtion nd ontrol of the nturl or rtifiil tutors, strting from myoeletri estimultion the one whih mngement n genertion ofset trjetory lgorithm bsed on the phy sil mthemtiin model of the rtiulte humn system. 113

2 40. SBAI - Simpósio Brsileiro de Automção Inteligente, São Pulo, SP, de Setembro de trnsllion vetor of n origin the other, where Ai. i+1 is resulling of lhe mtrix produt globl between the severl homogeneous trnsformtion mtrixes relted with rottions or suessive trnsltions oflhe different rtiultions (eqution 2). ". ;.' :" J..:. """,,.,..,.:-..- () Any rottion in the spe n be deomposed in group of elementry rottions long lhe xes X, Y nd Z. The elementry rottion mtrix used in the trnsformlion eqution is ssoited with the elementry rottion of the orresponding referentil in rellion to its previous one. This mthemlil proedure n be extended for every extension of the mode\. (b) Figure 2 - Utilised Referene System.: Ai. i+' = AI, 2 A2. 3. where... A i. i+' (I) (2) () Like this being, the orienttion mtrix of n interest point n be obtined for (2). (3) Figure 1 - PeIvi nd SpuIr Wist of the humn body i..._ 3 MODELlNG MATHEMATICS An ArliuIte System n be represented mthemtilly through n mobile bodies C, (i =1, 2,..., n) nd of fixed body Co, tied by n rtiultions, forming hin struture, nd lhese joints n be rottionl or prismti. To represent the severi bodies reitive sitution of the hin, is fstened to eh eiement Ci referentil R. We n relte ertin referentil Ri+1 (0;+1> Xi+1> Yi+1> Zi+') with previous one Ri (o, x., Yi, z.), s weil s the o-ordintes system of origin of the bse (figure 1) lhrough of eqution (1) where Ai, ;.., represent the rottion homogeneous trnsformtion mtrix nd Li the (d) Consequently the omplete positioning of rigid body in the spe, n be obtined esily through the eqution (1) tht supplies its vetoril position, nd the equ tion (3) represents the ssoited orienttion mtrix strting from the implementlion of the melhod of Euler or of the ngles RPY (Row, Pith, YIl) to the three rottion diretions ssoited to the orresponding o-ordintes xes. The systemti presented previously, ws pplied in the study of the spulr nd pelvi rtiultions of the humn body wists (figurei). Using robotis onepts, Kinemtis System ModeI ws developed to Artiulte Anthropomorphi, being onsidered lhe rtiuitions nd its respetive ngulr limits. The figure 3 nd 4 presents the Artiulte System kinemtis struture showing the SpuIr Wist nd lhe Pelvi Wist. In the model proposed in this work re defined the vribles desribed beiow tht use the methodology desribed previously. In the generted model kinemtis struture (figures 3 nd 4) two joints orresponding to lhe movement of the shouidereibow nd forerm re inluded nd of the hnd. The first ws nmed shouider intems joint (tsk of the joint interns of the humn rm lvile) nd seond of shouider externl joint (substitutes olher joints in the omplex shouider-rm s the glenohumeri joint nd the romion-lviulr joint). 114

3 simulte O : O : O 40. SBAI - Simpósio Brsileiro de Automção Inteligente, São Pulo.:SP, de Setembro de 1999 The elbow joint in the model ws substituted by simple rottion representing flexion-extension, In the forerm joint ws iniuded to o the forerm rottion developed between the rdio nd the uln. The prt of the reltive model lhe spulr wist extends of the Ivile interns joint to the hnd fingers nd lhe prt tht onsiders the pelvi wist re going from the bone of the femur to the foot fingers.,9",0 The whole system is interlinked for rtiultions, in hin struture, giving totl of fifty nine rottionl rtiultions for eh hemisphere, 82 o-ordintes systems tthed in importnt points of the rtiulte struture. 4 EXPERIMENTAL IMPLEMENTATION 4.1 Computtionl Simultion of Complete Kinemtis Model To pply the onept of the rottion nd trnsltion homogeneous trnsformtions, fter the referentil distribution, the different degrees of freedom of the rtiulte system re defined through of its o-ordintes systems. This wy the position nd orienttion of the points of the struture n be systemtiily defined. The mtrix nottion used will stili liow the development of numeri models for resolution of the kinemtis inverse problem. Like this being, ny objet in the work spe of the rm n be relted, nd strting from this to estblish ontrol lw bsed on the kinemtis model tht wili relte the position nd spe orienttion of the extremities of the mnipultor's onstituent elements. The system inertil hrteristis s weil s the efforts developed in the tsk of the rtiultions tution n be tken in onsidertion in dynmi study of the omplex. Strting from the rtiulte vribles is possible to determine the vetoril position nd the orienttion rntrix of the system in reltion to the inertil referentil fixed in the bse loted in the geometri entre ofthe humn body (Enlose 1). To simplify the omputtionl progrm mking, the symmetry property of lhe left nd right hemispheres ws used, tends s for modelling methodology the estblishrnent of the prmeters on the left side, filitting like this the determintion of the prmeters on the right side. Some of the simultion results re introdued in the EnIose 2. () Referentil Lol System (b)rottionl Artiultions Figure 3-Kinemtis Struture of the Arms nd Legs, :fio..,.,. -.' -., Figure 5-Bloks Digrm of the Trjetory Control ()Referentil Lol System (b) Rottionl Artiultions Figure 4 - Kinemtis Struture of the Hnds nd Feet. 4.2 Experimentl Prototype of Finger For the rel system simultion, ws developed in lbortory finger's prototype. (Figure 6). The joint tution ís mde through lhe use of motors CC nd to eh one n enoder ws oupled. The trnsmission system is mde by bles, whih rry out similr funtion the one of the tendons of nturl system. This prototype presents four degrees of freedom nd in them were developed the diret nd inverse kinemtis model using 115

4 .óx = Jl! SBAI- Simpósio Brsileiro de Automção Inteligente, São Pulo, SP, de Setembro de 1999 Jo bino for the inversion, tht is to sy, is known bout lhe 5 RESULTS ANALYSIS AND FUTURE WORKS diret geometri model, tht trnsformtion of the joints spe for the Crtesin spe is given, for smll displemnts, for: When one wnts to obtin the ngulr vlues orresponding to ertin rtiulte syslem onfigurtion, lhe used reltionship is: (4) (5) In this work ws proposed rnodelling melhodology of Biomehni Systems using utorntion nd robotis onepts, being elbor ted series of progrms, whih were tested prt of them in plne mnipultor, similr to n inditive finger of humn hnd, developed in lhe Lbortory of Integrted Automtion nd Robotis of FEM - UNICANP. As for next stges be rehed, will be developed lhe dynmi study of the efforts nd exerised torques so tht beomes initilly possible the n intelligent ontroller's implementlion to the finger, extending the implementtion Jter on to the omplete modej of the humn rtiulte systern, seeking the mk ing of proslheses ommnded by the own ptient's nervous system. strting from the signs red myoeletri of lhe eletrodes implnted in the mputted neurl termintions. 6 GRATEFULNESS We thnked CNPq speil wy tht for lhe support nd ollbortion, they did possible lhe omplishment of this work. 7 REFERENCES Bekey A., Tomovi R., Zeljkovi L, 1990, Control rhiteture goes the Belgrde/USC hnd, in Dextrous Robot Hnds. S. T. Venktrrnn nd T. Iberll, Eds., pp Jobsen., Everson. E.K., Knutti E.F., Johnson T.T., Biggers K.B., 1986, Design of lhe Ulh/MIT dextrous hnd. In Pro. IEEE Int. Conf. Robot. Automt., pp Lenri J., Umek A., 1994,Simple Model of Humn Arm Rehble Workspe. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL. 24, in the 8. Y. C. Tsi e A. H. Soni, 1981, Aessible Region nd Synthesis of Robot Arms, ASME J. Mehnil Design, voi.103, pp Figure 6 -Prototype developed Therefore, the finl expression tht supplies the vlue of the vribles rtiulte is supplied for : where i = 3 Ali lhe informtion of the vribles desribed until then re fundmentl in lhe implemenltion of trjetory genertion, whose mesh of orresponding ontrol is desribed in the figure 5, nd the used rnethodology n be pplied in lhe omplete system desribed previously. An exmple of simultion is introdued in the Enlose 3. (6) Tsuneo Yoshikw, Mnipulbility of Roboti Mehnisms, 1985, The Int. J. Robotis Reserh, vol. 4, pp K. YouefToumi e H. Asd, 1987, The Design of Open-Loop Mnipultor Arms with Deeoupled nd Configurtion- Invrint Inerti Tensors, ASME J. Dynmi Systern, Mes., Contr., vo1.109, pp Y. Lsh et i, 1992, on the evlution of multifuntionl prosthesis, 7 th Word Congress of the Int. Soe, Of Prosthesis And ortheses, Chigo, pp.185. It is intended in future work lo use metlli legues of form memory suh Iike NITINOL for the tution of lhe rtiultions, nd this metl, strting from lhe estblishment of 'áflow of ontrollble eletri urrent in them, lter its physil properties, ontrting nd being strethed out when olds, generting like this n order of similr movement the one of musulr system exited.. 116

5 40. SBAI - Simpósio Brsileiro de Automção Inteligente, São Pulo, SP, de Setembro de 1999 Enlose 1. Homogeneous Trnsformtion Mtrix (Rottion) ofthe Superior nd Inferior Members (Left Side) Rz(IO); 5.. C.. O O o 1 R,(ll)= R, (43); C O] - S" o CIl o s; C;, o s., C" o 5" C" o SI' C;, ;" o S" C" o 5" o S" C;, C; o C. l R,(44); C; S;] - 5" o C". C" o S"Jl R, (45); O. 1 o -S" o " Enlose 2. Exmple of Simultion o tet(l)= tet (2 )= tet(3) = tet(4)= lel(5)= o tet(6)= 155 ter (7)= O lel(8)= O _lei (9)= O 't. Ox(O) =O Oy(O) =O - Oz(O)=O Ox( 1 ) = O Oy( 1 )=O Oz( 1)=O Ox( 2)=5 Oy( 2)=O Oz( 2)= O Ox( 3)=5 Oy( 3)=3 Oz( 3 ) = O Ox( 4)= 5 Oy( 4 ) = 3 Oz( 4 ) = 60 Ox( 5 ) =-67 Oy( 5 ) =3 Oz( 5 ) = 60 Ox( 6 ) =-67 Oy( 6)= 158 Oz( 6 ) = 60 Ox( 7 ) =5 Oy( 7 ) = 158 Oz( 7 ) = 60 Ox( 8 ) =5 Oy( 8)= 198 Oz( 8 ) = 60 Ox( 9 ) =5 Oy( 9) = 198 Oz( 9)=-8 Ox( 10 ) = 5 Oy( 10) = 158 Oz( 10 ) =-8 Ox( 11) =5 Oy( 11) = 158 Oz( 11 ) =-294 Ox( 12)= Oy( 12)= 158 Oz( 12)= Ox( 13)= Oy( 13 ) = 158 Oz( 13 ) = Ox( 14 ) = Oy( 14) = 158 Oz( 14) : Ox( 15)= Oy( 15 ) = 158 Oz( 15 ) = Ox( 16 ) = Oy( 16) =158 Oz( 16) = ) = x!.,..!7.$=.' '1i1l..., M ' ".....,g.>;, &., mil ''': Ox(l7 ) = -108,2617 Oy( 17) = 158 Oz(l7) = :..' Nx = Sx = O Ax = Ny=O Sy=O Ay =0 Nz = Sz = O Az = R,(46) ; -5" o C" C" o 5,,] R,(47)= o 1 o - 5" o C".. OS''] R,(48); o 1-5" o C.. C" os",] R,(49); 1 o. -S", o.. R,(5C1)= r 00. _ r o. no l /U(51)=.. Ox( 67 Nx = Ny=O Nz = ' -'" Sx =O Sy=1 Sz=O 67) Ax = Ay=O Az =

6 40. SBAI- SimpósioBrsileirode Automção Inteligente, São Pulo,SP, 08-10de Setembro de 1999 Enlose 3. Some Results of Genertion of Trjetories for thfinger : h, h X. = , Y. = X. = , Y. = Xb= , Yb= X-= , Yb= dx= , dv = dx= , dv = \ '\ :.,'.... :... C h x ,Y. = X" , Y Xb= , Yb= X-= , Yb= dx , dv dx dv ". \ \.. \ '\ ;'/ '} 'z Ih L-.-- X. = , Y. = X. = , Y. = x.,= , Yb= Xb= , Yb= dx= ,dv= dx= , dv = b x,= , Y.= X. = , Y. = X- = , Yb= X-= , Yb= dx= dv= dx dy = b - - x , Y. = X" = ,Y. = X- = , Yb= X- = ,Yb= dx dv,.. ' dx dv