Modeling Dual-Arm Coordination for Posture: An Optimization-Based Approach

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1 SAE TECHICAL PAPER SERIES Modelg Dual-Arm Coordato for Posture: A Optmzato-Based Approach Kmberly Farrell, Tmothy Marler ad Karm Abdel-Malek Uversty of Iowa Dgtal Huma Modelg for Desg ad Egeerg Symposum Iowa Cty, Iowa Jue 14-16, Commowealth Drve, Warredale, PA U.S.A. Tel: (724) Fax: (724) Web:

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3 Modelg Dual-Arm Coordato for Posture: A Optmzato-Based Approach Kmberly Farrell, Tmothy Marler ad Karm Abdel-Malek Uversty of Iowa Copyrght 2005 SAE Iteratoal ABSTRACT I the feld of huma modelg, there s a creasg demad for predctg huma postures real tme. However, there has bee mmal progress wth methods that ca corporate multple lmbs wth shared degrees of freedom (DOFs). Ths paper presets a optmzato-based approach for predctg postures that volve dual-arm coordato wth shared DOFs, ad apples ths method to a 30-DOF huma model. Comparsos to moto capture data provde expermetal valdato for these examples. We show that ths optmzato-based approach allows dual-arm coordato wth mmal computatoal cost. Ths ew approach also easly exteds to models wth a hgher umber of DOFs ad addtoal ed-effectors. ITRODUCTIO Evaluato of huma postures ad reaches has become essetal workspace-desg ad smulato. However, curret posture-predcto methods are ofte lmted to sgle-arm reaches wth oe ed-effector. A more accurate huma upper body model should clude dualarm coordato, where each of two arms reaches a pot ad both deped o the movemet of the spe. Hece, a model should clude at least two edeffectors ad shared degrees-of-freedom (DOFs). I order to more accurately represet huma postures ad reaches, we have developed a method to hadle dualarm coordato wth shared DOFs. There are several curret approaches to huma posture predcto. Emprcal approaches calculate realstc postures usg athropometrcal data. Usg statstcal aalyses of the data, predctve posture models are formed, ad the used to select the most probable posture [2, 3, 5, 16]. Although ths method ca be accurate ad useful whe extesve moto capture data exsts, t has lmted applcato the absece of a accessble database. Iverse kematcs solutos, partcular pseudoverse methods, ca also provde suffcet posture predcto. I ths approach, the moto of each lmb s mathematcally modeled to formulate a set of goverg jot equatos [7, 8, 9, 10, 14, 15]. However, as the umber of DOFs creases, solvg the resultg system of equatos becomes creasgly computatoally challegg. Optmzato-based approaches to posture predcto have gaed mometum as a alteratve. These methods optmze to fd a set of jot values that mmze a gve huma performace measure(s), such as jot dsplacemet. The jot values become desg varables the optmzato ad are costraed by jot lmts. Restrctg the ed-effector to reach the pot s treated as aother costrat the optmzato problem [1, 13]. Ths approach requres o extesve data ad s computatoally effcet [6]. These approaches to posture predcto have bee prmarly cocered wth oly a sgle arm ad edeffector. The emprcal approach coceptually works for dual-arm coordato wth o modfcato; however, the creased umber of possble postures wll ecessarly requre a much larger moto capture database to mata accuracy. Hece, the method ca become progressvely more lmted as more DOFs ad multple ed-effectors are troduced. The optmzato-based approach, however, leds tself to easy ad effectve modelg of multple ed-effectors, ad ts advatages ths capacty are addressed ths paper. Km ad Mart (2004) preset aother approach for modelg multple lmbs wth shared DOFs, whch exteds verse kematcs solutos to solve the subsystem of each lmb separately [11]. I ths work, the subsystems cosst of the maual subsystem, whch cludes the torso ad rght arm, ad the vsual subsystem, whch cludes the torso ad eck. Gve a verse kematcs soluto for each subsystem, a secodary objectve s appled to recofgure the shared jot agles, whch occur the torso. Ths could be exteded to combe more subsystems, cludg the torso ad left arm. However, extedg verse kematcs solutos ca amplfy related ssues, such as computatoal complexty. I addto, several subsystems sharg the same jots could result dffcultes whe recofgurg the shared jot agles.

4 A ew method for dual-arm coordato s developed ths paper based o the optmzato-based approach to posture predcto. Rather tha solvg a separate problem for each subsystem, each ed-effector s smply assocated wth oe addtoal costrat the optmzato problem. Shared DOFs are optmzed exactly as depedet DOFs, ad are govered by the same huma performace measure(s). The objectves of ths paper are to 1) preset a method for modelg multple lmbs; 2) troduce a optmzato formulato corporatg multple ed-effectors; ad 3) provde tal valdato for the accuracy of ths approach appled to dual-arm coordato. METHOD FOR MODELIG MULTIPLE LIMBS For the purpose of represetg postures, a huma body ca be represeted by a seres of lks. I ths respect, modelg a huma closely parallels modelg a hgh- DOF robotc mapulator. Accordgly, a model corporatg the torso, spe, shoulders, ad arms ca characterze huma moto by usg geeralzed coordates q to represet jot dsplacemet. For a seres of degrees of freedom, a vector q R of geeralzed coordates represets a posture. Fgure 1 shows a geeral, -DOF cha of lks wth the edeffector defed at the ed of the cha. The global posto vector, x(q), represets the Cartesa posto of the ed-effector wth respect to the global coordate system. Fgure 2. SATOS : A 21-DOF sgle-arm huma model. However, for huma models wth multple lmbs, addtoal chas are ecessary, ad these chas ofte share lks. For example, modelg two arms requres a cha that starts at the wast ad eds at the rght had as well as a cha that starts at the wast ad eds at the left had. Both cases clude lks the torso. For our dual-arm model, the sgle-arm model Fgure 2 s reflected to the left arm for a addtoal 9 degrees of freedom. The result s the 30-DOF model show Fgure 3. Although the developmet of the left arm s coceptually the same as that of the rght, t s mportat to ote that ths addto leads to a double depedece o the torso. Hece, there are 12 DOFs torso that wll cotrbute to the postos of both the rght ad left edeffectors. Fgure 1. A geeral -DOF kematc cha. Fgure 3. SATOS : A 30-DOF dual-arm huma model. Creatg a sgle-arm huma model requres oly oe such cha ad yelds realstc results usg the 21-DOF model show Fgure 2 [6]. I terms of optmzato-based posture predcto, t s ecessary to compute the Cartesa posto x(q) R 3 of a ed-effector order to costra t to the specfed pot. Cosequetly, the Deavt-Harteberg (DH) method s used to calculate x(q) for each edeffector, gve a set of jot agles q [4]. Developg a model for the DH method volves embeddg local frames at each DOF, where the th z-axs represets axs of moto for the (+1) th DOF ad the th x-axs s perpedcular to the (-1) th z-axs as well as the th. The trasformato matrx -1 T relates posto ad oretato

5 the th frame to the (-1) th frame. It s expressed terms of the agle θ from x to x -1 about z -1, the dstace d from x to x -1 alog z -1, the agle α from z to z -1 about x, ad the dstace a from z to z -1 alog x. These values are show Fgure 4, where q +1 s the jot dsplacemet correspodg to frame. coordate frame of the lmb wth respect to the last shared coordate frame. T lmb descrbes the posto ad oretato of the last coordate frame of the lmb wth respect to the frst coordate frame of the lmb. These trasformatos are depcted Fgure 5. Fgure 5. The trasformatos T shared, T trasform, ad T lmb. Fgure 4. Parameters for the DH method. The global posto vector x(q) of the ed-effector s expressed terms of the trasformatos -1 T ad s gve by: x( q) = 1 T x (1) = 1 1 cosθ cosα sθ sα sθ a cosθ sθ cosα cosθ sα cosθ a sθ = (2) T 0 sα cosα d where x s the posto of the ed-effector wth respect to the th frame ad s the umber of DOFs. ote that rotatoal dsplacemet q +1 chages the value of θ. For modelg multple lmbs, t s possble to compute the posto of the ed-effector of each cha separately usg (1) ad (2). However, the trasformatos for the shared DOFs eed oly be calculated oce. I geeral, the posto x lmb (q) of a gve lmb s ed-effector ca be calculated by: ( ) = ( )( )( ) x q T T T x (3) lmb shared trasform lmb I referece to Fgure 3, there are two ed-effectors ad 12 shared DOFs, whch are the spe. From equatos (1), (2), ad (3), a ew formulato s gve as follows to calculate the global Cartesa postos x R ad x L of the rght ad left ed-effectors respectvely: 12 ( ) = ( )( ) 21 1 xr q Tspe T13 T x R (4) = ( ) = ( )( ) 31 1 xl q Tspe T22 T x L (5) = 23 T T (6) = 12 1 spe = 1 where x R ad x L are the local posto vectors for the rght ad left ed-effectors, respectvely. OPTIMIZATIO FORMULATIO The optmzato-based approach to posture predcto volves determg a set of jot values q that mmzes a gve huma performace measure(s). For a huma model wth multple ed-effectors, the optmal posture s foud by solvg the followg optmzato problem: where T shared s the trasformato matrx descrbg the posto ad oretato of the last shared coordate frame wth respect to the global coordate system. T trasform descrbes the posto ad oretato of the frst

6 Fd: q R (7) to mmze: Huma performace measure(s) x q x for each x(q) subject to: ( ) ε L U q q q ; = 1,2,, I ths case, the desg varables are the jot agles q. The frst costrat (7) requres that each edeffector meet ts correspodg Cartesa pot, where ε s a small postve umber suffcetly close to zero. The secod costrat (7) esures that the jot agles stay wth the lower jot lmts, q L, ad upper jot lmts, q U. ote that ths geeral formulato, the proposed optmzato-based approach allows us to restrct multple ed-effectors smply by usg addtoal costrats. 2 Dsplacemet ( ) = ( ) q (9) f w q q = 1 where q s the th jot value the fal posture, ad q s the th jot value for the eutral posture. Oe ca vew (9) as a weghted sum of objectves a mult-objectve optmzato problem, where each jot term the summato costtutes a dvdual objectve. The weghts w accout for the fact that certa segmets of the body artculate more readly tha others. Assgg a hgher value to w results a partcular objectve cotrbutg more sgfcatly to the sum ad thus havg a stroger effect o the fal soluto. Essetally, t becomes more mportat for a heavly weghted jot to be ear ts eutral posto. For ths study, the weghts are determed by tral ad error, ad are gve Table 1. Table 1. Weghts for dsplacemet objectve. q w Commets 2 To predct posture for the 30-DOF dual-arm model Fgure 3, the costrats must restrct both the rght ad left ed-effectors to reach ther pots. Usg (4) ad (5), the optmzato formulato becomes: Fd: q R (8) to mmze: Huma performace measure(s) q1, q4, q7, q10 q2, q5, q8, q Used wth both postve ad egatve values of q q Whe q q >0 Whe q q <0 subject to: x ( q) x ε R R 2 q, q, q, q Used wth both postve ad egatve values of q q 2 ( ) ε xl q x L q13, q Used wth both postve ad egatve values of q q L U q q q ; = 1,2,, where x R ad x L are the gve Cartesa pots for the rght ad left ed-effectors, respectvely. ote that the qualty of the result ths formulato wll deped o the same huma performace measure(s) that dctates the sgle-arm result. Usg ths ew optmzato-based approach for dual-arm coordato, the shared jots are treated equally wth the depedet jots wth respect to the objectve fucto. Ths optmzato formulato was mplemeted usg a huma performace measure based o jot dsplacemet. Objectve fuctos derved from jot dsplacemet have bee used sgle-arm, optmzato-based posture predcto wth some success [13]. Coceptually, jot dsplacemet refers to the dfferece betwee the fal posture ad a eutral posture. Ths eutral posture s selected to be a relatvely comfortable posture, typcally a stadg posto wth the arms at the sdes. Jot dsplacemet s mathematcally defed as: q q 50 Whe q q >0 17, 26 RESULTS The repercussos of corporatg multple lmbs that share commo DOFs ca be demostrated by vewg results wth sgle-arm posture predcto. Fgure 6 (a) shows a sgle-arm posture o SATOS, whereas Fgure 6 (b) shows a dual-arm posture usg the same pot for the rght ed-effector. ote how the shared DOFs the spe shft to facltate reachg both s.

7 (a) (b) Fgure 6. Posture predcto usg (a) sgle-arm ad (b) dual-arm. The predcted postures for three sets of pots were compared to moto capture results from a male subject. Target postos are gve wth respect to a global coordate frame located the torso, cocdet wth the zero th frame Fgure 3, ad are measured cetmeters. For set #1, the rght ed-effector, x R, s (-41.7, -4.3, 38.7) ad the left edeffector s, x L, s (39.1, -4.4, 40.1). The predcted posture s vsualzed o SATOS Fgure 7, whle the moto capture result for the same set are show Fgure 8. Both postures are smlar; however, the moto capture shows a slght bedg at the elbow that s ot predcted by ths model. Slghtly dfferet athropometres betwee SATOS ad the moto capture subject are a possble cotrbutg factor. However, mmzg jot dsplacemet coceptually meas that the model wll ted toward the eutral posture. Sce the eutral posture s defed wth a straght arm, the result of the optmzato wll ted toward a straght arm. Hece, more realstc results should be possble wth a more clusve huma performace measure(s). Fgure 7. Predcted posture o 30-DOF SATOS for set #1. For set #2, x R s (-65.3, 44.7, -41.0) ad x L s (39.4, -5.2, 40.6). Fgure 9 ad Fgure 10 depct the predcted result ad moto capture result, respectvely. Aga, the predcted result shows less bedg the elbow, ad also less twstg the arm. For set #3, x R s (-41.3, 44.5, 60.9) ad x L s (-36.4, 44.4, 63.8). The predcted result s show o SATOS Fgure 11 ad the moto capture result show Fgure 12. The predcted result more closely resembles the moto capture result ths case. Fgure 8. Moto capture result o 30-DOF model for set #1.

8 Fgure 9. Predcted posture o 30-DOF SATOS for set #2. Fgure 11. Predcted posture o 30-DOF SATOS for set #3. Fgure 10. Moto capture result o 30-DOF model for set #2. Fgure 12. Moto capture result o 30-DOF model for set #3.

9 Oe beeft of the optmzato-based approach to posture predcto s computatoal effcecy. Hece, posture predcto feedback ca be obtaed real-tme or ear real-tme speeds. Ths mght be especally useful to quckly evaluate workspace or compare a varety of postures over dfferet athropometres. I fact, the ew approach, corporatg multple lmbs ad shared DOFs, matas computatoal speed. The dual-arm posture predcto o the 30-DOF SATOS took oly approxmately 0.15 sec for each set of s o a 2.6GHz Petum4 CPU wth 512MB RAM. Sglearm posture predcto o the 21-DOF SATOS takes approxmately 0.10 sec o a smlar mache. COCLUSIO I ths paper, we have preseted a ew optmzatobased approach to modelg dual-arm coordato. Ths approach geeralzes to the modelg of multple lmbs that share DOFs. The optmzato formulato s coceptually straghtforward, ad allows us to corporate addtoal ed-effectors smply by addg addtoal costrats. I addto, the ew approach s computatoally effcet ad has provded realstc predcted postures ear real-tme. The results have bee valdated successfully usg moto capture. Valdato of the results dcates that the proposed method ca produce realstc postures. Although uaces of the fal postures ca deped of the partcular performace measure (objectve fucto) used the optmzato formulato, we have oetheless demostrated that usg the optmzatobased approach for posture predcto s easly ad effectvely adopted to models wth multple ed-effectors. However, these valdato studes are prelmary, ad there are opportutes for addtoal research terms of moto capture studes. Frst, the athropometry of the huma subject ad the SATOS model wll be vared order to study the geeralty of the ew approach. Such varatos are easly mplemeted the proposed model terms of kematc lk legths. Secod, a moto capture study volvg may multple subjects of varous athropometres wll provde addtoal sght cocerg posture predcto. As the eed for smulatg huma posture dgtal evromets grows, there s a demad to move beyod sgle-arm reaches to dual-arm coordato. The method preseted addresses ot oly dual-arm coordato, but ca also be easly exteded to more complex huma models wth multple ed-effectors ad shared DOFs. The optmzato-based approach dscussed hs paper offers a straghtforward way to corporate these addtoal ed-effectors wth mmal computatoal cost. ACKOWLEDGMETS The authors would lke to thak Dr. Salam Rahmatalla ad Xaol Ma for ther work wth the moto capture valdato study. Ths research was fuded by the US Army TACOM project: Dgtal Humas ad Vrtual Realty for Future Combat Systems (FCS). REFERECES 1. Abdel-Malek, K., Yu, W., ad Jaber, M., 2001, Realstc Posture Predcto, 2001 SAE Dgtal Huma Modelg ad Smulato. 2. Beck, D.J. ad Chaff, D.B., 1992, A evaluato of verse kematcs models for posture predcto, Computer Applcatos Ergoomcs, Occupatoal Safety ad Health, Elsever, Amsterdam, The etherlads, pp Das, B. ad Behara, D.., 1998, Three-dmesoal workspace for dustral workstatos, Huma Factors, Vol. 40, o. 4, pp Deavt, J. ad Harteberg, R.S., 1955, A kematc otato for lower-par mechasms based o matrces", Joural of Appled Mechacs, Vol. 77, pp Faraway, J.J., Zhag, X.D., ad Chaff, D.B., 1999, Rectfyg postures recostructed from jot agles to meet costrats, Joural of Bomechacs, Vol. 32, pp Farrell, K. ad Marler, R.T., 2004, "Optmzato- Based Kematc Models for Huma Posture", Uversty of Iowa, Vrtual Solder Research Program, Techcal Report umber VSR Jug, E.S. ad Choe, J., 1996, Huma reach posture predcto based o psychophyscal dscomfort, Iteratoal Joural of Idustral Ergoomcs, Vol. 18, pp Jug, E.S., Kee, D., ad Chug, M.K., 1992, Reach posture predcto of upper lmb for ergoomc workspace evaluato, Proceedgs of the 36 th Aual Meetg of the Huma Factors Socety, Atlata, GA, Part 1, Vol. 1, pp Jug, E.S., Kee, D., ad Chug, M.K., 1995, Upper body reach posture predcto for ergoomc evaluato models, Iteratoal Joural of Idustral Ergoomcs, Vol. 16, pp Kee, D., Jug, E.S., ad Chag, S., 1994, A mamache terface model for ergoomc desg, Computers & Idustral Egeerg, Vol. 27, pp Km, H.K. ad Mart, B.J., 2004, Modelg the Coordated Movemets of the Head ad Had Usg Dfferetal Iverse Kematcs, SAE Dgtal Huma Modelg for Desg ad Egeerg, Jue 15-17, 2004, Rochester, Mchga, USA. 12. Marler, R.T. ad Arora, J.S., 2004, "Study of a B- Crtero Posture Predcto Problem Usg Pareto Optmal Sets", Uversty of Iowa, Vrtual Solder Research Program, Techcal Report umber VSR M, Z., Yag, J., ad Abdel-Malek, K., 2002, "Real- Tme Iverse Kematcs for Humas," Proceedgs of 2002 ASME Desg Egeerg Techcal

10 Cofereces, DETC2002/MECH-34239, September 29-October 2, Motreal, Caada. 14. Tola, D., Goswam, A., ad Badler,., 2000, Real-Tme Iverse Kematcs Techques for Athropomorphc Lmbs, Graphcal Models, Vol. 62, o. 5, pp Wag, X.G., 1999, A behavor-based verse kematcs algorthm to predct arm preheso postures for computer-aded ergoomc evaluato, Joural of Bomechacs, Vol. 32, pp Zhag, X. ad Chaff, D.B., 1996, Task effects o three-dmesoal dyamc postures durg seated reachg movemets: a aalyss method ad llustrato, Proceedgs of the th Aual Meetg of the Huma Factors ad Ergoomcs Socety, Phladelpha, PA, Part 1, Vol. 1, pp COTACT Kmberly Farrell, Vrtual Solder Research (VSR) Program, Uversty of Iowa, Iowa Cty, IA 52242, USA. Emal kfarrell@ccad.uowa.edu