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1 Proceedings of the ASME 2010 Interntionl Mechnicl Engineering Congress & Exposition IMECE2010 November 12-18, 2010, Vncouver, British Columbi, Cnd Proceedings of the ASME 2010 Interntionl Mechnicl Engineering Congress & Exposition IMECE2010 November 12-18, 2010, Vncouver, British Columbi, Cnd IMECE IMECE EMPLOYING NEURAL NEWORKS FOR MANIPULABILIY OPIMIZAION OF HE DUAL-ARM CAM-LOCK ROBO B. R. JOUIBARY 1 rezein@kish.shrif.edu K. G. OSGOUIE 2 osgouie@shrif.edu A. MEGHDARI 3 meghdri@shrif.edu 1,2,3 Shrif University of echnology Interntionl Cmpus, Kish, Irn. ABSRAC Coopertive systems hve been extensively investigted in literture. Herein the criteri nd implementtion for employing neurl networks rtificil intelligence for finding the optiml configurtion of the Dul- Arm Cm-Lock (DACL) robot mnipultors t specific point with the objective to optimize the pplicble tsk-spce force in desired direction re ddressed. he DACL robot mnipultors re reconfigurble rms formed by two prllel coopertive mnipultors which operte redundntly but they my lock into ech other in specific joints to increse structurl stiffness in the cost of losing some degrees of freedom. Obtining the optiml configurtion demnds lots of computtionl time nd is not prcticl in rel-time pplictions. he neurl network is trined to pproximte the optimum configurtion considering the geometricl constrints of the plnr rms using genetic lgorithm s multi-objective optimizer. INRODUCION Coopertive robot systems re believed to offer enhnced cpbilities over current single-rm structures. Nonetheless, this reserch field covers the interesting cse of multi-fingered robot hnds [1], in which the sme kinds of issues re encountered. A coopertive strtegy with two rms becomes necessry to perform ll those tsks tht cnnot be esily executed by single robot rm. ypicl coopertion exmples include tsks such s hndling lrge, hevy, or non-rigid objects; ssembly nd mting mechnicl prts; nd spce robotic pplictions. In spite of the potentil benefits chievble with multiple rms, the nlysis nd control problem becomes more complex due to kinemtic nd dynmic interctions imposed by coopertion. his mens tht in ll those tsks requiring effective coopertion, one cnnot strightforwrdly extend the well-known results for the kinemtics, dynmics, nd control of single rm. herefore, for the solution of these problems, globl description for multi-rm system is needed. Referring to the simple cse of two-rm system two min pproches hve been proposed in the literture: mster-slve strtegy nd tsk-spce oriented formultion. he former consists in defining the desired motion of the object to be mnipulted, nd deriving the motion for the follower rm ccordingly to the set of holonomic constrints determined by the closed chin system [2]. he ltter strtegy hs been shown to be more effective for coordinted control schemes with equl importnce given to the two robots performing the given tsk. A suitble globl tsk spce sttic coordintes is defined in terms of bsolute generlized forces between the two endeffectors. Bsed on the dulity principle between kinemtics nd sttics, globl tsk spce kinemtic coordintes re derived tht describe bsolute velocities of the object nd reltive velocities between the two end-effectors. his formultion cn be formlly extended to the cse of multiple-rm systems s is shown in this work. In prticulr, internl forces re defined t object level, which is different from [3] where they re represented t end-effector level. In this scenrio, n importnt issue is the definition of quntittive mesures of the 1 Copyright 2010 by ASME

2 performnce offered by multi-rmm coopertion. he velocity nd force mnipulbility ellipsoids introduced in [4] re widely dopted s kinetosttic performnce indices for single rm. hese re not n bsolute numericl mesure of robot system cpbilities of the mechnicl system which is independent of the physicl force/velocity limittions; in other words, the ellipsoid does not give the mximumm force/velocity long different tsk directions but only indictes the preferred directions for the structures to perform force/velocity in given configurtion. his method ws revisited in [5] where the mnipultor is effectively regrded s the mechnicl trnsformer of velocities nd forces from the joint spce to the tsk spce. A dul-rm velocity mnipulbility ellipsoid is defined in [6] s the mximum volume ellipsoid determined by the intersection between the two single-rm velocity mnipulbility ellipsoids. he cse to lose coopertion is lso treted. Reltive velocity nd externl plus internl force effects re not investigted, lthough they re importnt for the nlysis of coopertion performnce. Only the dul-rm cse is ddressed, nd the extension to the multi-rm cser does not seem to be strightforwrd. An lterntive pproch hs been proposed in [7] bsed on the use of polytopes tht properly ccount for the physicl limits on the joint ctutors. Although the method is techniclly correct, its prcticl ppliction is limited due to the lck of closed-form lgorithm to derive the polytope in nontrivil cses. Forml definitions of force nd velocity mnipulbility ellipsoids for multiple coopertive rms re estblished in [8], ccording to the bove globll tsk-spce formultion tht regrds the closed chin system s whole t the object level nd then independently from the number of rms involved in the coopertion. For given force/velocity tsk, the evlution of the ttitude of the rms is focused rther thn computing the ctul physicl limits of the multi-rm system. Artificil neurl network (ANN) is form of prllel computing lgorithm. ANNs re composed of simple elements clled neurons. rnsfer functions re pplied to the network by the connections between neurons. Network cn be trined to perform specificc function by djusting the vlues of the connections (weights) between elements. ody ANNs re used to solve sophisticted problems which re difficult to solve for conventionl computers or humn beings. hey cn be pplied in different res such s engineering, finncil, medicl nd etc. ANNs re especilly useful for non-liner sttisticl dt modeling. In generl their tsks cn be defined into three ctegories of Function pproximtion, Clssifiction, nd Dt processing. An importnt re of ppliction of neurl networks is in the field of robotics. Until now, they hve been extremely employed for robotic ims such s inverse kinemtic of robotic rms, control of robot mnipultors nd etc. A lrge mount of reserches hve been done in the ANN s employment in the subject of robot mnipultors ncluding their dynmics nd control. In the present pper, the Dul-Arm Cm-Lock (DACL) robot is considered [9]. his robot hs two rms with joints enbled to lock into ech other. When some joints re locked, the robot loses some degrees-of-freedom but menwhile the rms gin improved stiffness. he concept of this mnipultor is described more in section II of this pper. When different joints re locked into ech other, the dynmics of the robot chnges nd one must ssesss which configurtion of the robot is most suitble for the specified tsk. Herein we re interested in finding the best structure for the DACL robot, in which the mnipultor exerts mximum possible force in specificc point/ direction in its dexterous work-spce. he DACL robot considered here is composed of two 4 degrees-of-freedom plnr rms. he closed-chin system grsps the object rigidly. Due to its redundnt nture, the DACL robot my tke vrious configurtions when holding n object in specific point in its - plnr work-spce. Unlike other coopertive redundnt rms currently consideredd in current literture, the Dul-Arm Cm- Lock mnipultor tkes the dvntge of locking joints to improve its kinemtic nd dynmic performnces. his is n optimiztion problem under severl constrints [12] nd in this pper, popultion bsed method is proposed to find the optiml configurtion of the robot rms. he genetic lgorithm (GA) method is powerful generl optimizer which cn hndle nonliner nd non-differentible constrints. Hence, the solution method presented here is genetic lgorithm bsed pproch. his pper is orgnized in this order: Next section provides brief overview of the DACL mnipultor concept. hen the mnipulbility mesure is introduced nd optiml configurtions of the robot re studied. Afterwrds, ppliction of neurl network modeling nd its implementtion on the mnipultor is described nd discussed in detils. Finlly, the pper is concluded with finishing remrks nd plns for future improvements. Fig. 1: Schemtics of the Dul-Arm Cm-Lock robot [10] HE DUAL-ARM CAM-LOCK MANIPULOR A dul-rm mnipultor is composed of two multi-link open- loop kinemtics chins s shown schemticlly in figure 1. Its 2 Copyright 2010 by ASME

3 body is formed by number of cms. Whenever needed mnipultor is ble to lock some cms of left nd right side together nd thus gin more rigid structure but of less degrees of freedom. his lock chnges the configurtion of the robot nd its degrees of freedom. he locking process is ssumed to be rigid nd idel (without ny loss due to impct, friction, or etc). Some pplictions nd other configurtions of the DACL mnipultor re described in references [9], [10], nd [11]. () (d) Fig. 2: Schemtics of DACL mnipultor () first nd second links re cm-locked, third nd fourth links re cm-locked, first links re cm-locked, (d) when no links re locked. In this pper DACL mnipultor with ech rm hving four degrees of freedom is considered. he mnipultor s tsk-spce is two dimensionl nd point object is to be held by our mnipultor in the tsk-spce. Regrding the number nd the loction of the links from left nd right rms locked in ech other, this kind of DACL mnipultor is ble to undertke four different configurtions:. First nd second links locked in ech other respectively b. hird nd fourth links locked in ech other respectively c. First links locked in ech other d. No lock configurtion Figure 2 depicts schemtics of the mnipultor in these configurtions. MANIPULABILIY MEASURE o hve mesurement for mnipulbility, herein the resistivity ellipsoid is obtined for dul-rm coopertive system. he object to be mnipulted is considered point object (s shown in fig. 2). If ech rm is to exert some force to the object ( F R from right rm nd F L from left rm), their mgnitude cn be relted to joint torques s: τ R = J R.FR nd τ L = J L.FL (1) for right nd left rm respectively. We cn unify these equtions nd constitute combined reltion: τ = J.F (2) In which τ [ ] = τr τ nd L F [ F ] R FL = re vectors contining joint torques nd tip point forces for both rms, respectively. he Jcobin mtrix relting these torques nd JR 0 forces is J = J in which 0 is mtrix of proper 0 L dimensions with ll its members zero. At the object level, the vector of the exerted force is F with equl dimensions s F R nd F L tht is the dimension of tskspce. By simple sttic equilibrium condition of the object, one my imply tht: F = FR + FL (3) his cn be written s: F = G.F (4) in which G = (5) is clled the grsp mtrix. As simple reltion between the force exerted by the mnipultor ( F ) nd the joint torques vector ( τ ), one my write n eqution like (1) s: τ = J.F (6) In which J my be defined s the pprent Jcobin of the whole mnipultor. Substituting (4) in (6) yields: τ = J.G.F (7) Compring (7) to (2) revels tht: J = J.G (8) his implies: J = J.G (9) With G being the pseudo-inverse of the grsp mtrix, defined s: 1 G = G.(G.G ) (10) Note tht (G.G ) is 2 2 full-rnk mtrix nd thus cn be 3 Copyright 2010 by ASME

4 inverted. As described erlier, the DACL mnipultor considered here, consists of two 4 degrees-of-freedom rms. hus the totl DOF of the mnipultor is 8. But s the rms cooperte with ech other in their common workspce, geometric coincidence type constrint is imposed on ech rm to mintin its tip-point on the object. here is lso constrint for ech joint ngle tht keeps it in rechble limits by the corresponding ctutor. he robot is to hndle the point object using two rms. o this end, the joint vlues re clculted so s to mximize the robot s bility to exert force in desired direction [ dx dy ] when the tip-points of the right nd left rms re holding the object t its loction ( P,P x y). o be ble to define mnipulbility mesure, the effort of the robot is kept constnt, by mintining the joint torque vector norm s unity, τ = 1. ht is to sy: τ. τ = 1 (11) Substituting (6) in (11) gives: F.J.J.F = 1 (12) It is desired to optimize the exerted force, F, to its mximum mgnitude in the specified direction. hus we will write it s: F = f. [ dx dy ] = f.fˆ (13) In which f is the mgnitude of the coopertive force, F, nd ˆF is vector of unit length on its direction. Substituting (13) in (11) yields: 2 f.( F ˆ ˆ.J.J.F) = 1 (14) In order to mximize f it is suitble to minimize the term in prenthesis. So the optimiztion criterion is: Minimize : 1 = ( F ˆ ˆ.J.J.F 2 ) (15) f o obtin the optimum configurtion of DACL mnipultor to exert mximum force in desired direction to point object, expression in (15) must be minimized. o this end, genetic lgorithm is employed nd pplied in different lock cses described erlier in figure 2. In this process ll necessry constrints re imposed: ) to prevent link segments to cross ech other, b) to keep joint ngles in rechble domin of joint ctutors, nd c) to keep permnent contct between the rms nd the object to be mnipulted. his wy, for specific problem, n optiml configurtion is obtined for ech lock cse. By compring mximum pplicble forces of optiml configurtions for different lock cses, the best lock cse is chosen [14]. ARIFICIAL NEURAL NEWORK MODELING In present work, Artificil Neurl Network (ANN) is utilized for function pproximtion. For ll four different DACL robot lock cses (described in figure 2), seprte ANN hs been designed. he neurl networks being used for these problems re ll multi-lyered perceptrons (MLP) with bck propgtion lerning lgorithm. All four networks hve equl number of lyers in their structure but, s will be explined in this section, with different number of neurons in ech lyer. Bck propgtion ws creted by generlizing the Widrow- Hoff lerning rule for multiple-lyer networks nd nonliner differentible trnsfer functions. Input vectors nd the corresponding trget vectors re used to trin the network until it cn pproximte function. According to the universl pproximtion theorem [15], ANNs with bises, sigmoid hidden lyers, nd liner output lyer cn pproximte ny function with finite number of discontinuities. here re mny vritions of bckpropgtion lgorithm. In the simplest one the network weights nd bises updte in the opposite direction of the grdient. An itertion of this lgorithm cn be written: (16) Where: x is vector of current weights nd bises, g : is the current grdient, α : is the lerning rte. In this pper heuristic technique with dptive lerning rule is used, s bckpropgtion lgorithm is ble to perform fst trining compring to other methods. For ech lock cse n ANN is formed nd trined using the dt obtined from genetic lgorithm described in previous section. Cse 1: First nd Second Links Cm-Locked In this cse, s discussed before, robot hs two degrees of freedom, hence when the tip point is mounted in position of the object, p,p, there is no kinemtic redundncy. herefore for this configurtion of DACL mnipultor, f my be defined s the only output for ANN, where f is equl to : 1 f (17) Where : f is the mximum of pplicble force in desired direction nd point s introduced before. So the ANN shll be formed s: ANN Inputs: (d,d,p,p ANN Output: f o trin this network we used input mtrix nd output mtrix (180 smple points selected throughout the workspce). All dt hve been obtined using genetic lgorithm optimiztion method s described before. 4 Copyright 2010 by ASME

5 Fig. 3: ANN for First nd Second links locked configurtion the network is composed of two hidden lyers ech including twenty neurons with sigmoid trnsfer functions nd liner ctive function in its output lyer. Input dt hve been divided up into trining, vlidtion nd test subsets. One fourth of dt is used for vlidtion set, one forth for test, nd the remining dt s trining set. he network is such tht it will normlize ech given dt in the rnge of (-1,1) nd fter the needed computtions been done, the ssocited output will utomticlly be denormlized. Figure 4 shows the regression grphs for trining, test, nd vlidtion dt subsets seprtely. he Men squred error (MSE) hs been defined s the performnce function for this problem. () Fig. 4: he regression grphs of First-Second locked configurtion () he trining regression grph he test regression grph he vlidtion regression grph Figure 3 depicts the structure of the trined network which hs been obtined fter trying different networks with vrious numbers of lyers, neurons nd trining lgorithms. As seen, Fig. 5: Performnce grph of ANN trining for First nd Second links locked configurtion After 24 trining itertions (epochs) the network met the performnce gol (error less thn 5 10 ). Vritions of performnce function (MSE) for ll three subsets re indicted in the Figure 5. Herein Resilient Bckpropgtion lgorithm is used s trining method. he nonliner nture of the problem forces using sigmoid functions in hidden lyers. he slope of these functions must pproch zero s the input gets lrge. he grdient cn hve very smll mgnitude nd hence it cuses smll chnges in the weights nd bises, fr from their optiml vlues. his mkes difficulty when using steepest descent to trin n MLP with sigmoid functions. he Resilient Bckpropgtion trining lgorithm elimintes these detrimentl effects of the mgnitudes of the prtil derivtives. Only the sign of the derivtives is used to determine the direction of the weight updte. Resilient Bckpropgtion is generlly much fster thn the stndrd steepest descent lgorithm. It lso requires only modest increse in memory requirements. he updte vlues for ech weight nd bis re needed to be stored. his is equivlent to storge of the grdient. Cse 2: hird Links Cm-Locked In this cse the mobility of the mnipultor is equl to three, 5 Copyright 2010 by ASME

6 hence when the tip point is locted in the desired position of the object, the configurtion of the robot cn be defined by the only one vrible of θ. Hence, the ANN will hve the inputs nd outputs s below: ANN Inputs mtrix: (,,, ANN Outputs mtrix: (, he network trined for this configurtion, is n MLP with twenty neurons in the first hidden lyer nd twenty five neurons in the second hidden lyer. It hs two neurons with liner trnsfer function in its output lyer (Fig. 6). he network hs been trined by Resilient Bckpropgtion lgorithm. he regression grphs re shown in the Fig. 7. It took 75 epochs for the network to be trined with the trining performnce gol of Figure 8 shows the MSE chnges over epochs for ll dt subsets. Fig. 6: ANN for hird lock configurtion () Fig. 8: Performnce grph of ANN trining for third links locked configurtion Cse 3: First Links Cm-Locked In this configurtion, DACL mnipultor hs four degrees of freedom. herefore fter positioning the tip point on the point object, its configurtion cn be specified by two vribles of θ nd θ. he trined ANN hs following inputs nd outputs: ANN Inputs mtrix: (d,d,p,p ANN Outputs mtrix: (f,θ,θ Fig. 7: he regression grphs of hird locked configurtion ()he trining regression grph he test regression grph he vlidtion regression grph Fig. 9: ANN for First lock configurtion 6 Copyright 2010 by ASME

7 he trined ANN hs two hidden lyers with 25 nd 40 neurons respectively (Fig.9). he output lyer consists of three neurons. It took 63 epochs to trin the network. he performnce gol ws 10. he regression grphs re shown in the Fig. 10. Figure 11 shows the MSE chnges over epochs for ll dt subsets. he network for this configurtion is composed of the number of twenty neurons in first hidden lyer, fifty ones in the second one nd five output neurons (Fig. 12). () Fig. 11: Performnce grph of ANN trining for first links lock configurtion Similr to the previous nets, Resilient Bckpropgtion lgorithm ws pplied to trin the network. It took 77 itertions for the ANN to be trined nd meeting the performnce gol 10. Fig. 10: he regression grphs for First lock configurtion ()he trining regression grph he test regression grph he vlidtion regression grph Cse 4: No Links Cm-Locked In this cse, mnipultor hs the mobility of six. By positioning the tip point on the point object, it will lose two degrees of freedom. Hence robot s configurtion will be defined by these four vribles: (θ,θ,θ,θ. his ANN hs the inputs nd outputs s below: ANN Inputs mtrix: (d,d,p,p ANN Outputs mtrix: (f,θ,θ,θ,θ Fig. 12: ANN for No lock configurtion Figure 13 indictes the regression grphs for this network. As seen, even with five vribles s output, it hs n cceptble fit nd hs been well trined. Figure 14 shows the MSE chnges over epochs for ll dt subsets. Utilizing ANN nd Compring the Results Hving trined four rtificil neurl networks (ANNs) to find the optimum configurtion of the DACL mnipultor for ech lock cse, the best configurtion of the robot cn be given by compring the optimum pplicble force obtined by ech of networks. In this section for four points in the workspce of the robot nd for directions, the trined ANNs re utilized to get the optiml configurtions nd their corresponding pplicble 7 Copyright 2010 by ASME

8 forces. ble 1 depicts these results. As seen in tble 1, for ech desired point for object nd desired direction for force ppliction, there re four different force mgnitudes. One must choose the best configurtion which is cpble of pplying the lrgest mgnitude of force. (ANN) is utilized. For ech lock cse of the robot n ANN is trined to give the optimum configurtion of the robot. Among the obtined results the best configurtion cpble of pplying mximum force cn be selected. Due to the highly non-liner nture of the problem the dt re scttered but the trined ANN hs given proper model for the system which cn be used in rel-time pplictions. () Fig. 14: he performnce grph of ANN trining for no links locked configurtion Fig. 13: he regression grphs for No lock configurtion ()he trining regression grph he test regression grph he vlidtion regression grph CONCLUSION he concept of the Dul-Arm Cm-Lock (DACL) robot is reviewed. A DACL mnipultor with four links in ech rm is chosen to hold point object nd pply force in desired direction. Keeping the Euclidin norm of the joint torques vector s unity, the mgnitude of the pplicble force in the desired direction is found using Genetic Algorithm. his wy the best configurtion of robot is obtined. As Genetic Algorithm is time consuming lgorithm nd my not be usble for rel-time pplictions, rtificil neurl network ble 1: Exmples of the best configurtions nd their corresponding pplicble forces for the DACL mnipultor in four different points/directions No Lock st Lock st,2 nd Lock rd Lock Best 3 rd Lock 1 st Lock No Lock 1st,2 nd Lock REFERENCES [1] J. K. Slisbury, J. J. Crig, Articulted hnds: Force control nd kinemtic issues, Int. J. Robotics Res., Vol. 1(1), 1982, pp [2] J. Y. S. Luh, Y. F. Zheng, Constrined reltions between two coordinted industril robots for motion control, Int. J. Robotics Res., Vol. 6(3), 1987, pp P. Duchez, M. Uchiym, Kinemtic formultion for two force-controlled cooperting robots, in Proc. 3rd Int. Conf. Advnced Robotics (Versilles, Frnce), 1987, pp [3] Y. Nkmur, K. Ngi,. Yoshikw, Mechnics of coordintive mnipultion by multiple robotic mechnisms, in 8 Copyright 2010 by ASME

9 Proc. IEEE Int. Conf. Robotics Automt. (Rleigh, NC), 1987, pp [4]. Yoshikw, Mnipulbility of robotic mechnisms, Int. J. Robotics Res., Vol. 4(1), 1985, pp [5] S. Chiu, sk comptibility of mnipultor postures, Int. J. Robotics Res., Vol. 7(5), 1988, pp [6] S. Lee, Dul redundnt rm configurtion optimiztion with tsk-oriented dul rm mnipulbility, IEEE rns. Robotics Automt., Vol. 5(1), 1989, pp [7]. Kokkinis, B. Pden, Kinetosttic performnce limits of cooperting robot mnipultors using force-velocity polytopes, in Proc. ASME Winter Annul Meeting-Robotics Res. (Sn Frncisco), [8] P. Chicchio, S. Chiverini, L. Sivicco, B. Sicilino, Globl tsk spce mnipulbility ellipsoids for multiple-rm systems, IEEE rns. on Robotics nd Automtion, Vol. 7(5), 1991, pp [9] A. Meghdri, Conceptul Design nd Dynmics Modeling of Coopertive Dul-rm Cm-Lock Mnipultor, Robotic, Vol. 14(4), 1996, pp [10] A. Meghdri, he Coopertive Dul-rm Cm-Lock Mnipultor, Proc. Of the IEEE Int. Conf. on Robotics for Automtion, Sn Diego, CA., U.S.A. Ptent Pending, U.C. Pt. # , Nov. 9, Vol. 2, 1994, pp [11] A. Meghdri, Conceptul Design nd Chrcteristics of Dul-Arm Cm-Lock Mnipultor, Proc. Of the ASCE SPACE-94 Int. Conf. on Robotics for Chllenging Environments, Albuquerque, N.M., USA, 1994 pp [12] K. G. Osgouie, A. Meghdri, S. Sohrbpour, Optiml configurtion of plnr dul rm system bsed on tsk-spce mnipulbility, Robotic, Cmbridge University Press, doi: /s , [13] K. G. Osgouie, A. Meghdri, S. Sohrbpour, Genetic Algorithm Bsed Optimiztion for Dul-Arm Cm-Lock Robot Configurtion, Proceedings of the 2007 IEEE/ASME Interntionl Conference on Advnced Intelligent Mechtronics AIM 2007, September 4-7, 2007, EH Zurich, Switzerlnd. [14] R. H. Nielsen, heory of the bckpropgtion neurl network, Interntionl Joint Conference on Neurl Networks, pp , Copyright 2010 by ASME