Keyvan Hashtrudi-Zaad and Septimiu E. Salcudean. University of British Columbia. Vancouver, B.C., Canada V6T 1Z4

Transcription

1 ,,,, DSC7A-5 BILATERAL PARALLEL FORCE/POSITION TELEOPERATION CONTROL Keyvan Hahtrudi-Zaad and Septimiu E. Salcudean Department of Electrical and Computer Engineering Univerity of Britih Columbia Vancouver, B.C., Canada V6T 1Z4 ABSTRACT The application of parallel force/poition control to teleoperation ytem i conidered in thi paper. Higher priority i given to poition control at the mater ide and to force control at the lave ide of the teleoperation ytem. The tability and performance of the propoed controller i invetigated by analyzing the three decoupled ytem obtained from projecting the cloed-loop ytem dynamic onto the lave tak-pace orthogonal direction. Experimental reult demontrate the excellent force and poition tracking performance provided by the new controller. INTRODUCTION Teleoperation ytem are employed to enable human to execute remote or dangerou tak with enhanced afety, at lower cot, or even better accuracy. One of the major objective in deigning bilateral teleoperation control ytem i achieving tranparency, that i a match between the mater and lave poition and force. In the pat decade, a number of control architecture have been propoed to provide higher tranparency performance (Salcudean, 1997), and only a few of thoe cheme have ucceeded in oering perfect tranparency under ideal condition (Yokokohji and Yohikawa, 1992),(Lawrence,1993). However, in practice due to the meaurement noie, model uncertaintie, and communication channel time-delay, the ytem performance i compromied and new mechanim hould be devied to provide enhanced force/poition error regulation (Salcudean,1997). A a imple olution, in thi work, the idea of parallel force/poition control, propoed in (Chiaverini and Sciavico, 1988,1992,1993,1994) for ingle robot compliant control i expanded and applied to teleoperation ytem. In the application of parallel force/poition control, higher priority i given to poition control at the mater ide and to force control at the lave ide. Thi paper rt review a imple verion of parallel force/poition control for a three degree-of-freedom (DOF) robot, and then dicue the ytem tability and teadytate performance on any type of LTI ma-dampingpring environment. Next, bilateral parallel force/poition teleoperation control i introduced by applying parallel force/poition control to a 3-DOF lave robot and the dual of that controller to a 3-DOF mater robot. Following that, the patial behavior of the operator-mater pair i invetigated uing the geometrical tool provided earlier in the paper. Experimental reult conducted on a ingle axi teleoperation ytem are preented next, and nally concluion are drawn. PARALLEL FORCE/POSITION CONTROL OF A SINGLE ROBOT In thi ection, the contact geometry of a 3-DOF manipulator in contact with a plannar environment tudied in (Chiaverini and Sciavico, 1988), and a imple linear verion of parallel force/poition control propoed in the ame paper are reviewed. In addition, the tability of the controlled ytem conidering a linear ma-damper-pring environment model i further analyzed. Thee provide the preliminary tool for the introduction and analyi of bilateral parallel force/poition control for a 3-DOF teleoperation ytem to be preented in the next ection. Conider the end-eector of a 3-DOF manipulator in contact with a planar environment, a hown in Fig. 1. Auming a linear ma model for the manipulator 1 and 1 It i aumed that the nonlinear term of the manipulator dynamic, if any, are cancelled out uing invere dynamic (Chiaverini and Sciavico, 1988).

2 Figure 1. Environment Contact Surface n End-Effector t2 t1 Robot end-eector in contact with a planar environment. only tranlational motion for the end-eector, the dynamic equation for the coupled ytem can be written a f c = M r x e + f e (1) where M r ; x e ; f e and f c denote the robot ma matrix, the end-eector poition, the environment contact force, and the control force command to the robot actuator, repectively 2. Auming negligible friction at the contact and neglecting the eect of contact local deformation due to the high rigidity of the environment (Chiaverini and Sciavico, 1988), the environment force f e i alway orthogonal to the plane and ha no tangential component to the urface. Therefore, if an orthonormal tak coordinate frame C T i dened with a unit bai vector n along the contact normal, and the other two bai vector t 1 and t 2 tangent to the contact urface, the contact force and poition can be repreented a (Chiaverini and Sciavico, 1988) f e = f e1 t 1 + f e2 t 2 + f en n = f en n (2) x e = x e1 t 1 + x e2 t 2 + x en n ; (3) where x e1 ;x e2 and f e1 = f e2 = are the poition and force component in the tangential direction, and x en and f en are the poition and force component in the normal direction. Alo, a linear ma-damper-pring model for the environment in the latter direction i aumed, that i f en = M en x en + B en _x en + K en (x en, x eon ) ; (4) where x eon i the reting point of the environment inthe normal direction at which f en =. In our cae, it i aumed that the reting point i tationary, that i _x eon =.From (2)-(4), one can how that F e = Z e (X e, X eo ) ; (5) 2 In thi paper, all matrice and vector are in boldface letter, and all variable are expreed with repect to a xed orthonormal Carteian reference coordinate frame C R. where F e ; X e and X eo are the Laplace tranform of f e ; x e and x eo, and Z e i the environment impedance matrix de- ned a Z e := ( R R T )diag(; ;Z en )( R R T ) T = Z en nn T := (M en 2 + B en + K en )nn T : (6) Here, R R T =[t 1 t 2 n] denote the rotation matrix from C T to C R, and the upercript T i the tranpoe operator. In a general contact tak, manipulator are expected to follow the force/poition prole f ed = f ed1 t 1 + f ed2 t 2 + f edn n (7) x ed = x ed1 t 1 + x ed2 t 2 + x edn n ; (8) where if there i enough information about the environment, the planning i done o that f ed1 = f ed2 = (Raibert and Craig, 1981). Unfortunately, due to the environment mechanical impedance propertie, it i uually impoible for the end-eector to fulll x en = x edn and f en = f edn imultaneouly. Therefore, a compromie between contact poition and force tracking i made (Chiaverini and Sciavico, 1988),(Hogan, 1985). Often, for the afety of the environment and manipulator, force tracking i given higher priority than poition tracking, uch a in parallel force/poition control (Chiaverini and Sciavico, 1988, 1992, 1993, 1994). In general, the control methodology enjoy the implicity of the impedance control and at the ame time provide the force/poition control benet of the hybrid control in arti- cial/natural direction, while taking full advantage of all the meaurement. An eay to implement linear verion of thi control trategy (Chiaverini and Sciavico, 1993, 1994) which i going to be ued for teleoperation control purpoe in the next ection, conit of PD poition and PI force control term with control parameter matrice K p ; K v and K f ; K i given by f c = M r x ed + K v ( _x ed, _x e )+K p (x ed, x e ) Z t + K f (f ed, f e )+K i (f ed, f e )d + f e : (9) Combining (1) and (9) yield the cloed-loop dynamic M r (x e, x ed )+K v ( _x e, _x ed )+K p (x e, x ed )+ Z t K f (f e, f ed )+K i (f e, f ed )d =; (1) or imply (M r 2 +K v +K p )(X e,x ed )+(K f + K i )(F e,f ed )= (11)

3 in the -plane domain, where X ed and F ed are the Laplace tranform of x ed and f ed. Auming M r = M r I 33;M r > (without lo of generality), and etting K v = K v I 33, K p = K p I 33, K f = K f I 33, K i = K i I 33, to add an iotropic behavior to the control law (1), the cloed-loop dynamic (5){(8) and (11) are decoupled and can be decompoed onto the tak-pace direction t 1 ; t 2 and n according to (M r 2 + K v + K p )X e1;2 =(M r 2 + K v + K p )X ed1;2 +(K f + K i )F ed1;2 (12) [(M r + K f M en ) 2 +(K v + K f B en + K i M en ) +(K p + K f K e + K i B en )+ K ik en ]X en = (M r 2 + K v + K p )X edn +(K f + K i )F edn +(K f + K i )(M en 2 + B en + K en )X eon (13) where ( 1;2 ) notation i ued to condene the ytem dynamic repreentation in t 1 and t 2 direction into one equation. If the ytem i aymptotically table, the deired force i contant, and the deired poition in tangential direction i time-varying and in normal direction i contant, then in teady tate x e1;2 = x ed1;2 + K i K p f ed1;2 t ; fe1;2 = (14) x en = x eon + 1 K en f edn ; fen = f edn (15) hold, where () denote the teady tate value of the argument. If there i ucient information about the ytem, then f ed1;2 =, and poition tracking i atied in the tangential direction; otherwie, a drifting phenomenon happen at a rate depending on K p and K i. In the normal direction, the integral term on force give it control a higher priority at the expene of poition error (Chiaverini and Sciavico, 1993, 1994). Toachieve aymptotic tability 3, from the econd-order ytem (12), the poition control parameter K v and K p have to be poitive, and from the third-order ytem (13), the force control parameter K f and K i have to atify K i K en > ; M r + K f M en > ; K v + K f B en + K i M en > and (K v + K f B en + K i M en )(K p + K f K en + K i B en ) > 3 In (Chiaverini and Sciavico, 1993), the tability analyi ha only been conducted for environment modeled by a linear pring. (M r + K f M en )K i K en (16) to render (13) Hurwitz. In mot practical ituation, the environment tine i dominant over damping and ma propertie. Therefore, the tability condition come down to the imple inequality <M r K i K en <K v (K p + K f K en ) (17) by etting B en and M en in (16). Interetingly enough, even if the tine i not dominant, (16) can be rearranged a [K v K i B en + K i M en (K p + K i B en )+ K f B en (K p + K f K en + K i B en )] + [K v (K p + K f K en ), M r K i K en ] > (18) implying that if K v ;K p ;K f ;K i >, and (17) or M r K i, K v K f < K pk v K en : (19) hold, then the cloed-loop ytem i aymptotically table. Condition (19) i atied for any environment tine value if M r K i <K v K f (2) Therefore, for any robot modeled by the LTI ytem (1) and in contact with any environment modeled by the linear ma-damper-pring dynamic (5), parallel force/poition control (9) i aymptotically table provided that all the control parameter are poitive and (2) i atied. Thi how that to guarantee tability when operating on unknown environment, a minimum amount of velocity and force feedback are neceary. If the dynamic range of the environment tine i known apriori, then the above minima can be reduced by employing ucient poition feedback. In the next ection, the parallel force/poition trategy i employed in a bilateral teleoperation control ytem, and the analyi tool provided in thi ection will be ued to invetigate the ytem performance and tability. BILATERAL PARALLEL FORCE/POSITION CONTROL Conider a teleoperation ytem with two 3-DOF mater and lave manipulator modeled by linear ma dynamic a f mc = M m x h, f h (21) f c = M x e + f e (22)

4 where x h ; x e ; f h ; f e ; f mc and f c are vector of the mater and lave tranlational poition, force exerted by the operator on the mater, force applied on the environment by the lave and the mater and lave actuating control command, repectively. Auming the ame environment a ued for the ingle robot in the previou ection, and dening the ame takpace coordinate frame C T, (2)-(6) can be employed to repreent the interaction dynamic between the lave and the environment, with M r = M. However, unlike the laveenvironment contact, ince the operator grap the mater hand-controller, he/he can apply force in every direction, and therefore the operator dynamic follow F h = F? h, Z hx h ; (23) where X h ; F h and F? h are the Laplace tranform of x h; f h and the operator' exogenou input force f? h, repectively, and Z h denote the operator' arm impedance matrix de- ned a Z h := ( R R T )diag(z h1 ;Z h2 ;Z hn )( R R T ) T = Z h1 t 1 t T 1 + Z h2 t 2 t T 2 + Z hn nn T : (24) Here, it i aumed that the operator' arm dynamic can be adequately modeled by Z h1;2 := M h1;2 2 +B h1;2 +K h1;2 and Z hn := M hn 2 + B hn + K hn in the three normal lave tak-pace direction t 1 ; t 2 and n. Therefore, (23) can be decompoed into where F h1;2 = F? h1;2, (M h1;2 2 + B h1;2 + K h1;2 )X h1;2 (25) F hn = F? hn, (M hn 2 + B hn + K hn )X hn ; (26) X h := X h1 t 1 + X h2 t 2 + X hn n (27) F h := F h1 t 1 + F h2 t 2 + F hn n (28) F? h := F h1t? 1 + F h2t? 2 + F hnn? : (29) To implement parallel force/poition control at both the mater and lave ide, intuitively, one hould give higher priority to force control rather than poition control at the lave ide. Thi i becaue the level of information known from the lave ide i much le than that from the mater ide, and in mot of the application the environment ha to be protected from exceive contact force. In addition, the lave force accommodation feature can be helpful in coping with the eect of unplanned colliion that reult from the lave operating on unknown environment, epecially when there are ignicant time-delay in the ytem and the lave momentarily operate in open-loop mode. At the mater ide though, ince the mater i expected to mimic the environment impedance and the force are matched by the lave controller, in a dual manner, higher priority ha to be given to poition control. Note that the force error integral term can alo be added to the mater controller; however, thi bring no advantage a force error regulation i already obtained at the lave ide. Setting x ed = x h ; x hd = x e ; f ed = f h and f hd = f e, the bilateral parallel force/poition control law f mc = M m x e + K xvm ( _x e, x_ h )+K xpm (x e, x h ) Z t + K xim (x e, x h )d, K fpm (f e, f h ), f h (3) f c = M x h + K xv ( _x h, _x e )+K xp (x h, x e ) Z t + K fp (f h, f e )+K (f h, f e )d + f e (31) are propoed where K xvm = K xvm I 33, K xpm = K xpm I 33, K xim = K xim I 33, K fpm = K fpm I 33, K xv = K xv I 33, K xp = K xp I 33, K fp = K fp I 33, and K = K fi I 33 are the mater and lave poition and force control matrice, and without lo of generality it i aumed that M m = M m I 33;M m >, and M = M I 33;M >. Note that the calar control gain are ued to render the control law (3)-(31) iotropic. After eliminating f mc and f c from (21)-(22) and (3)-(31), one obtain the dynamic of the cloed-loop ytem a (M m 2 + K xvm + K xpm + K xim )(X h, X e )= K fpm (F h, F e ) (32) (M 2 + K xv + K xp )(X h, X e )= (K fp + K )(F e, F h ) : (33) With the above choice of control matrice, the ytem degree of freedom are decoupled and (32)-(33) can be eaily decompoed along the three lave tak-pace direction t 1 ; t 2 and n uing (2)-(4), (25)-(29) and F e1;2 =, according to [(M m + K fpm M h1;2 ) 2 +(K xvm + K fpm B h1;2 ) +(K xpm + K fpm K h1;2 )+ K xim ]X h1;2 (34),(M m 2 + K xvm + K xpm + K xim )X e1;2 = K fpm F? h1;2 [(M m + K fpm M hn ) 2 +(K xvm + K fpm B hn ) +(K xpm + K fpm K hn )+ K xim ]X hn,[(m m, K fpm M en ) 2 +(K xvm, K fpm B en ) +(K xpm, K fpm K en )+ K xim ]X en = K fpm F hn? (35)

5 for the mater ide, and [(M, K 2 fpm h1;2) +(K xv, K fpb h1;2, K fim h1;2) Ze Fe*= Environment +(K xp, K fpk h1;2, K fib h1;2), KfiKh1;2 ]X h1;2,(m 2 + K xv + K xp)x e1;2 = (36),(K fp + Kfi )F h1;2? Xe C -1 Z C Fe Slave [(M, K fpm hn) 2 +(K xv, K fpb hn, K fim hn) +(K xp, K fpk hn, K fib hn), ( KfiKhn )]X hn C4 C3 C2 C1 Communication Channel,[(M + K fpm en) 2 +(K xv + K fpb en + K fim en) +(K xp + K fpk en + K fib en) + KfiKen ]X en =,(K fp + Kfi )F? hn (37) for the lave ide. Unlike the ingle robot ytem decribed in the lat ection, the deired lave force command (f ed = f h ) might have a component in the tangential direction. The reaon i that the exogenou input force f h? ha component in all direction and the mater hand-controller i capable of generating reiting force in any direction, including t 1 and t 2. Auming contant operator exogenou input, the teady-tate analyi of (34){(35) yield x h1;2 =x e1;2 = f? h1;2 K h1;2 ; fh1;2 = f e1;2 = (38) x hn =x en = f? h1;2 K hn + K en ; fhn = f en = K enf? hn K hn + K en : (39) A it i een from (38), although f h1;2? 6=, unlike in (14), x h1;2 do not how any growing drift. Thi i becaue in thi cae f e1;2 =, and x e1;2 acting a the mater deired poition command are not exogenou and independent of the mater dynamic. In fact, x h1;2 =x e1;2 are adjuted in uch away that f h1;2? are aborbed in the operator' arm and conequently the mater how no reitance to the operator in the tangential direction, that i f h1;2 =. The other iue i that all the poition and force component match, wherea for a ingle robot only force error i regulated. Thi i becaue the mater poition and force that act a lave poition and force command embed the environment propertie and are adjuted at the mater ide to comply with the environment force/poition requirement. To get better inight on poition and force tracking, one can tudy the ytem tranparency condition. Conider the block diagram of a general four-channel architecture teleoperation control ytem a hown in Fig. 2, where C 1 ; :::; C 6 ; C m ; C are rational tranfer function control matrice, and Z m = M m 2 ; Z = M 2 ; Z h and Z e denote the mater and lave ytem dynamic, operator Figure 2. Fh Fh* C6 Zh Zm -1 Cm Xh Mater Operator General block diagram of a four-channel teleoperation control ytem after Lawrence (1992), (Hahtrudi-Zaad and Salcudean, 1999). impedance and lave impedance matrice, repectively. By comparing the ytem cloed-loop dynamic (32)-(33) with the general ytem dynamic equation (Hahtrudi-Zaad and Salcudean, 1999) (Z m + C m )X h =(C 6 + I)F h, C 4 X e, C 2 F e (4) (Z + C )X e =,(C 5 + I)F e + C 1 X h + C 3 F h (41) derived from Fig. 2, one reache 8 C 1 = Z + C = M 2 + K xv + K xp >< C 2 = C 6 + I = K fpm C 3 = C 5 + I = K fp + K C 4 =,(Z m + C m ) >: =,(M m 2 + K xvm + K xpm + Kxim ) ; (42) which i the condition et for perfect tranparency (Lawrence, 1993),(Hahtrudi-Zaad and Salcudean, 1999). Since the ytem i decoupled in all the three axe of C T,a condition et imilar to (42) alo applie in each direction. To analyze ytem tability, tudying the tability of the ixth-order decoupled dynamic (34,36) and (35,37) i too involved. Intead, a hown in (Hahtrudi-Zaad and Salcudean, 1999), if the operator and environment are both paive, then the ytem tability i implied to

6 C 2 (Z m + C m )+C 3 (Z + C )= (43) being Hurwitz, or K fpm 2 (M 2 + K xv + K xp )+ (44) (K fp + K fi )(M m 3 + K xvm 2 + K xpm + K xim ) =(M m K fp + M K fpm ) 4 +(M m K fi + K xvm K fp + K xv K fpm ) 3 +(K xvm K fi + K xpm K fp + K xp K fpm ) 2 (45) +(K xpm K fi + K xim K fp ) +(K xim K fi )= being Hurwitz. In the tangential direction where f e1 = f e2 =, or equivalently K fpm =, or when the lave i not in contact, the characteritic equation (44) implie to the mater and lave poition control characteritic equation M m 3 + K xvm 2 + K xpm + K xim = (46) M 2 + K xvm + K xpm = (47) being table and K fp ;K fi >, which i eay to atify. In thi way, one can ue (46)-(47) and the deired free pace tranient performance to derive the poition control parameter, and then nd a feaible range of value for (K fpm ;K fp ;K fi ) to preerve tability by nonlinear programming tarting from (; 1; ). It eem that by adding the integral term, not only dynamic lag ha been introduced in the cloed-loop dynamic cauing probable reduction in tability robutne, but alo the ytem tranparency ha remained untouched a the perfect tranparency condition would till be atied if K xim = K fi =. However, in practice, a will be een in the next ection, a perfectly tranparent ytem with no integral term may how ignicant tracking error, and the addition of the integral term will reduce both the poition and force error dratically. The idea of parallel force/poition can alo be applied to non-tranparent teleoperation ytem to obtain virtually zero force and poition error. Thee will be demontrated in the next ection. EXPERIMENTAL RESULTS Figure 3 how a photograph of the teleoperation experimental etup, coniting of two Maxon DC motor with handle acting a one-degree-of-freedom mater (right) and lave (left) device. The handle, equipped with JR 3 force enor to meaure operator and contact force, are connected to the lave and mater motor haft through a 5:1 harmonic and a 1:1 ingle tage planetary gearhead, repectively. The motor are alo equipped with poition Figure 3. Picture of the 1-DOF experimental etup. encoder. The enor are connected to a VME-baed computer ytem, coniting of data acquiition board and a Sun SPARC 1e CPU board running the VxWork real-time operating ytem. The ytem i networked to the local Ethernet and C program are cro-compiled in the UNIX environment. The digital control loop i implemented at the ampling frequency 3(Hz). After compenating for the mater and lave Coulomb and vicou friction torque (Tafazoli et al., 1996), the SISO ytem dynamic can be expreed in term of the motor calar variable a in (21)-(22), where here f mc and f c are the motor torque control command, f h and f e denote the external torque applied by the operator on the mater motor haft and created by the lave motor haft to be exerted on the environment, x h and x e are the mater and lave motor haft rotational poition, and nally Z m := I m ; I m = 3:35 1,5 (Nm 2 =rad) and Z := I ; I =3: 1,5 (Nm 2 =rad) are the mater and lave eective inertia, repectively. Note that the reaon for uing the motor variable i to have a pair of imilar mater and lave ytem. After cloing the local feedback loop and feeding forward the poition and torque information, the dynamic equation (4){(42) are obtained where the poition control tranfer function C m =:34 +: :73 and C =:24 +:48, are choen to place the pole of the mater and lave free motion dynamic (46)-(47) at -4, - 4, -2 and -4, -4, repectively. Note that the velocity term are derived from poition meaurement and no acceleration term i ued, that i C 1 = C and C 4 =,C m. To nd the force control parameter, uing (44)-(45), a imple numerical earch ha been conducted in K fpm ;K fp 2 (; 2:);K fi 2 (; 4:) range of force control parameter to check ytem tability. The earch howed a table ytem at all of thee point, a long a the operator and environment are paive.

7 3 Applying Parallel Force/Poition cheme to an ideally tranparent control ytem 3 Applying Parallel Force/Poition cheme to a non tranparent control ytem (C 2 =.5) 2 2 Poition (rad) 1 1 Poition (rad) x h x e with integral term without integral term x h x e with integral term without integral term Torque (Nm/rad) f h f e with integral term without integral term Torque (Nm/rad) f h f e with integral term without integral term Torque (Nm/rad) k xim x e x h k fi f h f e f mc f c w integral term w/o integral term Time () Figure 4. Application of the bilateral parallel force/poition control to ideally tranparent ytem (C2 = C6 +1: = 1:) reduce the force error ignicantly. Torque (Nm/rad) Figure 5. k xim x e x h k fi f h f e f mc f c w integral term w/o integral term Time () Application of the bilateral parallel force/poition control to a nontranparent ytem (C2 = :5 6= C6 + 1: = 1:) reduce the poition and force error ignicantly. The experiment conducted are categorized baed on the control ytem ideal performance when the integral term are not preent in the control loop (K xim = K fi =) a follow: i) the control ytem i perfectly tranparent with C 2 = C 6 +1=1: and C 3 = C 5 +1=1: (Lawrence, 1993), and ii) the ytem loe it tranparency by reducing the lave force feedback by 5%, that i C 2 =:5 6= C 6 +1: =1: and C 3 = C 5 +1=1:. In each experiment which lat for 8 econd, the operator pull and puhe the mater lever o that the lave make ix contact with an environment of approximate tine 55; (N=m) (or equivalently K en =:48(Nm=rad) if perceived from the lave motor) to maintain a deired contact torque at :4; :8 or 1:2(Nm) level a hown in Fig. 4 and 5. For the rt three contact, parallel force/poition control, i.e. addition of the integral term, with K xim =1:73 and K fi =2: are employed and in the following three the integral term are removed for comparion. A een from the poition and force prole in Fig. 4, even for a ytem that i perfectly tranparent in theory, due to the preence of noie, parametric and dynamic uncertaintie, and time-delay, there i an average of 5% error in poition tracking and a ignicant amount of 18% error in force tracking in contact regime (econd et of three contact). However, granting higher priority to poition control at the mater ide and force control at the lave ide have coniderably reduced the average poition and force tracking error down to :3% and :2%, repectively (rt et of three contact). Thi poitive eect i alo eaily viible in Fig. 5 for a non-tranparent ytem. If the integral coecient K xim and K fi are choen to be mall and the lave i puhed into the contact for a long time, the integral of poition and force error may grow dratically. Thi may caue a reitive torque that keep the lave puhing againt the environment and the mater reiting the operator' motion when he/he intend to pull

8 the mater back. In other word, the unilateral environment contraint i tranformed into a bilateral contraint. To olve thi problem, the force/poition error dynamic can be made fater by proper increae of the control coecient. Thi reult in maller integrator windup. Alo, one can pa the integral term through a aturation lter to avoid integral windup eect. The control prole in Fig. 4 and 5 clearly how the eect of the integral term in the control eort f mc and f c in providing better tracking. In concluion, although bilateral parallel force/poition approach may caue ome phae lag in the control loop, the poition and force tracking reduction i ignicant if the control parameter are properly choen. The concept of higher priority for force control at the lave ide and for poition control at the mater ide can be implemented on any tranparent (ideally) or non-tranparent bilateral control ytem to obtain enhanced poition and force tracking reult. Thi trategy ha been ued by Anderon in (Anderon, 199) to make the mater deired force command and lave deired poition command converge to the lave coordinating force command and the mater poition in teady tate in the preence of time-delay. CONCLUSIONS The idea of parallel force/poition control for a ingle robot ha been tailored and extended to teleoperation ytem by providing force control dominance at the lave ide and poition control dominance at the mater ide. For the rt time, the ytem tability and performance have been invetigated by decoupling and projecting the materlave cloed-loop ytem dynamic onto the lave tak-pace orthogonal direction. It ha been hown that by proper election of poition and force control parameter, tability i maintained and the mater faithfully mimic the environment in all direction in teady-tate. The experimental reult conducted on a ingle axi teleoperation ytem ha hown ignicant enhancement inlow peed poition and force tracking. Future reearch will be directed toward the implementation of the bilateral parallel force/poition control on multi-dof teleoperation ytem. ACKNOWLEDGMENT Thi work wa upported by the Canadian IRIS/PRECARN Network of Centre of Excellence, Project IS-4. The author wih to thank Wen{Hong Zhu for helping with the experimental etup. REFERENCES Anderon R.J., 199, \Improved Tracking for Bilateral Teleoperation with Time Delay," Robotic Reearch, DSC-Vol. 26, pp Chiaverini S., and Sciavicco L., 1988, \Force/Poition Control of Manipulator in Tak Space With Dominance in Force", Proc. IFAC Robot Control, pp Chiaverini S., and Sciavicco L., 1992, \Edge-Following Strategie Uing Parallel Control Formulation," Proc. IEEE Int. Conf. Cont. Appl., pp Chiaverini S., and Sciavicco L., 1993, \The Parallel Approach to Force/Poition Control of Robotic Manipulator," IEEE Tran. Rob. & Auto., Vol. 9, pp Chiaverini S., and Sciavicco L., 1994, \Force/Poition Regulation of Compliant Robot Manipulator,"IEEE Tran. Auto. Cont., Vol. 39, No. 3, pp Hahtrudi-Zaad K., and Salcudean S.E., 1999, \On the Ue of Local Force Feedback for Tranparent Teleoperation," Proc. IEEE Int. Conf. Rob. & Auto., pp Hogan N., 1985, \Impedance Control: An Approach to Manipulation," Part I-III, Tran. ASME. J. Dyn. Syt. Mea., Cont., Vol. 17, pp Lawrence D.A., 1992, \Deigning Teleoperator Architecture for Tranparency," Proc. IEEE Int. Conf. Rob. & Auto., pp. 146{1411. Lawrence D.A., 1993, \Stability and Tranparency in Bilateral Teleoperation," IEEE Tran. Rob. & Auto., Vol. 9, No. 5, pp Raibert M.H., and Craig J.J., 1981, \Hybrid Poition/Force Control of Manipulator,"Tran. ASME J. Dyn. Syt. Mea., Cont., Vol. 13, pp Salcudean S.E., 1997, \Control for Teleoperation and Haptic Interface", Control Problem in Robotic and Automation, B. Siciliano and K.P.Valavani (Ed.), Springer-Verlag Lecture Note in Control and Information Science, Vol. 23, pp. 5{66. Tafazoli S., de Silva C.W., and Lawrence P.D., 1996, \Friction Modeling and Compenation in Tracking Control of an Electrohydraulic Manipulator," Proc. IEEE Mediterranean Symp. New Dir. Cont. & Auto., pp. 375{38. Yokokohji Y., and Yohikawa T., 1992, \Bilateral Control of Mater-lave Manipulator for Ideal Kinethetic Coupling: Formulation and Experiment," Proc. IEEE Int. Conf. Rob. &Auto., pp. 849{858.