Achieving High Transparency in Bilateral Teleoperation Using Stiffness Observer for Passivity Control

Transcription

1 Acieving Hig Transparency in Bilateral Teleoperation Using tiffness Observer for Passivity Control Reza Monfaredi Karan Razi aeed iri Gydari eied Medi Rezaei Depart. of Mecanical Eng. Depart. of Electrical Eng. Depart. of Coputer Eng. Depart. of Mecanical Eng. Airkabir Univ. of Tec. Airkabir Univ. of Tec. Airkabir Univ. of Tec. Airkabir Univ. of Tec. Teran, Iran Teran, Iran Teran, Iran Teran, Iran Abstract In tis paper a new approac is developed tat increases transparency in bilateral teleoperation. We define a stiffness observer wic detects ard contact instant by analyzing te generated force in te slave side to activate a passivity controller. Tis approac uses passivity based idea of onitoring energies flowing in and out of te teleoperator. It iproves perforance of previous works by eliinating instability in transition to ard contact. It also provides a ore general and less conservative approac to passivity control of teleoperated systes. Te perforance of te new approac as been investigated troug siulation results. Index Ters teleoperation, transparency, passivity control, force feedback, aster-salve robot I. INTRODUCTION oe robotic applications require uan intelligence to operate well in te reote environent. Te ost powerful tool for tese applications is a aster-slave robot. In tis syste te reote robot (slave) is being anipulated in real tie troug te aster robot by uan operator wo takes visual feedback fro te slave robot. Recent researces in tis field focus on adding iproved force feedback to te syste for creating ore transparent interface for uan operator (bilateral teleoperator)[1][2],[3],[4]. In bilateral teleoperation, te contact forces affecting te slave are fed back to te aster to give te operator a feeling of te actual operation. Te ter transparency is used to describe ow close tis feeling is to te feeling wen perforing te sae task anually witout te teleoperator [4]. It is desirable to build and control te teleoperator suc tat te transparency is as ig as possible. However, tere is a trade off between transparency and stability of bilateral teleoperators. ince transparency ust often be reduced in order to guarantee stable operation in wide range of environent ipedances. In typical control etods for teleoperated systes te dynaic odels of operator and environent ust be involved in te syste design, owever te environent and operator ave nonlinear and unknown dynaic odels tat can not be easily extracted. One proising approac is te use of passivity to guarantee stable operation witout exact knowledge of odel inforation [5]. Anderson and pong [5] ave used te passivity concept for telerobotic systes wit tie delay. Tey used passivity to design a syste tat is passive for all operating conditions. It is known tat tis etod is over conservative and reduces te syste transparency [3], [6]. Hannaford and Rya [3] developed a passivity controller tat controls te teleoperation syste s passivity, using a passivity observer (P.O.) and a passivity controller (P.C.). By application of passivity control, te stability and transparency can be treated separately, witout affecting eac oter, so te perforance of te syste can be iproved by increasing transparency. Passivity controller reduces te transparency by affecting te force/velocity signals. Tis can be solved by liiting passivity control to situation wen te teleoperation goes to instability. In tis paper it is sown tat te passivity observer introduced in [3] and [6] is a conservative etod to detect instability, because passivity is sufficient condition for stability[2],[6]. It is not a necessary condition. Tis as te effect tat in soe cases of free otion and soft contact, te syste igt be stable wile te passivity observer sows negative value. In te oter and, in soe cases wen a ard contact occurs, te passivity observer cannot turn on te passivity controller iediately until te internal energy becoes negative. Tis will reduce transparency of te syste and will cause instability in transition to te ard contact. Analyzing tese cases for a typical teleoperation syste as well as te syste is developed in tis paper. It is sown tat P.O./P.C. approac isn't applicable for all teleoperation systes in general as well as te syste developed in tis paper wit specific dynaic. o a new approac sould be developed to control passivity in wide Varity of teleoperation systes. Te ard contact in presence of tie delay is a ain cause of instability in teleoperated systes [2],[3],[4],[5]. Instability could be eliinated by detection of ard contact and iediate application of passivity controller after contact. In tis paper passivity observer is substituted wit a stiffness observer wic analyses te generated force in slave side to detect wen te slave robot contacts to te ard environent. Te stiffness observer detects ard contact by estiating stiffness and turns te passivity controller on wen ard contact occurs.

2 X F Xs Operator Master lave Object Fr X Controller Fs Xs Fig. 1 Te general odel of a teleoperation syste nae TABLE I DIFFERENTIAL EQUATION OF TELEOPERATION COMPONENT Differential equation 1) Huan X M + ( X X ) B + ( X X ) K = Fr 2) aster J θ = Fr L Ta 3) controller T T a as a T is te tie delay of signals = PID.[ T ( t) T ( t T)] G s s a = PID.[ θ ( t) θ ( t T)] G 4) alve J θ = Tas ( t) Ls 5) Environent L Be + L keθ = θ as a otor s otor Te perforance of tis etod as been investigated troug siulation results. II. TELEOPERATOR TRUCTURE Teleoperation systes involve five distinct sections, 1) uan, 2) aster robot, 3) controller, 4) salve robot and 5) environent [7]. Fig. 1 sows sceatic of a typical aster-salve syste.[1] Tere are five arcitectures for te controller design.[4] 1) Position-position (position error) 2) Force position (force- velocity) 3) Position force (velocity- position) 4) Force force 5) Four cannel controller We use te second arcitecture, Force-position, for V Ta our controller design, in wic te position/velocity signal is fed forward fro aster robot to te slave robot and te force signal is fed backward for salve robot to te aster robot. III. TELEOPERATION YTEM MODELING Yokokoji [8] discusses a odel in wic te dynaics of te uan ar/and are assued to be a siple spring, daper and ass syste. Te environent is odeled as a siple daper-spring syste. We odeled our syste's operator and environent respectively as a ass_daper_spring and daper_spring syste. Te differential equation of eac part of teleoperation syste of one degree of freedo is arranged in Table I. Were J and J s are te aster and slave rotational inertia, θ and θ s are te angular position of aster and slave robots Vs Operator Master Controller lave Object Fr V Tas Vs Fig. 2 Te teleoperation syste odel

3 F 1 V 1 N V 2 F 2 Position() respectively, T a and T as are te torque generated by aster and slave otors. G and G s are te aster robot s otor and save robot s otor transfer function (containing ecanical and electrical constant of otors), respectively. K e and B e represent environent caracteristic. And finally, X represents uan operator displaceent. Fig. 2 sows te odel of teleoperation syste tat is used in tis paper. In te following section te passivity teore and passivity controller are briefly explained. We ten analyzed te passivity concept for a typical teleoperation syste as well as our supposed syste wit specific dynaic to sow tat P.O./P.C. is not a general controller to be applied to all teleoperation systes. Ten in section 5 we developed a new observer to detect ard contact as a easure for instability initiation and activate te passivity controller after instability detection. IV- PAIVITY THEORY uppose a two-port network syste, N, suc as sown in Fig. 3. Now te passivity concept could be defined as following: A. Passivity Definition A two-port network syste, wit initial energy storage E (0) is passive if and only if: [ F ( t) V ( t) + F ( t) V ( t)]( dt) + E( 0) 0, 1 1 Fig. 3 A two-port network syste 2 2 t 0 ( 1) Te sign convention for all forces and velocities is defined so tat teir product is positive wen power enters te syste port. [9], [10], [11]0. In following we sow tat passivity is only a sufficient condition for stability and we will conclude tat P.O./P.C. isn't applicable for all teleoperation systes and it's application doain is liited to soe special teleoperation systes. B. Passivity is a sufficient condition for stability It is known tat passivity is only sufficient condition for stability[2],[6] and not a necessary condition, It eans tat if a syste is passive ten it is Energy (N) Tie(s) Tie(s) Fig. 5 Free otion a) aster and slave position b) syste energy stable, but a syste tat is active isn't necessarily an unstable syste. Indeed, a teleoperation syste ay go to instability if it losses energy increasingly, so wen te internal energy of te syste is bounded by finite negative value te syste could be stable. In te next tree subsections te internal energy of a typical teleoperation syste as well as tis researc s teleoperated syste is discussed. Tree possible odes, 1) Free otion, 2) oft contact and 3) Hard contact are considered. C. Passivity in free otion uppose teleoperation controller as a two- port network syste as sown in fig. 4, in te free otion tere is no external force in te slave side, so te force applied to te aster, F, is to be also zero. In te oter and as te slave ar as to follow te aser position so it requires energy. Integration of V s F s over tie results in negative value. In tis situation te syste is active and stable. Te gravity and friction copensations ay cange te configuration of te energy flow in and out of te teleoperated systes [6]. In tis study only te systes Position() Position() Tie(s) Fig. 4 Te controller as a two-port network syste Tie(s) Fig. 6 Te aster and slave forces in free otion siulation. a) Witout passivity controller b) Wit passivity controller.

4 Fig. 8 Master and slave a) positions and b) forces, in soft contact (k= 50 N/) siulation, witout passivity controller Position () Position () Fig. 9 Master and slave a) positions and b) forces, in soft contact (k= 50 N/) siulation, wit passivity controller wic don t ave any gravity and friction copensator are discussed. Fig. 5 (a) sows te aster and salve positions in free otion for te syste. In tis siulation a step torque is applied to te aster ar by operator. Fig. 5(b) sows tat altoug te internal energy of syste becoes negative, owever te syste is stable. Turning on te passivity controller in tis state will reduce te transparency of te syste. Fig. 6 sows siulation results wen passivity controller is on. Tis figure sows tat activating passivity controller in free otion results Position Force V >0 V <0 V =0 V s >0 V s =0 V s =0 X X s Tie in oscillating salve force tat will reduce te syste perforance. D. Passivity in soft contact Fig. 7 sows a response of a typical teleoperated syste to a step input, in soft contact. In te tie interval between T 1 and T 2, te value of V s is alost zero, because te slave ar as contacted to external object, owever V is negative. Using (1), we know tat te teleoperated syste gives energy to te environent and is active, owever te syste is stable. Activating te passivity controller in tis situation reduces te syste transparency. iulation sows tat in soft contact, te syste is stable, but passivity observer sows tat te syste generates energy, so it isn't passive. Fig. 8 and Fig. 9 sow te positions and forces of te aster and slave robot wen a soft contact occurs, witout and wit passivity controller, respectively. As sown in fig. 9(b), te passivity controller results in soe oscillation and reduces transparency. Te contacts for different environents stiffness are siulated. Te results sow tat passivity controller activation is useful only for environent stiffness greater tan a specific value. Tis stiffness value certainly depends on te teleoperation syste dynaic. iulation of supposed syste in presence of 40 s tie delay sows tat our systes needs to be stabilized by passivity controller for stinffness greater tan 400 N/. T 1 T 2 Fig. 7 oft contact F F s Tie E. Passivity in ard contact Previous experients[3],[6], sow tat in soe cases, te passivity observer cannot turn on te passivity controller iediately until te internal energy becoes negative, resulting delay in stabilizing te syste, and force bounces suc as force bounces reported by Hannaford [3].

5 Fig. 10 A passivity controller Passivity control is a conservative approac tat guarantees te syste s stability by aking syste passive in all of situations. In general, passivity observer is not a suitable observer to detect instability, because as is sown it is probable for internal energy to becoe negative in free otion and soft contact. Passivity observer also could cause proble in ard contact. In next section passivity observer is substituted wit a stiffness observer. Tis observer analyses te force generated in te slave side to detect wen te slave robot contacts to te ard environent for identifying te syste instability tie. It sould be not tat ard contact could be defined as different values for environent corresponding to operation syste dynaic caracteristics. V. TIFFNE OBERVER Pervious experients [3], [4] sow tat a syste wit tie delay goes to instability wen contacting to a ard environent. As entioned before our syste gets unstable for stiffness values greater tan 400 N/. so ard contact could be defined as k 400 N /. If a stiffness observer is used to detect ard contact instant and ten te passivity controller is turned on, te syste stability for any desired stiffness is guarantied. Using environent odel sown in TABLE I, te stiffness observer equation could be derived as Follows: L B eθ + L. keθ = BeL sθ K e = (2) L θ RL etod could be used to identify k e and b e values but using RL etod increase te syste tie delay and it could result in instability. It is known tat a ard environent as no daping caracteristics, so Be could be eliinated in (2) for siplification. Tis siplification akes te observer to be conservative, because it estiates te stiffness of te external object ore tan wat it is. Te siplified equation can be written as follows: K e = (3) L θ Were θ is easured fro te contact tie. Tis stiffness observer detects ard contacts, if te tresold is set to 400 N/, ten te stiffness observer could be able to detect ard contact, i.e. wen K e 400 N /. Wen te ard contact is detected, te passivity controller is turned on to stabilize te syste. Using ipedance causality approac, and Position () Position () Fig. 11 Contact wit a ard environent (5000 N/), a) te aster and slave position b) te aster and slave otor torque, c) syste energy, witout passivity controller. Energy (N) Energy (N) Fig. 12 Contact wit a ard environent (5000 N/), a) te aster and slave position b) te aster and slave otor torque, c) syste energy, wit passivity controller.

6 supposing tat te operator and environent are passive in nature [8],[5], te passivity controller is ipleented by adding α1 and α 2 to te teleoperation odel as sown in Fig. 10. For ore details about α and estiation see [3]. 1 α 2 VII. IMULATION REULT iulation is done using te iulink/matlab environent. A step torque is applied to te aster ar (F =0.5 N). k e is set to 5000 (N/) in t =1 s. Te syste is supposed to ave a tie delay of 40 s. Fig. 11 sows tat te syste goes to instability wen ard contact occurs (k>=400 N/). Ten te stiffness observer is applied to detect ard contact instant and te passivity controller is activated wen ard contact is occurred. As Fig. 12 sows, tis eliinates oscillations and stabilizes te teleoperated syste. Note tat only one force bounce is produced in ard contact, as sown in fig. 12(b). Te stiffness observer iproves te teleoperated syste transparency. It also provides ore general way for detecting instability. As discussed in section V, te teleoperated systes generally ave negative internal energy in free otion and soft contact, so transition fro positive internal energy to negative internal energy, could not be used as a easure of syste instability. VIII. CONCLUION In tis paper a new approac is developed tat increases te syste transparency. Passivity observer is substituted wit a stiffness observer wic analyses te force generated in slave side to detect wen te slave robot contacts to ard environent. Te stiffness observer detects ard contact by estiating stiffness and turns te passivity controller on wen ard contact occurs. It is discussed tat passivity observer is a conservative observer for instability detection, because passivity is sufficient condition for stability[2]and it is not a necessary condition. Tis as te effect tat in soe cases of free otion and soft contact, te syste igt be stable wile te passivity observer sows negative value and turns on te passivity controller to reduce te syste transparency. iulation results sow tat using stiffness observer increases te syste transparency by eliinating force bounces tat are reported in pervious works. To estiate stiffness, siplification was done by neglecting te daping ratio in stiffness estiation tat ay cause te observer to act conservatively. In future, te researc will be concentrated on developing new observer suc as ipedance observer, cattering observer and also a learning etod to activate te passivity controller and to reduce conservatis in instability detection. REFERENCE [1] Frisoli, E. otgiu and ceccacci, "Teoretical and experiental evaluation of a 2-cannal bilateral force reflection teleoperation syste [2] D. Lawrence, A., tability and transparency in bilateral teleoperation, IEEE Transactions on robotics and autoation, October 1993, Vol. 9, No. 5, pp [3] B. Hannaford, J. Rya, and D. Kwon, table teleoperation wit tie doain passivity control, Proc. IEEE Int. Conf. Robotics and Autoation, 2002 [4] H. Fleer, Control design and perforance analysis of force reflective teleoperators- passivity based approac, doctoral tesis, Departent of acine design, Royal institute of tecnology, [5] R. J. Anderson and M. W. pong, asyptotic stability for force reflecting teleoperators wit tie delay, Int, J. Robot. Res., vol.11, no. 2, pp , [6] B. Hannaford and H. Rya, Tie Doain passivity control of aptic interfaces, IEEE trans. Robotics and Autoation,Vol. 18, No. 1, pp. 1-10, [7] H. Fleer, B. Eriksson and J. Wikander, Passivity issues in bilateral teleoperation- a pase property, doctoral tesis, Departent of acine design, Royal institute of tecnology, [8] Y. Yokokoji, T. Yosikawa, Bilateral control of aster and slave anipulators for ideal kinestetic coupling-forulation and experient, IEEE transaction on robotics and autoation, Vol. 10, No 5, October 1994, pp [9] R. J. Adas and B. Hannaford, table aptic interaction wit virtual environents, IEEE tran.. Robot. Autoat., Vol 15, pp [10] C. A. Desoer and M. Vidyasagar, edback systes: Inputoutput properties, New York: Acadeic, 1975 [11] A. J. van der scaft, L2-Gain and passivity tecniques in nonlinear control", ser. Counications and control engineering series. New york: springer, [12]J. C. Willes, Dissipative dynaical systes-part I: General teory, Arc. Rat. Mec. An.,vol. 45, pp ,1972.

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