CEIT, Mechanical Department, P Lardizabal 15, PO Box 1555,20018 San Sebastian, Spain

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1 Proceedings of the 2003 EEEASME nternational Conference on Advanced ntelligent Mechatronics (AM 2W3) Transparent Telemanipulation in the Presence of Time Delay Kevin B. Fitel, Michael Goldfarbl2, and Angel Rubio Department of Mechanical Engineering, Vanderbilt University, Nashville, Th CET, Mechanical Department, P Lardizabal 15, PO Box 1555,20018 San Sebastian, Spain Abstract This paper presents a method for providing stability and robust transparency in bilateral teleoperator loops that include a time delay in the communication channels. Specifically, the proposed approach incorporates an adaptive Smith predictor within a frequency domain loop shaping approach that addresses both stability and transparency of the teleoperator loop. Experimental results are presented that demonstrate the effectiveness of the approach. 1 ntroduction A bilateral telemanipulator enables human interaction with environments that are remote, hazardous, or otherwise inaccessible to direct human contact. The performance of such a system is often characterized by transparency, which quantifies the capacity of the system to present the undistorted dynamics of the environment to the human operator. A common goal of bilateral telemanipulation is to maintain transparent behavior and overall loop stability in the presence of changes in the dynamics of both the environment and the human operator. The introduction of time delay, often encoetered in the communication channels of a teleoperation system when the slave manipulator is remotely located from the master, can have,deleterious effects on the teleoperation system, and in particular with respect to the stability of the buman/telemanipulator/environment loop. 2. Priorwork Several researchers have focused on the issue of time delay in bilateral telemanipulation. The majority of the research adopts concepts of passivity to ensure stability in the presence of time delay. Anderson and Spong [] derived a control law based on passivity and scattering tbeory to ensure teleoperative stability subject to any time delay. The controller ensures that the communication channel remains passive independent of the time delay, but performance was shown to degrade as the time delay was increased. Niemeyer and Slotine [2] also proposed an approach based on passivity and scattering theory to address time delay in teleoperation. The authors additionally present prediction techniques that further improve the system s performance under time delay. Lawrence [3] addressed time delay in four-channel bilateral telemanipulation. Using passivity theory, filters were derived that ensured the stability of the teleoperation loop in the presence of time delay in the four communication channels. Yoshikawa and Ueda [4] used scattering theory to assess the stability of four conventional teleoperation architectures subject to time delay, and based on this analysis proposed a control scheme that can stabilize a timedelayed force-force type architecture. Munir and Book [5] incorporated a Smith predictor and Kalman filter to improve the performance of a wave-based teleoperator in the presence of a varying time delay. Their predictor compensated for the effects of time delay on the performance of the teleoperator, mitigating the oscillatory behavior exhibited by the time-delayed response. Fite et al. [6] proposed a methodology for the control of a bilateral telemanipulator that utilized a kequencydomain (as opposed to passivity) approach to address both the performance and stability robustness of the buman/telemanipnlator/environment loop. The present work proposes the use of a Smith predictor in the architecture of the bilateral teemanipulator system proposed in [a] to compensate for the destabilizing effects due to the presence of time delay, and includes a model adaptation scheme in the predictor to attain transparency robustness to changes in the dynamics of the environment. hcorporation of the Smith predictor effectively compensates for the destabilizing effects of communication delay, leaving intact the freequencydomain approach presented in [6] for attaining transparency and stability robustness without time delay. The approach enables a less conservative control design relative to passivity-based approaches, and therefore better stability and transparency propelties. 3 Bilateral Telemanipulation with Time Delay Fig. 1 depicts the general notion of two-channel bilateral telemanipulation, in which a human operator interacts with a force-control led^ master manipulator, which is in tum coupled to a position-controlled slave manipulator interacting with an environment. The two subsystems are coupled through scaled motion and force communication channels, where C, and C, represent the motion and force scaling gains, respective1y;and the e- operators represent the time delay present in each communication channel. The motion command from the masterhuman subsystem, X,, is the combined effect of human voluntary motion and the feedthrough motion from the teleoperator loop. The latter results from a commanded motion X, that is filtered by the slave/environment dynamics and in tum generates a force at the master, Fh, which in tum ads upon the human admittance resulting in a component of the commanded motion. nstability will result when the phase lag goldfarb@vuse.vanderilt.edu /03/$ EEE 254

2 in the teleoperator loop is such that this force is out of phase with the commanded motion and the loop gain is at least unity. n order to assess the transparency and relative stability of the loop, the teleoperator system must be restructured so that the human voluntary input, which is essentially an exogenous input (i.e., not part of the feedback loop), is parsed from the teleoperator feedback loop. Consider, for example, a linear single-degree-of-freedom masterhuman subsystem, modeled as shown in Fig. 2. n this model, the master manipulator is considered a simple mass-damper mtem (b., m.) that is kinematically coupled to the human arm. The arm is modeled as a massspring-damper system (mh, b2, k2) with an additional stiffness and damping (bf, kf) at the bumadmaster interface (i.e., compliance in the human grip). Human voluntary input X, is commanded directly into the base of the arm mass-spring-damper system, and is therefore filtered by these dynamics before resulting in motion of the master manipulator, a notion consistent with prior studies in human motor control [7]. The iconic model clearly indicates that slave motion command Xh can result from either the voluntary human input X, or the feedthrough force Fh. Assuming that the master closed-loop force controller is described by the transfer function C, the masterhuman dynamics can be written in the block diagram form shown in Fig. 3(a), where G, G2, and G3 are transfer function matrices given by: where G,=[O e 0 Or C2=[0 0 0 %r G, = C(s1- A)- O (&*+) AL m. % m. m. and C=[-k, -b, k, b,] (5) and where Yh is the admittance of the human operator, given by: a h - [w + (4 + 4 )s + (k, + k, )s (6) - ; = mh4s3 +(m,k, +b,b2)s2+(k,b, + k,b,)s+ k,k, A1 parameters in (1-6) are as defined in Fig. 2. The block diagram of Fig. 3(a) can be rearranged as shown in Figs. 3@) through 3(d) until the respective paths of the human voluntary input X, and the feedthrough force Fh contributing to the command motion X, are separated completely. Specifically, the transfer function describing the force component acting on the human admittance resulting from human voluntary input is given by Gh and the transfer function describing the force component acting on the human admittance resulting kom the feedthrough force is given by G., as shown in Fig. 3(d). The slave/environment dynamics depicted in Fig. 1 can he represented by the equivalent schematics of Figs. 4(a) and 4@), both of which clearly indicate the dynamic coupling between the slave and environment. n the figures, Z., Y,, and C, represent the environment impedance, and slave manipulator admittance and position controller, respectively, and g, represents the closed-loop single-input, single-output slave transfer function, which is clearly a function of the environment impedance. The control architecture described in [a] incorporates two modifications to the two-channel bilateral structure shown in Fig. 1 to address the transparency and stability robustness of the system First, the closed-loop slave dynamics includes local feedback of the interaction force between the slave manipulator and environment, as shown in Fig. 4(c). This component effectively compensates for the coupled slave/environment interaction, yielding closedloop slave dynamics G, independent of the environment, as depicted in Fig. 4(d). Second, the control architecture includes a loop-shaping compensator, G,, operating on the command motion X, that enables frequencydomain manipulation of both the transparency and stability robustness properties of the teleoperation loop. The resulting teleoperator loop can be modeled as shown in Fig. 5, where G, Gh and G, are transfer functions as defined by Figs. 3 and Transparency and Stability Robustness Assuming unity scaling gains and neglecting communication channel time delay, the transmitted impedance (i.e., the impedance of the teleoperator loop as seen by the human operator) is given by: Z, = - F, = G,G,G,Z, (7) SX.4 The transparency transfer function, defined as the ratio of the transmitted impedance to the environment impedance, is written as: G, = G,G,G,,, (8) Sufficient transparency should provide a magnitude of unity and phase of zero within the motor and sensory bandwidth of the human operator. The stability robustness of the teleoperator loop is assessed by rearranging the loop into a Nyquist-like unityfeedback structure, enabled by parsing the human voluntary force 60m the feedthrough force, as previously described. The resulting open-loop transfer function goveming the stability robustness is given by: G = -G,G,G,Z,Y, (9) 255

3 Fig. 1. Two channel bilateral telemanipulation. The loop-shaping compensator, G,, is chosen such that the mp provides the desired bandwidth of transparency while maintaining sufficient stability robustness properties. The compensation is effectively addressed with a lead-lag compensator of the form: Fig. 2. Model of masterhuman dynamics. -h--dl"u (4 Fig. 3. Parsing the masterhuman dynamics.1nrirowmmcnt... Fig m, w-llym& la) Slave/environment dynamics. x rl.1 sl.&~p.n."h Fig. 5. Time delay in each communication channel. where the parameters k,, N, ai, and K~ are utilized to shape the compensator in the eequency domain. 3.2 Time Delay Compensation n the case that a time delay Tis present in the communication channels, the open-loop and transparency transfer function are given by: G = -G,G,G,Z,Y, e-"' (11) and G, = G,G,G, e-ztj. (12) An approach originally proposed by Fite et al. [6] for time delay compensation involved the use of a low order Pad6 approximation of e2t as a supplement to the compensator, G,. This approach, however, produced an unstable closed loop. Rather than utilize the unstable inverse Pad6 approximation, one could alternatively utilize a model-based approach to time delay compensation. The method proposed by Smith [8] to compensate fa! the adverse effects of time delay on the stability of feedback systems utilizes a model-based prediction to effectively cancel the effects of time delay on the characteristic equation of the closedloop system. Mnnir and Book [5] utilize such a predictor, in combination with a Kalman filter, to achieve enhanced performance ib a wave-based teleoperation system. The form of a Smith predictor in the context of the teleoperator loop described in Fig. 5 is given by: P=(l-e-*n)G,&s (13) where 6, represents the model of the closed-loop slave dynamics and 2. represents the model of the environment impedance. Fig. 6 depicts the bilateral teleoperation architecture with the predictor explicitly sham. n the ideal case (i.e., when the models of the slave and environment correspond to the actual slave and environment dynamics), the effects of time delay on both the stability and transparency of the teleoperation loop would be removed. As the models for the slave and environment deviate fiom the actual dynamics, the presence of time delay arises in both the closed-loop characteristic equation and the transparency transfer function. n order to directly assess the stability robustness of the teleoperation loop with time delay and the model-based predictor, the loop is rearranged into a Nyquist-like structure. Assuming unity scaling gains, the closed-loop transfer function governing the predictor dynamics is given by: 256

4 and the open-loop transfer function becomes: G = -G,G,G,G,Z,Y,e (15) ncluding the effects of the predictor on the impedance transmitted to the human operator, the transparency transfer function is then given by: 2? z, G, =G,G,G,e-* +G,6,G,(l-e-Z )- (16) To the extent that models for the dynamics of the slave and environment differ kom that of the actual slave and environment, the transparency transfer function will depend upon the time delay present in the comuuication channels. Though the dynamics of the position<ontrolled slave manipulator are unlikely to change, the environment impedance will in general vq. As such, the transparency of the loop will in general be maintained only for small deviations of the actual environment away kom the model. - - _ _ S&? tailed explanation of the important concepts of modelbased adaptation. Fig. 7 depicts the bilateral teleoperation system with inclusion of a general adaptive Smith predictor. For an environment characterized by a pure stiffness, the actual impedance is given by: and the modeled impedance:. The adaptation law for the modeled stiffness parameter is then given by: 6, = Y( F: - 1kx; ) (19) This fundamental approach can be extended to more general environments with little difficulty. For the purposes of this paper, the environment impedance used in the experimental demonstration is a pure stiffness for which the above adaptation law is directly applicable.. -0llmdn -- Fig. 7. Architecture with adaptive Smith predictor. 3.3 Environment Model Adaptation Adaptive control techniques can be applied to the teleoperation loop in order to adapt the model of the environment in the Smith predictor to the actual environment dynamics. n such a scheme, the measured motion of the coupled slave/environment (is., the input to the environment impedance) is used to compute the predicted interaction force. Comparison of the predicted and actual output forces of the environment impedance yields an error used to adjust the parameters of the environment model. Provided that the form of the environment model is an adequate representation of the true impedance, such an adaptation method should prove effective in tuning the parameters of the model. Slotine and Li [9] provide a de- Fig. 8. (Left) Top view of slave manipulator interacting with an environment stiffness and (right) side view of human operator gripping the master manipulator. 4 Experimental Teleoperation with Time Delay To verify the proposed time-delay compensation, the Smith predictor with model adaptation was experimentally implemented on a single degree-of-keedom telemanipulation system. Both master and slave consisted of a DC brushed servomotor (PM1 N12M4T) and a rotary potentiometer (Midon CPP45B) for rotor position measurement. The rotational motion of the motor was transformed to linear motion via rack and pinion. A rotational inertia was additionally mounted to each servomotor to represent the inertia of a typical manipulator. The master manipulator incorporated a handle mounted on the end of a cantilever beam coupled to the translating rack to provide an intelface with the human operator. Strain gages mounted on the cantilever measured the interaction forces occurring between the human operator and the manipulator. The slave manipulator incorporated a cantilever beam that connected its endpoint to a pair of springs suppolted by a shaft mounted parallel to the linear motion. The springs imposed a bidirectional stiffness in series with 257

5 the slave motion, providing a simple yet challenging environment with which to assess the teleoperative performance. Similar to the master, the slave incorporated strain gages on the cantilever beam to measure the interaction forces between the slave and environment. Each manipulator was capable of exerting a maximum continuous force of approximately 45 N through a workspace of approximately 6 cm. The slave and master manipulators are, pictured in Fig. 8. The control architecture was implemented with the real-time interface provided by MATLAB/Simulink (The Mathworks, nc.) at a sampling rate of 1 E. The transparency of this system was assessed by measuring the experimental fkquency response of the transparency transfer function. Specifically, the human operator excited the closed-loop system with a semi-random excitation. Measurements of the motion, and resulting imposed force, occurring at the interface between the master and human operator were made over a 30 second time interval. The experimental ffequency response was obtained from the measured data from the ratio of the cross power to the auto power spectra. The transparency transfer function was then obtained by dividing the experimental 'measure of the transmitted impedance by the actual environment impedance. The stability margins were experimentally obtained by breaking the loop at the motion command to the slave and introducing sinusoidal excitation to measure the openloop (time-based) response of.the system. The gain margin of the loop was determined by measuring the sinusoidal magnitude of the loop transfer function for excitation at the frequency where the output human motion lagged the input by 180'. The phase margin was found by measuring the amount of lag between the input and output for excitation at the-frequency for which the sinusoidal magnitude of the output equals that of the input. mplementation of the (adaptive) Smith predictor requires models for both the closed-loop position-controlled slave manipulator and the environment. The nominal slave dynamics consist of an inertia that models the linear transformation of the rotary inertia coupled to the rotor and a damping term to represent the viscous damping in the bearings and brushes of the motor. The admittance of the slave manipulator is therefore given by: 1 r, =- (20) m,s + b, where m, = 4.5 kg and bs = 80 Nsim. The parameters were identified &om experimental data of the slave manipulator. The slave compensator is a proportionalderivative controller that includes a fust-order filter to attenuate high frequency noise resulting from differentiation. The compensator is given by: t s + c, k, =- S+l where kp8 = 2360 N/m, kb = 260 Ndq and = 0.01 s. The resulting closed-loop transfer fimction goveming the model of the position-controlled slave manipulator is written as: The environment impedance was giveh by (17), where the nominal stiffness was k. = 750 N/m t should be noted that while the Smith predictor (without adaptation) requires a predetermined numerical value for the stiaess of the environment model, the adaptive predictor begins with an initial value of zero for the modeled stifhess and quickly converges to the correct value (i.e., no parameterization of the environment was required). A proportional force controller was implemented on the master manipulator. Similar to the slave, the nominal master dynamics consist of an inertia and viscous damping. Though not used in the control architecture, the parameters of the master are given by m. = kg and b, = 100 Ndm The compensator used to control the force occurring at the interface between the master manipulator and human operator is given by C, = kf where kp, = 8 NM. The loop shaping compensator, G,, was experimentally designed such that the teleoperative loop exhibited a nominal (is., without time delay) transparency bandwidth of 3 Hz and nominal stability margins of 8 db and 35'. The resulting loop-shaping compensator is dehed by (10) and the parameters k, = 1.66, +l, a~0.133, and q= TimeDeGy A time delay of T = 0.05 seconds was imposed on each commnnication channel between master and slave. Note that since two communication l i i exist in the control loop, the time delay for purposes of the closed loop is 2T, or in this case 0.1 seconds. With this time delay, the previously described teletnanipulation system with the previously described compensator was quite unstable, with measured gain and phase margins of -9.5 db and -54, respectively. Due to the degree of instability, the transparency for the uncompensated system could not be experimentally measured. 4.2 Transparency and Stability Robustness nclusion of the Smith predictor as shown in Fig. 6 robustly stabilized the teleoperation system in the presence of the time delay, providing measured gain and phase margins of l l db and 29'. respectively. For the (design) environment of 750 N/m, the architechlre provides a transparency bandwidth of approximately 3 Hz, which is the same as the architecture without time delay and Smith predictor. This transparency, however, is not particularly 258

6 robust to variations in the environment dynamics. Fig. 9 shows the teleoperative transparency for environment stiffnesses ranging &om 75 Nim to 1275 N/m, implemented by changing the springs attached to the output of the slave manipulator. Provided that the actual environment stiflkess remained larger than 500 N/m, the transparency of the loop with the Smith predictor remained around 3 Hz. As the stiffhess of the environment fell below 500 N/m, the transmitted impedance became considerably amplified, and the transparency suffered. The lack of transparency robustness in the presence of environment variation results &om the presence of the environment in the model for the Smith predictor, as indicated by (16). -Km.,. Fig. 9. The transparency transfer function for values of sz. ranging &om 75 N/m to 1275 N/m, using the Smith predictor. i.-rm Fig. 10. The transparency transfer function for values of sz. ranging fiom 75 N/m to 1500 N/m, using the adaptive Smith predictor. 4.3 Transparency Robustness Due to the lack of transparency robustness achieved using the nominal Smith predictor, the previously described adaptation scheme was implemented in the control architecture. nclusion of the adaptive Smith predictor provided measured gain and phase margins of 12 db and 35, respectively. While these margins represent a slight improvement in stability robustness relative to implementation without adaptation, the primary purpose for including the adaptation is to provide hslnsparency robustness, ena- bling a desired transparency bandwidth in the case of significant parametric variation in the environment. Fig. O shows the measured transparency for environment stiffnesses ranging %om 75 N/m to 1500 N/m. The loop with the adaptive Smith predictor exhibited a transparency bandwidth of at least 2 Hz for each value of the actual environment impedance. nclusion of the adaptation scheme in the predictor model therefore resulted in good transparency robustness for environment parametric uncertainty for the timedelayed teleoperation loop, as evidenced by comparison of Figs. 9 and O. 5 Conclusion An adaptive Smith predictor was introduced into a previously published loop shaping approach to telemanipulator control that provides robust compensation in the presence of time delay. The approach was shown to effectively provide robust stability, and additionally was shown to maintain a uniform transparency bandwidth independent of parametric variation in the environment. References []Anderson, R J. and Spong, M.W., Bilateral Control of Teleoperators with Time Delay. EEE Transactions on Automatic Control, Vol. 34, No. 5, pp ,1989. [ZNiemeyer, G. and Slotine, J. E., Stable Adaptive Teleoperation. EEE Journal of Oceanic Engineering, Vol. 16,No. 1,pp , [3] Lawrence, D.A., Stability and Transparency in Bilateral Telemauipulation. EEE Transactionr on Robotics anddutomation, Vol. 9, No. 5, pp , [4] Yoshikawa, T. and Ueda, J., Analysis and Control of Master-slave systems with Time Delay. Proceedings of the EEE Conference on ntelligent Robots and Systems, pp ,1996. [5] Munir, S. and Book, W. J., ntemet-based Teleoperation Using Wave Variables with Prediction. EEE/ASME Transactions on Mechatronics, Vol. 7, No. 2, pp ,2002. [6]Fite, KB., Speich, J.E., and Goldfarb, M., Transparency and Stability Robustness in Two-Channel Bilateral Telemanipulation. ASME Joumal of Dynamic Systems, Measurement, and Control, Vol. 123, No. 3, pp ,2001. [7]Hogan, N., Mechanical mpedance of Single- and Multi-Articular Systems, in Multiple Muscle Systems: Biomechanics and Movement Organization, J.M. Winters and SLY. Woo (ed.), Springer-Verlag, [S Smith, O.J.M., Closer Control of Loops with Dead Time. Chemical Engineering Progress, Vol. 53, No. 5,pp , [9] Slotine, J. E. and Li, W., AppliedNonlinear Control, Prentice Hall, Englewood Cli&,NJ,