THE INTERNET-BASED TELEOPERATION: MOTION AND FORCE PREDICTIONS USING THE PARTICLE FILTER METHOD

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1 Proceedngs of the ASME 2 Internatonal Mechancal Engneerng Congress & Exposton IMECE2 November 2-8, 2, Vancouver, Brtsh Columba, Canada IMECE THE INTERNET-BASED TELEOPERATION: MOTION AND FORCE PREDICTIONS USING THE PARTICLE FILTER METHOD Jae-young Lee School of Engneerng Scence Smon Fraser Unversty Burnaby, BC, Canada jla55@sfu.ca Shahram Payandeh School of Engneerng Scence Smon Fraser Unversty Burnaby, BC, Canada shahram@cs.sfu.ca Ljljana Trajkovć School of Engneerng Scence Smon Fraser Unversty Burnaby, BC, Canada ljlja@cs.sfu.ca ABSTRACT In ths paper, we present moton and force predctons n Internet-based teleoperaton systems usng the partcle flter method. The partcle flter, also known as the sequental Monte Carlo (SMC method, s a probablstc predcton or estmaton technque wthn a sequental Bayesan framework: Data at a current tme step are predcted or estmated by recursvely generatng probablty dstrbuton based on prevous observatons and nput states. In ths paper, we frst formulate the partcle flter method usng a predcton-based approach. Moton and force data flows, whch may be mpared by the Internet delay, are formulated wthn a sequental Bayesan framework. The true moton and force data are then predcted by employng the predcton-based partcle flter method usng the mpared observatons and prevous nput states. We performed experments usng a haptc devce that nteracts wth a mechancs-based vrtual 3D graphcal envronment. The haptc devce s used as a master controller that provdes postonng nputs to a 4-degree of freedom (4-DoF vrtual robotc manpulator whle recevng feedback force through nteractons wth the vrtual envronment. We smulate the Internet delay wth varatons typcally observed n a user datagram protocol (UDP transmsson between the master controller and the vrtual teleoperated robot. In ths expermental scenaro, the partcle flter method s mplemented for both moton and force data that experence the Internet delay. The proposed method s compared wth the conventonal Kalman flter. Expermental results ndcate that n nonlnear and non-gaussan envronments the predcton-based partcle flter has dstnct advantage over other methods. INTRODUCTION An Internet-based teleoperaton system s an nteractve applcaton where though a master devce, a human operator transmts moton data whle smultaneously recevng reflectng force data from a slave robot controller. Unlke other Internet applcatons that manly focus on the relable data transmsson, nteractve applcatons are hghly delay-senstve. The Internet delay, whch s unknown and vares over tme accordng to network condtons, may cause nstablty of an overall teleoperaton system. Furthermore, the transmtted moton and force data are often mpared by sgnfcant delay and delay jtter durng the Internet transmsson []. Varous approaches have been suggested n order to solve the tme delay ssue of Internet-based teleoperaton systems. In the area of control systems, the wave varables transformaton and ts extensons have focused on the stablty of overall teleoperaton systems n the presence of constant delay [2], [3], Copyrght 2 by ASME

2 [4]. In the area of Internet transport protocols, several proposals have been suggested based on modfcatons to transport control protocol (TCP and user datagram protocol (UDP to enable faster transmssons of data packets [5], [6]. In the area of sgnal processng, predcton-based methods that perform moton and force predctons have been proposed [7], [8]. The Kalman flter method, whch provdes a recursve soluton to the lnear predcton and estmaton, was proposed as a predcton-based approach [9]. These methods have been used to compensate for the transmtted moton and force data that are mpared by varatons of the Internet delay. Moton and force data are often dffcult to predct n systems wth nonlnear and non-gaussan characterstcs. For example, fne hand moton commands from a master controller may be hghly nonlnear and the tradtonal Kalman flter may fal to provde ther accurate predcton. Force data may be even more dffcult to predct snce the data need to be sent at relatvely hgh frequences to guarantee realstc force wthout dscontnuty and to avod closed-loop nstablty of an overall teleoperaton system. Furthermore, the moton and force data may contan a non-gaussan nose such as an mpulse nose durng the transmsson, whch leads to further challenges n predcton. The partcle flter method, also known as the bootstrap flter or the Condensaton, s a sequental Monte Carlo (SMC method that provdes a sub-optmal soluton n recursve Bayesan approaches [], []. Due to ts robust predcton and estmaton performance n nonlnear and non-gaussan envronments, the partcle flter method has been wdely appled n the areas of communcatons, mage and speech sgnal processng, control systems, and robotcs [2], [3]. Snce the partcle flter method can be appled to any sgnal usng a dscrete tme state-space formulaton, t has been appled to nonlnear moton and force data flows n an Internet-based teleoperaton system [4]. In ths paper, we employ the partcle flter method to predct moton and force data that may be nonlnear and non- Gaussan n addton to beng subject to the Internet delay. We frst ntroduce the predcton-based partcle flter method appled to moton and force data flows usng a dscrete tme state-space formulaton. We descrbe an expermental study based on the mplemented partcle flter method [4]. In ths paper, the proposed method s verfed n both nonlnear and non-gaussan envronments. We also present the comparson of predcton performance between the proposed partcle flter and the conventonal Kalman flter methods. The stablty ssue of an overall teleoperaton system n the presence of the Internet delay s dscussed. MOTION AND FORCE PREDICTIONS IN INTERNET- BASED TELEOPERATION SYSTEMS Moton data generated from a master controller are transmtted to a slave controller through the Internet. Based on the desgn of the slave controller, reflected force data are generated by any contact wth an object or surroundng envronment and they are fed nto the master controller through the Internet. A smple llustraton of moton and force data flows n an Internet-based teleoperaton system s shown n Fgure. The moton and force data are represented n dscrete tme statespace formulatons, whch are confgured n a recursve Bayesan framework. Snce the moton and force data experence varatons of the Internet delay, the true data may be mpared and stablty of an overall teleoperaton system may not be mantaned. In order to compensate for such Internet delay, we employ the predcton-based partcle flter method for the moton and force data flows. x k fˆ f% k n x% k n xˆ Fgure. State-space formulatons of moton and force data flows n an Internet-based teleoperaton system. The proposed predcton approach employs the partcle flter method. Moton Predcton The moton data flow n an Internet-based teleoperaton system, whch conssts of postons samples over tme, s represented as a dscrete tme state-space formulaton as shown n Fgure. In a sngle DoF teleoperaton system, the true poston x k at tme k s transmtted through the Internet and t s delayed by n tme steps. The mpared observaton receved at the slave controller can be expressed as x% k n. The dscrete tme nonlnear moton data flow n a state-space formulaton may be expressed as: xk = gk( xk, uk, ( x % k n= hk n( xk n, v k n where x k and x% k n are the system state at tme k, and the system observaton at tme k n, g k and h k n are nonlnear state and observaton transton functons, and u k and v k n are f k 2 Copyrght 2 by ASME

3 state and observaton nose sequences, whch may be non- Gaussan. In a state-space formulaton, the predcton of the true poston at tme s calculated based on the current state x k n and avalable observaton x% : k n. In a recursve Bayesan approach, the optmal predctor of the true state at tme k n+ s expressed by the condtonal mean: xˆ k n k n= xk n+ p( xk n x% + + : k n dx where xˆ k n denotes the predcton of the state x gven avalable observatons x% : k n. The posteror densty n (2 s evaluated recursvely solvng two densty functons [9]: k n, (2 p( x x% = p( x p( x x% (3 : k n xk n k n : k n dxk n px ( % k n x :k n = px (% px ( x% k n xk n px (% x% k n k n : k n : k n. (4 u k to have a Gamma dstrbuton, whch s typcally observed n an mpulse nose [7]. The non-gaussan nose can be modeled usng the Gamma densty functon: α β p( uk = u ( α! α u k k e β for u. (9 The mean and varance of the Gamma densty functon (9 are α β and α β 2, respectvely. Note that the Gamma densty functon apples to the state nose uk and does not apply to the observaton nose v k. Gven these nose assumptons, the mportance weght (8 s further smplfed as: 2 ( xk n x k n 2 w e σ. ( = % Equaton ( gves the mportance weght of the -th partcle at tme k n+ and needs to be normalzed so that: k Equatons (3 and (4 provde the predcton and update procedures for the optmal soluton, respectvely. They are not computatonally tractable due to ther ntegral forms. Hence, the partcle flter method s used to approxmate the posteror densty as a suboptmal soluton. Based on the predcton-based partcle flter method, (3 s approxmated as [5], [6]: N s + x% k n : w δ ( k n+ = px ( k n x x, (5 where N s s the number of partcles, δ ( s the Drac delta functon, and w s the mportance weght computed as: w px (% x px ( x, wk n qx ( xk nx% %. (7 + qx ( k n + xk n, xk n + = px ( k n xk n w wk np( xk n xk n k n. (6 In order to mnmze the varance of mportance weghts, the mportance densty q( may be chosen to be equal to the pror densty such that: Hence, the mportance weght s smplfed as: %. (8 In ths paper, we consder the moton data flow n nonlnear and non-gaussan envronments. Hence, we assume the state nose N S wk n + = =. ( The resamplng step should be performed to regenerate the predcted samples based on measurements of the mportance weghts. When cumulatve dstrbuton functons (CDF of the normalzed weghts ( are constructed, each element of the CDF s compared wth a unformly dstrbuted functon n order to determne whether the weghts are hgh or low. Based on ths comparson, partcles wth low weghts are elmnated and partcles wth hgh weghts are used to predct the true states. Therefore, a new set of states x s determned and ths procedure s repeated for the next tme step. Each step of the partcle flter method for the moton data predcton s descrbed n Table. Table. Partcle Flter Method for Moton Predcton. Step. Intalzaton Randomly choose the ntal state and defne ntal parameters Step 2. Predcton Evaluate x ~ p( x x, N k n S Step3. Update Evaluate mportance weghts (8 and normalze. Step 4. Resamplng Multply/suppress samples wth hgh/low mportance weghts Step 5. Iteraton Increase tme step and go to Step 2. 3 Copyrght 2 by ASME

4 Force Predcton Force data, generated by any contact wth an object and fed nto the master controller, may be predcted by a smlar approach. As shown n Fgure, the transmtted force data over the Internet may also be formulated wthn a nonlnear and non- Gaussan state-space framework. The true force data are then predcted by the predcton-based partcle flter method gven avalable observatons. For a sngle DoF teleoperaton system, let f k be the true force data generated by the slave controller at tme k. The force data transmtted to the master controller through the Internet s delayed by n tme steps. Ths s the mpared observaton that may be expressed as % fk n. Smlar to the representaton of the moton predcton (2, the predcton of the true force f s calculated based on the current state f k n and avalable observatons f % :k n. Hence, n a recursve Bayesan approach, the optmal predctor of the true force at tme k n+ s gven as: Assembly Robot Arm (SCARA manpulator confguraton s shown n Fgure 2. Based on movements from the master controller, contact force data that feed nto the master controller are generated when the tp of the SCARA manpulator colldes wth objects n the graphcal scene. In ths experment, postons of the 4-DoF vrtual SCARA robot are knematcally mapped to the master controller, whch s able to manpulate 4-DoF. In conjuncton wth the mechancs-based model of the 3D graphcal envronment, the haptc devce provdes postonng nputs to the slave controller whle recevng feedback force through nteractons wth the vrtual envronment. fˆ k n= fk n p( fk n f% + + : k n dfk n. (2 Usng the predcton-based partcle flter method, the predcted force fˆ k n s calculated by approxmatng the posteror densty functon p( f f % : k n by usng (5 (8. Smlar to the moton predcton case, the force predcton s performed by computng each step n Table. After the ntalzaton step, whch randomly selects an ntal state of moton data, the predcton step s performed to obtan samples f from the pror densty p( f, where f k n N. In the update step, the new state f s assgned s by usng mportance weghts. In the force predcton case, we assume that the non-gaussan state nose s modeled usng the Gamma densty functon (9. Then, after normalzng the computed mportance weghts, the resamplng step s performed n order to regenerate a new set of states f based on hgh weghted samples. EXPERIMENTS In order to evaluate the proposed partcle flter method for Internet-based teleoperaton systems, we performed experments usng the PHANTOM Desktop haptc devce as a master manpulator. The expermental setup consstng of the haptc devce and the vrtual robot based on a Selectve Complance Fgure 2. Expermental scenaro: The PHANTOM Desktop haptc devce and vrtual 3D graphcal representaton are used for master and slave controllers, respectvely. TCP and UDP are two wdely used Internet transport protocols. TCP, whch provdes relable data transmsson, often ntroduces relatvely large varatons of the Internet delay due to ts retransmsson and congeston control mechansms. Hence, UDP has been suggested as a transport protocol for Internetbased teleoperaton systems even though t does not guarantee relable data transmsson and may cause data loss []. In ths experment, we employed a model for the Internet delay and used parameters typcally observed n a UDP transmsson [], [7]. A random number generator was used to generate delay varatons, whch are shown n Fgure 3. The maxmum and average delays over a fve-second nterval were 32 msec and 63 msec, respectvely. In ths experment, we assumed that both the moton data transmtted to the slave controller and the force data fed to the master controller experenced the dentcal delay shown n Fgure 3. 4 Copyrght 2 by ASME

5 Delay (ms Tme (s Fgure 3. The Internet delay wth UDP transmsson. Moton and Force Predcton To verfy the predcton performance of the partcle flter method, one-dmensonal moton and force data were collected over a fve-second nterval. Snce the expermental scenaro s based on the 3D vrtual graphc representaton, the samplng rate of the moton data was 5 Hz so that human eyes could perceve contnuous moton. The samplng rate of the force data rendered by the PHANTOM Desktop haptc devce was, Hz n order to mantan realstc force wthout dscontnuty. In general haptc applcatons, t s advsed that moton and force data should be sampled at no less than 3 Hz and, Hz, respectvely to prevent dscontnuty of haptc data and to preserve closed-loops stablty of an overall teleoperaton system. 6 5 True poston Delayed poston 6 5 True poston Predcted poston 4 4 Axs Poston (mm 3 2 Axs Poston (mm Tme (s Tme (s 2.5 True force Delayed force 2.5 True force Predcted force Axs Force (N Axs Force (N Tme (s Fgure 4. True and delayed moton data (top and true and delayed feedback force data (bottom collected from the master and slave controllers over a fve-second nterval Tme (s Fgure 5. Predcted moton data (top and feedback force data (bottom collected from the slave and master controllers over a fve-second nterval. 5 Copyrght 2 by ASME

6 The one-dmensonal moton and force data collected at the master controller and slave controller, respectvely, are shown n Fgure 4. Also shown are observatons of the moton and force data that are delayed based on the delay shown n Fgure 3. The delayed moton and force data are mpared by varatons of the Internet delay as shown n Fgure 4. Based on the collected moton and force data, we smulated non-gaussan state nose usng the Gamma densty functon (9 wth α = 2 and β = 3. We then evaluated the predcton performance of the partcle flter method. In both moton and force predcton cases, we used 2 partcles. The predcted moton and force data usng the proposed partcle flter method are shown n Fgure 5. In order to compare them wth the true data, transmsson delays of the predcted moton and force data were not consdered. In general, a large number of partcles mproves the predcton performance. However, t ntroduces computatonal complexty that results n relatvely longer computaton tme. In Internet-based teleoperaton systems, such computatonal delay may affect stablty of an overall teleoperaton system. Hence, a number of partcles should be selected effcently to avod an ncrease n the computatonal cost. In Table 2, the mean square errors (MSE of the moton and force predctons are computed when the number of partcles vares from to 5. The MSE were measured when the Gamma densty functon was added as a non-gaussan nose. Snce errors tend to converge, a large number of partcles may not be necessary. Number of partcles Table 2. Number of Partcles vs. MSE. Moton error (mm Force error (mn * The moton and force unts are mllmeter and mllnewton, respectvely. Comparson wth the Kalman Flter The Kalman flter s a well-known recursve state predctor or estmator that provdes an optmal soluton n Bayesan probablstc approaches. Snce the tradtonal Kalman flter s only sutable n lnear and Gaussan envronments, the extended Kalman flter has been used to predct or estmate states of nonlnear dynamc systems [8]. In ths experment, we mplemented the extended Kalman flter to the force predcton case shown n Fgure 5. The comparson of the force predcton performance between the partcle flter and extended Kalman flter s shown n Fgure 6. Snce the largest delay occurs between 3. and 3.5 seconds as shown n Fgure 3, we present the comparson of predcton performance wthn that range n Fgure 6. The MSE of the partcle flter and extended Kalman flter are 98 and 846 mn, respectvely. The proposed partcle flter method outperforms the Kalman flter n nonlnear and non-gaussan envronments, as shown n Fgure 6. Axs Force (N Tme (s True force Partcle flter Kalman flter Fgure 6. Predcton performance of partcle flter and extended Kalman flter n nonlnear and non-gaussan envronments. DISCUSSION AND CONCLUSION In ths paper, we presented moton and force predctons n Internet-based teleoperaton systems. The predcton-based partcle flter method was ntroduced and appled for moton and force data flows modeled by state-space formulatons. Experments usng the haptc devce n conjuncton wth a vrtual teleoperator demonstrated that the partcle flter method was well suted for predctng moton and force data, whch may be mpared by the hghly uncertan Internet delay. Furthermore, the partcle flter method outperformed the conventonal Kalman flter n extreme condtons such as nonlnear and non-gaussan envronments. One lmtaton of the partcle flter method s ts computatonal complexty. Snce ths method s used n a closed-loop teleoperaton system, computatonal complexty that may cause addtonal delay s undesrable. The partcle flter method that adaptvely selects a number of partcles has been ntroduced for real-tme trackng [9]. A large number of partcles may be necessary n the case of predctng an ntal state or hghly uncertan state. Otherwse, a small number of partcles may be used f uncertanty s low and moton and reflected force data at the next state are predctable. In ths paper, we ntroduced a sgnal processng approach to force-reflectng teleoperaton systems to overcome the varyng Internet delay. Such sgnal processng approach may be combned wth an approprate controller n order to address 6

7 stablty of an overall teleoperaton system. In the case of constant delay, the wave varables transformaton has been used to acheve stablty [2]. However, n the presence of varyng delay, t s dffcult to address stablty of an overall teleoperaton system snce moton and force data may be mpared durng transmsson. In ths paper, we demonstrated that mparments of haptc data are compensated by a predcton-based approach. By ntroducng a novel controller, the proposed sgnal processng approach may enhance the stablty even n the presence of the varyng Internet delay. REFERENCES [] E. Kamran, H. Momen, and A. Sharafat, Modelng Internet delay dynamcs for teleoperaton, n Proc. IEEE Int. Conf. on Control Applcatons, Toronto, ON, Canada, Aug. 25, pp [2] G. Nemeyer and J. Slotne, Desgnng force reflectng teleoperators wth large tme delays to appear as vrtual tools, n Proc. IEEE Int. Conf. on Robotcs and Automaton, Albuquerque, NM, USA, Apr. 997, pp [3] K. Kawashma, K. Tadano, G, Sankaranarayana, and B. Hannaford, Blateral teleoperaton wth tme delay usng modfed wave varables, n Proc. IEEE Int. Conf. on Intellgent Robots and Systems, Nce, France, Sept. 28, pp [4] T. Mrfakhra and S. Payandeh, On usng delay predcton n controllng force reflectng teleoperaton over the Internet, Robotca, vol. 23, no. 6, pp , 25. [5] Y. Uchmura, T. Yakoh, and K. Ohnsh, Blateral robot system on the real-tme network structure, IEEE Trans. on Industral Electroncs, vol. 5, no. 5, pp , Oct. 24. [6] R. Wrz, M. Ferre, R. Marín, J. Barro, J. Claver, and J. Ortego, Effcent transport protocol for networked haptcs applcatons, n Proc. The 6th Int. Conf. on Haptcs: Percepton, Devces, and Scenaros, Madrd, Span, June 28, vol. 524, pp [7] S. Clarke, G. Schllhuber, M. Zach, and H. Ulbrch, Predctonbased methods for teleoperaton across delayed networks, Sprnger-Verlag, Multmeda Systems, vol. 3, no. 4, pp , Oct. 27. [8] S. Clarke, G. Schllhuber, M. Zach, and H. Ulbrch, The effects of smulated nerta and force predcton on delayed telepresence, Presence, vol. 6, no. 5, pp , Oct. 27. [9] S. Munr and W. Book, Internet-based teleoperaton usng wave varables wth predcton, IEEE/ASME Trans. on Mechatroncs, vol. 7, no 2, pp , June 22. [] M. Sanjeev Arulampalam, S. Maskell, N. Gordon, and T. Clapp, A tutoral on partcle flters for onlne nonlnear/non-gaussan Bayesan trackng, IEEE Trans. on Sgnal Processng, vol. 5, no. 2, pp , Feb. 22. [] A. Doucet, N. de Fretas, and N. Gordon, An ntroducton to sequental Monte Carlo methods, n Sequental Monte Carlo Methods n Practce, A. Doucet, N. de Fretas, and N. Gordon, Eds. New York: Sprnger-Varlag, 2, pp [2] R. Mottag and S. Payandeh, An overvew of a probablstc tracker for multple cooperatve trackng agents, IEEE Int. Conf. on Advanced Robotcs, Seattle, WA, USA, July 25, pp [3] N. Farfeld, G. Kantor, and D. Wettergreen, Towards partcle flter SLAM wth three dmensonal evdence grds n a flooded subterranean envronment, n Proc. IEEE Int. Conf. on Robotcs and Automaton, Orlando, FL, USA, May 26, pp [4] J. Lee, S. Payandeh, and L. Trajkovć, Applcaton of predcton-based partcle flters for teleoperatons over the Internet, n Proc. IASTED Int. Conf. on Robotcs and Applcatons, Cambrdge, MA, USA, Nov. 29, pp [5] G. Ktagawa and S. Sato, Monte Carlo smoothng and selforgansng state-space model, n Sequental Monte Carlo Methods n Practce, A. Doucet, N. de Fretas, and N. Gordon, Eds. New York: Sprnger-Varlag, 2, pp [6] F. Desbouvres and B. At-El-Fquh, Drect versus predctonbased partcle flter algorthm, n Proc. IEEE Workshop on Machne Learnng for Sgnal Processng, Cancun, Mexco, Oct. 28, pp [7] L. Smth and V. Atken, The auxlary extended and auxlary unscented Kalman partcle flters, n Proc. IEEE Canadan Conf. on Electrcal and Computer Engneerng, Vancouver, BC, Canada, Apr. 27, pp [8] T. Robertazz and S. Schwartz, On applyng the extended Kalman flter to nonlnear regresson models, IEEE Trans. on Aerospace and Electronc Systems, vol. 25, no. 3, pp , May 989. [9] C. Kwok, D. Fox, and M. Mela, Real-tme partcle flters, Proceedngs of the IEEE, vol. 92, no. 2, pp , Mar