Position synchronization for an uncertain teleoperation system with time delays using L1 theory

Document Type : Article

Authors

1 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, P.O. Box 1439957131, Iran

2 - School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, P.O. Box 1439957131, Iran - Department of Mechanical Engineering, Lassonde School of Engineering, York University, Toronto, Canada

3 Biomechatronics and Cognitive Engineering Research Lab, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, P.O. Box 16765163, Iran

Abstract

The problem of position tracking in teleoperation systems containing latencies and dynamical uncertainties is addressed in this work. In many applications, such as telesurgery, safe interaction with the external environment is a factor which may undermine the synchronization of the positions. For nondestructive contact with the environment, in addition to an errorless steady-state position tracking, the closed-loop system requires to have a response with the least possible overshoot. To this end, a state-feedback controller based upon L1 theory is proposed in this work. The compensator is synthesized utilizing the linear matrix inequality (LMI) technology, and the asymptotic stability of the system is verified employing Lyapunov-Krasovskii functional. Another advantage of the proposed control scheme is that it is robust to asymmetric randomly varying time delays in the communication channels. The L1-based controller is finally compared to the well-known sliding mode controller via simulation, and is proved to outperform it from maximum error point of view, while preserving low steady-state error. The proposed controller is also illustrated to be effective even in the presence of model uncertainties.

Keywords


References:
1. Meshram, D.A. and Patil, D.D. "5G enabled tactile internet for tele-robotic surgery", Procedia Computer Science, 171, pp. 2618-2625 (2020).
2. Kebria, P.M., Abdi, H., Dalvand, M.M., et al. "Control methods for internet-based teleoperation systems: A review", IEEE Transactions on Human-Machine Systems, 49(1), pp. 32-46 (2018).
3. Tabatabaei, S.H., Zaeri, A.H., and Vahedi, M. "Design an impedance control strategy for a teleoperation system to perform drilling process during spinal surgery", Transactions of the Institute of Measurement and Control, 41(10), pp. 2947-2956 (2019).
4. Ji, P., Ma, F., and Min, F. "Terminal traction control of teleoperation manipulator with random jitter disturbance based on active disturbance rejection sliding mode control", IEEE Access, 8, pp. 220246-220262 (2020).
5. Chan, L., Naghdy, F., and Stirling, D. "Application of adaptive controllers in teleoperation systems: A survey", IEEE Transactions on Human-Machine Systems, 44(3), pp. 337-352 (2014).
6. Hosseini-Suny, K., Momeni, H., and Janabi-Sharifi, F. "Model reference adaptive control design for a teleoperation system with output prediction", Journal of Intelligent & Robotic Systems, 59(3-4), pp. 319-339 (2010).
7. Namnabat, M., Zaeri, A., and Vahedi, M. "A passivitybased control strategy for nonlinear bilateral teleoperation employing estimated external forces", Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(12), pp. 1-10 (2020).
8. Franco, E. "Combined adaptive and predictive control for a teleoperation system with force disturbance and input delay", Frontiers in Robotics and AI, 3, p. 48 (2016).
9. Uddin, R. and Ryu, J. "Predictive control approaches for bilateral teleoperation", Annual Reviews in Control, 42, pp. 82-99 (2016).
10. Yazdankhoo, B. and Beigzadeh, B. "Increasing stability in model-mediated teleoperation approach by reducing model jump effect", Scientia Iranica, 26(Special Issue on: Socio-Cognitive Engineering), pp. 3-14 (2019).
11. Yazdankhoo, B., Nikpour, M., Beigzadeh, B., et al. "Improvement of operator position prediction in teleoperation systems with time delay: Simulation and experimental studies on phantom omni devices", JJMIE, 13(3), pp. 197-205 (2019).
12. Nikpour, M., Yazdankhoo, B., Beigzadeh, B., et al. "Adaptive online prediction of operator position in teleoperation with unknown time-varying delay: simulation and experiments", Neural Computing and Applications, 33(13), pp. 7575-7592 (2021).
13. Shokri-Ghaleh, H. and Alfi, A. "Bilateral control of uncertain telerobotic systems using iterative learning control: Design and stability analysis", Acta Astronautica, 156, pp. 58-69 (2019).
14. Gormus, B., Yazici, H., and Kucukdemiral, I.B. "Robust H-infinity control of an uncertain bilateral teleoperation system using dilated LMIs", Transactions of the Institute of Measurement and Control, 44(6), pp. 1275-1287 (2022).
15. Bavili, R.E., Bavil, A.F., and Akbari, A. "Control of a bilateral teleoperation system in the presence of varying time delay, model uncertainty and actuator faults", International Journal of Dynamics and Control, 9, pp. 1261-1276 (2021).
16. Kang, J.S., Lee, M.C., and Yoon, S.M. "Bilateral control based rupture protection method in surgical robot using improved master device", International Journal of Control, Automation and Systems, 14(4), pp. 1073-1080 (2016).
17. Li, Y., Liu, Z., Wang, Z., et al. "Adaptive control of teleoperation systems with prescribed tracking performance: a BLF-based approach", International Journal of Control, 95(6), pp. 1600-1610 (2020).
18. Vidyasagar, M. "Optimal rejection of persistent bounded disturbances", IEEE Transactions on Automatic Control, 31(6), pp. 527-534 (1986).
19. Blanchini, F. and Sznaier, M. "Rational L1 suboptimal compensators for continuous-time systems", IEEE Transactions on Automatic Control, 39(7), pp. 1487- 1492 (1994).
20. Zhu, J. and Chen, J. "Stability of systems with time-varying delays: An L1 small-gain perspective", Automatica, 52, pp. 260-265 (2015).
21. Li, Y., Lam, J., and Luo, X. "Convex optimization approaches to robust L1 fixed-order filtering for polytopic systems with multiple delays", Circuits, Systems & Signal Processing, 27(1), pp. 1-22 (2008).
22. Li, Y. and Liang, Y. "Gain-scheduled L-one control for linear parameter-varying systems with parameterdependent delays", Journal of Control Theory and Applications, 9(4), pp. 617-623 (2011).
23. Maiti, R., Sharma, K.D., Sarkar, G., et al. "Modelling and control of delayed, nonlinear, uncertain, disturbed air heater employing fuzzy PDC-L1 adaptive scheme", IEEE Transactions on Industrial Electronics, 68(11), pp. 11328-11338 (2021).
24. Nguyen, K.-D. and Dankowicz, H. "Delay robustness and compensation in L1 adaptive control", Procedia IUTAM, 22, pp. 10-15 (2017).
25. Sadeghi, M.S., Momeni, H.R., and Amirifar, R. "H1 and L1 control of a teleoperation system via LMIs", Applied Mathematics and Computation, 206(2), pp. 669-677 (2008).
26. Hua, C.-C. and Liu, X.P. "Delay-dependent stability criteria of teleoperation systems with asymmetric time-varying delays", IEEE Transactions on Robotics, 26(5), pp. 925-932 (2010).
27. Gu, K., Chen, J., and Kharitonov, V.L., Stability of Time-Delay Systems, Springer Science & Business Media (2003).
28. Park, J.H. and Cho, H.C. "Sliding mode control of bilateral teleoperation systems with force-reflection on the internet", IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000), 2, pp. 1187-1192 (2000).
29. Hilliard, T. and Pan, Y.-J. "Stabilization of asymmetric bilateral teleoperation systems for haptic devices with time-varying delays", American Control Conference, pp. 4538-4543 (2013).
30. Khadivar, F., Sadeghnejad, S., Moradi, H., et al. "Dynamic characterization of a parallel haptic device for application as an actuator in a surgery simulator", 2017 5th RSI International Conference on Robotics and Mechatronics (ICRoM), pp. 186-191 (2017).