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Decentralized Fault Tolerant Control of Modular Manipulators System Based on Adaptive Dynamic Programming


This paper presented an original decentralized fault tolerant control approach for modular manipulators which based on adaptive dynamic programming (ADP) algorithm. First, the dynamic model of modular manipulators is established via joint torque feedback technique. Then, the fault tolerant controller is designed which composes of model-based compensation controller, observer-based fault tolerant controller and ADP-based optimal controller. According to ADP algorithm, the Hamiltonian-Jacobi-Bellman (HJB) equation can be tackled by critic neural network (NN). The closed-loop modular manipulators system is guaranteed asymptotic stable based on Lyapunov theory. Experiments are performed to verify the proposed method, and the results have guaranteed its effectiveness.

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  1. Y. Li, F. Zhou, and B. Zhao, “Dynamic output feedback based active decentralized fault-Tolerant control for reconfigurable manipulator with concurrent failures,” Mathematical Problems in Engineering, November 2014.

  2. J. Zhao, S. Jiang, and F. Xie, “A novel nonlinear fault tolerant control for manipulator under actuator fault,” Mathematical Problems in Engineering, vol. 28, no. 5, pp. 1808–1829, March 2018.

    MathSciNet  MATH  Google Scholar 

  3. N. Chang, J. Hong, and H. Kim, “Neural network based adaptive actuator fault detection algorithm for robot manipulators,” Journal of Intelligent & Robotic Systems, vol. 95, no. 1, pp. 137–147, July 2019.

    Article  Google Scholar 

  4. A. Elghoul, A. Tellili, and M. N. Abdelkrim, “Reconfigurable control of flexible joint robot with actuator fault and uncertainty,” Journal of Electrical Engineering-elektrotechnicky Casopis, vol. 70, no. 2, pp. 130–137, April 2019.

    Google Scholar 

  5. S. F. A. Latip, A. R. Husain, Z. Mohamed, and M. A. M. Barsi, “Adaptive PID actuator fault tolerant control of single-link flexible manipulators,” Transactions of the Institute of Measurement and Control, vol. 41, no. 4, pp. 1019–1031, February 2019.

    Article  Google Scholar 

  6. B. Zhao, C. Li, and D. Liu, “Decentralized sliding mode observer based dual closed-loop fault tolerant control for reconfigurable manipulators against actuator failure,” Plos One, vol. 10, no. 7, July 2015.

  7. Werbos, “Approximate dynamic programming for real time control and neural modeling,” D. A. White and D.A Sofge (eds.), Handbook of Intelligent Control: Neural, Fuzzy, and Adaptive Approaches, Van Nostrand Reinhold, 1992.

  8. Z. Su, A. Chow, N. Zheng, Y. Huang, E. Liang, and R. Zhong, “Neuro-dynamic programming for optimal control of macroscopic fundamental diagram systems,” Transportation Research Part C-Emerging Technologies, vol. 116, Transportation Research Part C, July 2020.

  9. Y. Chen, F. Liu, M. Jay, C. Chen, K. Asama, and Y. Zhou, “Efficient approximate dynamic programming based on design and analysis of computer experiments for infinite-horizon optimization,” Computers & Operations Research, vol. 124, December 2020.

  10. C. Karim, “An overview on recent machine learning techniques for Port Hamiltonian systems,” Physica D-nonlinear Phenomena, vol. 411, October 2020.

  11. D. Oindrilla and M. Ahmed, “Reducing the risk of cascading failure in active distribution networks using adaptive critic design,” IET Generation Transmission & Distribution, vol. 14, no. 13, pp. 2592–2601, July 2020.

    Article  Google Scholar 

  12. R. Song and L. Zhu, “Optimal fixed-point tracking control for discrete-time nonlinear systems via ADP,” IEEE/CAA Journal of Automatic Sinica, vol. 6, no. 3, pp. 657–666, 2019.

    Article  MathSciNet  Google Scholar 

  13. Y. Huang and D. Liu, “Neural-network-based optimal tracking control scheme for a class of unknown discrete-time nonlinear systems using iterative ADP algorithm,” Neurocomputing, vol. 125, pp. 46–56, February 2014.

    Article  Google Scholar 

  14. Y. Yang, C. Xu, D. Yue, X. Zhong, X. Si, and J. Tan, “Event-triggered ADP control of a class of non-affine continuous-time nonlinear systems using output information,” Neurocomputing, vol. 378, pp. 304–314, February 2020.

    Article  Google Scholar 

  15. L. Cui, X. Xie, X. Wang, Y. Luo, and J. Liu, “Event-triggered single-network ADP method for constrained optimal tracking control of continuous-time non-linear systems,” Applied Mathematics and Computation, vol. 352, pp. 220–234, July 2019.

    Article  MathSciNet  Google Scholar 

  16. X. Yang, H. He, and D. Liu, “Adaptive dynamic programming for robust neural control of unknown continuous-time non-linear systems,” IET Control Theory and Applications, vol. 11, no. 14, pp. 2307–2316, September 2017.

    Article  MathSciNet  Google Scholar 

  17. H. Yang, Y. Li, H. Yuan, and Z. Liu, “Adaptive dynamic programming for security of networked control systems with actuator saturation,” Information Sciences, vol. 460, pp. 51–64, September 2018.

    Article  MathSciNet  Google Scholar 

  18. B. Zhao, D. Liu, and Y. Li, “Online fault compensation control based on policy iteration algorithm for a class of affine non-linear systems with actuator failures,” IET Control Theory and Applications, vol. 10, no. 15, pp. 1816–1823, October 2016.

    Article  MathSciNet  Google Scholar 

  19. M. Vimalesh, B. Ashwin, C. Kishen, and B. Sandipan, “Methods for dimensional design of parallel manipulators for optimal dynamic performance over a given safe working zone,” Mechanism and Machine Theory, vol. 147, May 2020.

  20. G. Yu, J. Wu, and L. Wang, “Optimal design of the three-degree-of-freedom parallel manipulators in a spray-painting equipment,” Robotica, vol. 38, no. 6, pp. 1064–1081, June 2020.

    Article  Google Scholar 

  21. H. Hamidreza, H. K. Moharam, and H. Mohammad, “Optimal trajectory planning for increased stability of mobile flexible manipulators undergoing large deflection,” Proceedings of the Institution of Mechanical Engineers Part B-Journal of Engineering Manufacture, vol. 231, no. 1, pp. 85–95, June 2017.

    Article  Google Scholar 

  22. Q. Jia and W. K. S. Tang, “Consensus of multi-agents with event-based nonlinear coupling over time-varying digraphs,” IEEE Transactions on Circuits and Systems II-Express Briefs, vol. 65, no. 12, pp. 1969–1973, December 2018.

    Article  Google Scholar 

  23. S. Tong, L. Zhang, and Y. Li, “Observed-based adaptive fuzzy decentralized tracking control for switched uncertain nonlinear large-scale systems with dead zones,” IEEE Transactions on Systems Man Cybernetics-Systems, vol. 46, no. 1, pp. 37–47, June 2016.

    Article  Google Scholar 

  24. H. Wang and G. Yang, “Decentralized state feedback control of uncertain affine fuzzy large-scale systems with unknown interconnections,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 5, pp. 1134–1146, October 2016.

    Article  Google Scholar 

  25. Z. Li, W. Melek, and C. Clark, “Decentralized robust control of robot manipulators with harmonic drive transmission and application to modular and reconfigurable serial arms,” Robotica, vol. 27, pp. 291–302, March 2009.

    Article  Google Scholar 

  26. T. Bian, Y. Jiang, and Z. Jiang, “Decentralized adaptive optimal control of large-scale systems with application to power systems,” IEEE Transactions on Industrial Electronics, vol. 62, no. 4, pp. 2439–2447, April 2015.

    Article  Google Scholar 

  27. B. Zhao and Y. Li, “Model-free adaptive dynamic programming based near-optimal decentralized tracking control of reconfigurable manipulators,” International Journal of Control, Automation, and Systems, vol. 16, no. 2, pp. 478–490, April 2018.

    Article  Google Scholar 

  28. I. Jun, “Robust control of robot manipulators based on joint torque sensor information,” The International Journal of Robotics Research, vol. 13, no. 5, pp. 434–442, October 1994.

    Article  Google Scholar 

  29. B. Dong, K. Liu, and Y. Li, “Decentralized control of harmonic drive based modular robot manipulators using only position measurements: theory and experimental verification,” Journal of Intelligent & Robotic Systems, vol. 88, no. 1, pp. 3–18, October 2017.

    Article  Google Scholar 

  30. B. Armstrong-Hélouvry, P. Dupont, and C. C. de Wit, “A survey of models, analysis tools and compensation methods for the control of machines with friction,” Automatica, vol. 30, no. 7, pp. 1083–1138, 1994.

    Article  Google Scholar 

  31. G. Liu, A. Goldenberg, and Y. Zhang, “Precise slow motion control of a direct-drive robot arm with velocity estimation and friction compensation,” Mechatronics, vol. 14, no. 7, pp. 821–834, 2004.

    Article  Google Scholar 

  32. G. Liu, “Decomposition-based friction compensation of mechanical systems,” Mechatronics, vol. 12, no. 5, pp. 755–769, 2002.

    Article  Google Scholar 

  33. B. Dong, T. An, F. Zhou, K. Liu, and Y. Li, “Decentralized robust zero-sum neuro-optimal control for modular robot manipulators in contact with uncertain environments: Theory and experimental verification,” Nonlinear Dynamics, vol. 97, no. 13, pp. 503–524, 2019.

    Article  Google Scholar 

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Correspondence to Yuanchun Li.

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This work is supported by the National Natural Science Foundation of China (Grant nos. 61773075, 62173047 and 61703055), the Scientific Technological Development Plan Project in Jilin Province of China (Grant no. 20200801056GH) and the Science and Technology project of Jilin Provincial Education Department of China during the 13th Five-Year Plan Period (Grant nos. JJKH20200672KJ, JJKH20200673KJ and JJKH20200674KJ).

Fan Zhou received her M.S. and Ph.D. degrees from Changchun University of Technology, China, in 2015 and 2018, respectively. She is currently a lecturer in Changchun University of Technology. Her research interests include intelligent mechanical, robot control, and robust control.

Fujie Nie received his B.S. and M.S. degrees from Changchun University of Technology, China, in 2018 and 2021, respectively. He is currently a embedded software engineer in GINLONG Science and Technology Shares Limited Company. His research interests include robot control, and dynamic programming.

Tianjiao An received his B.S. and M.S. degrees from the Changchun University of Technology, China, in 2017 and 2020, respectively, where he is currently pursuing a Ph.D. degree with the Department of Control Science and Engineering. His research interests include robot control and adaptive dynamic programming.

Bing Ma received her B.S. and Ph.D degrees from Changchun University of Technology, China, in 2016 and 2021, respectively. She is currently a lecturer in Changchun University of Technology. Her research interests include robot control, position-force control and adaptive dynamic programming.

Yuanchun Li received his M.S. and Ph.D. degrees from Harbin Institute of Technology, China, in 1987 and 1990, respectively. He is currently a Professor in Changchun University of Technology, China. His research interest covers complex system modeling, intelligent mechanical, and robot control.

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Zhou, F., Nie, F., An, T. et al. Decentralized Fault Tolerant Control of Modular Manipulators System Based on Adaptive Dynamic Programming. Int. J. Control Autom. Syst. 20, 3252–3263 (2022).

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  • Adaptive dynamic programming
  • decentralized control
  • fault tolerant control
  • modular manipulators