Integrated Observer-based Fixed-time Control with Backstepping Method for Exoskeleton Robot
Abstract
To achieve the fast convergence and tracking precision of a robotic upper-limb exoskeleton, this paper proposes an observer-based integrated fixed-time control scheme with a backstepping method. Firstly, a typical 5 DoF (degrees of freedom) dynamics is constructed by Lagrange equations and processed for control purposes. Secondly, second-order sliding mode controllers (SOSMC) are developed and novel sliding mode surfaces are introduced to ensure the fixed-time convergence of the human-robot system. Both the reaching time and settling time are proved to be bounded with certain values independent of initial system conditions. For the purpose of rejecting the matched and unmatched disturbances, nonlinear fixed-time observers are employed to estimate the exact value of disturbances and compensate the controllers online. Ultimately, the synthesis of controllers and disturbance observers is adopted to achieve the excellent tracking performance and simulations are given to verify the effectiveness of the proposed control strategy.
Keywords
Upper-limb exoskeleton sliding mode control (SMC) fixed-time control disturbance observe backsteppingPreview
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Notes
Acknowledgements
This work was supported by National Natural Science Foundation of China (Nos. 61703134, 61703135, 61773151, 61503118 and 61871173), Natural Science Foundation of Hebei Province (Nos. F2015202150, F2016202327 and F2018202279), Natural Science Foundation of Tianjin (No. 17JCQNJC04400), the Foundation of Hebei Educational Committee (Nos. QN2015068 and ZD2016071), the Colleges and Universities in Hebei Province Science and Technology Research Youth Fund (No. ZC2016020) and the Graduate Innovation Funding Project of Hebei Province (No. CXZZBS2017038).
References
- [1]A. J. Young, D. P. Ferris. State of the art and future directions for lower limb robotic exoskeletons. IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 25, no. 2, pp. 171–182, 2017. DOI: https://doi.org/10.1109/TNSRE.2016.2521160.CrossRefGoogle Scholar
- [2]B. Brahmi, M. Saad, C. Ochoa-Luna, M. H. Rahman, A. Brahmi. Adaptive tracking control of an exoskeleton robot with uncertain dynamics based on estimated time-delay control. IEEE-ASME Transactions on Mechatronics, vol. 23, no. 2, pp. 575–585, 2018. DOI: https://doi.org/10.1109/TMECH.2018.2808235.CrossRefGoogle Scholar
- [3]Z. Li, W. H. Ma, Z. G. Yin, H. J. Guo. Tracking control of time-varying knee exoskeleton disturbed by interaction torque. ISA Transactions, vol. 71, pp. 458–466, 2017. DOI: https://doi.org/10.1016/j.isatra.2017.08.004.CrossRefGoogle Scholar
- [4]L. Zhao, H. Y. Cheng, Y. Q. Xia, B. Liu. Angle tracking adaptive backstepping control for a mechanism of pneumatic muscle actuators via an AESO. IEEE Transactions on Industrial Electronics, vol. 66, no. 6, pp. 4566–4576, 2019. DOI: https://doi.org/10.1109/TIE.2018.2860527.CrossRefGoogle Scholar
- [5]Z. J. Li, C. Y. Su, L. Y. Wang, Z. T. Chen, T. Y. Chai. Nonlinear disturbance observer-based control design for a robotic exoskeleton incorporating fuzzy approximation. IEEE Transactions on Industrial Electronics, vol. 62, no. 9, pp. 5763–5775, 2015. DOI: https://doi.org/10.1109/TIE.2015.2447498.CrossRefGoogle Scholar
- [6]H. D. Lee, B. K. Lee, W. S. Kim, J. S. Han, K. S. Shin, C. S. Han. Human-robot cooperation control based on a dynamic model of an upper limb exoskeleton for human power amplification. Mechatronics, vol. 24, no. 2, pp. 168–176, 2014. DOI: https://doi.org/10.1016/j.mechatronics.2014.01.007.CrossRefGoogle Scholar
- [7]H. B. Kang, J. H. Wang. Adaptive control of 5 DOF upper-limb exoskeleton robot with improved safety. ISA Transactions, vol. 52, no. 6, pp. 844–852, 2013. DOI: https://doi.org/10.1016/j.isatra.2013.05.003.CrossRefGoogle Scholar
- [8]Z. J. Li, Z. C. Huang, W. He, C. Y. Su. Adaptive impedance control for an upper limb robotic exoskeleton using biological signals. IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 1664–1674, 2017. DOI: https://doi.org/10.1109/TIE.2016.2538741.CrossRefGoogle Scholar
- [9]J. Niu, Q. Q. Yang, X. Y. Wang, R. Song. Sliding mode tracking control of a wire-driven upper-limb rehabilitation robot with nonlinear disturbance observer. Frontiers in Neurology, vol. 8, Article number 646, 2017. DOI: https://doi.org/10.3389/fneur.2017.00646.
- [10]J. Wang, Q. Zong, R. Su, B. L. Tian. Continuous high order sliding mode controller design for a flexible air-breathing hypersonic vehicle. ISA Transactions, vol. 53, no. 3, pp. 690–698, 2014. DOI: https://doi.org/10.1016/j.isatra.2014.01.002.CrossRefGoogle Scholar
- [11]A. H. D. Markazi, M. Maadani, S. H. Zabihifar, N. Doost-Mohammadi. Adaptive fuzzy sliding mode control of under-actuated nonlinear systems. International Journal of Automation and Computing, vol. 15, no. 3, pp. 364–376, 2018. DOI: https://doi.org/10.1007/s11633-017-1108-5.CrossRefGoogle Scholar
- [12]Y. Zhao, J. H. Wang, F. Yan, Y. Shen. Adaptive sliding mode fault-tolerant control for type-2 fuzzy systems with distributed delays. Information Sciences, vol. 473, pp. 227–238, 2019. DOI: https://doi.org/10.1016/j.ins.2018.09.002.MathSciNetCrossRefGoogle Scholar
- [13]A. Riani, T. Madani, A. Benallegue, K. Djouani. Adaptive integral terminal sliding mode control for upper-limb rehabilitation exoskeleton. Control Engineering Practice, vol. 75, pp. 108–117, 2018. DOI: https://doi.org/10.1016/j.conengprac.2018.02.013.CrossRefGoogle Scholar
- [14]J. A. Moreno, M. Osorio. Strict Lyapunov functions for the super-twisting algorithm. IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 1035–1040, 2012. DOI: https://doi.org/10.1109/TAC.2012.2186179.MathSciNetCrossRefGoogle Scholar
- [15]N. Sun, T. Yang, H. Chen, Y. C. Fang, Y. Z. Qian. Adaptive anti-swing and positioning control for 4-DOF rotary cranes subject to uncertain/unknown parameters with hardware experiments. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 7, pp. 1309–1321, 2019. DOI: https://doi.org/10.1109/TSMC.2017.2765183.CrossRefGoogle Scholar
- [16]P. Yang, G. W. Zhang, J. Wang, X. Z. Wang, L. L. Zhang, L. L. Chen. Command filter backstepping sliding model control for lower-limb exoskeleton. Mathematical Problems in Engineering, vol. 2017, Article number 1064535, 2017. DOI: https://doi.org/10.1155/2017/1064535.MathSciNetGoogle Scholar
- [17]Y. Long, Z. J. Du, W. D. Wang, W. Dong. Robust sliding mode control based on GA optimization and CMAC compensation for lower limb exoskeleton. Applied Bionics and Biomechanics, vol. 2016, Article number 5017381, 2016. DOI: https://doi.org/10.1155/2016/5017381.CrossRefGoogle Scholar
- [18]H. J. Yang, M. Tan. Sliding mode control for flexible-link manipulators based on adaptive neural networks. International Journal of Automation and Computing, vol. 15, no. 2, pp. 239–248, 2018. DOI: https://doi.org/10.1007/s11633-018-1122-2.CrossRefGoogle Scholar
- [19]J. X. Liu, Y. B. Gao, X. J. Su, M. Wack, L. G. Wu. Disturbance-observer-based control for air management of PEM fuel cell systems via sliding mode technique. IEEE Transactions on Control Systems Technology, vol. 27, no. 3, pp. 1129–1138, 2019. DOI: https://doi.org/10.1109/TCST.2018.2802467.CrossRefGoogle Scholar
- [20]Y. F. Yin, J. X. Liu, J. A. Sánchez, L. G. Wu, S. Vazquez, J. I. Leon, L. G. Franquelo. Observer-based adaptive sliding mode control of NPC converters: An RBF neural network approach. IEEE Transactions on Power Electronics, vol. 34, no. 4, pp. 3831–3841, 2019. DOI: https://doi.org/10.1109/TPEL.2018.2853093.CrossRefGoogle Scholar
- [21]T. Madani, B. Daachi, K. Djouani. Non-singular terminal sliding mode controller: Application to an actuated exoskeleton. Mechatronics, vol. 33, pp. 136–145, 2016. DOI: https://doi.org/10.1016/j.mechatronics.2015.10.012.CrossRefGoogle Scholar
- [22]Y. Q. Wu, C. L. Zhu, Z. C. Zhang. Finite-time stabilization of a general class of nonholonomic dynamic systems via terminal sliding mode. International Journal of Automation and Computing, vol. 13, no. 6, pp. 585–595, 2016. DOI: https://doi.org/10.1007/s11633-015-0931-9.CrossRefGoogle Scholar
- [23]B. L. Tian, L. H. Liu, H. C. Lu, Z. Y. Zuo, Q. Zong, Y. P. Zhang. Multivariable finite time attitude control for quadrotor UAV: Theory and experimentation. IEEE Transactions on Industrial Electronics, vol. 65, no. 3, pp. 2567–2577, 2018. DOI: https://doi.org/10.1109/TIE.2017.2739700.CrossRefGoogle Scholar
- [24]G. W. Zhang, P. Yang, J. Wang, J. J. Sun. Multivariable finite-time control of 5 DOF upper-limb exoskeleton based on linear extended observer. IEEE Access, vol. 6, pp. 43213–43221, 2018. DOI: https://doi.org/10.1109/ACCESS.2018.2863384.CrossRefGoogle Scholar
- [25]S. Mohammed, W. G. Huo, J. Huang, H. Rifai, Y. Amirat. Nonlinear disturbance observer based sliding mode control of a human-driven knee joint orthosis. Robotics and Autonomous Systems, vol. 75, pp. 41–49, 2016. DOI: https://doi.org/10.1016/j.robot.2014.10.013.CrossRefGoogle Scholar
- [26]S. Mefoued. A second order sliding mode control and a neural network to drive a knee joint actuated orthosis. Neurocomputing, vol. 155, pp. 71–79, 2015. DOI: https://doi.org/10.1016/j.neucom.2014.12.047.CrossRefGoogle Scholar
- [27]B. L. Tian, Y. X. Ma, Q. Zong. A continuous finite-time output feedback control scheme and its application in quadrotor UAVs. IEEE Access, vol. 6, pp. 19807–19813, 2018. DOI: https://doi.org/10.1109/ACCESS.2018.2822321.CrossRefGoogle Scholar
- [28]J. K. Ni, L. Liu, C. X. Liu, X. Y. Hu, S. L. Li. Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 2, pp. 151–155, 2017. DOI: https://doi.org/10.1109/TCSII.2016.2551539.CrossRefGoogle Scholar
- [29]J. P. Li, Y. N. Yang, C. C. Hua, X. P. Guan. Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode. IET Control Theory & Applications, vol. 11, no. 8, pp. 1184–1193, 2017. DOI: https://doi.org/10.1049/iet-cta.2016.1143.MathSciNetCrossRefGoogle Scholar
- [30]A. Polyakov. Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2012. DOI: https://doi.org/10.1109/TAC.2011.2179869.MathSciNetCrossRefGoogle Scholar
- [31]Z. Y. Zuo. Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory & Applications, vol. 9, no. 4, pp. 545–552, 2015. DOI: https://doi.org/10.1049/iet-cta.2014.0202.MathSciNetCrossRefGoogle Scholar
- [32]B. L. Tian, Z. Y. Zuo, X. M. Yan, H. Wang. A fixed-time output feedback control scheme for double integrator systems. Automatica, vol. 80, pp. 17–24, 2017. DOI: https://doi.org/10.1016/j.automatica.2017.01.007.MathSciNetCrossRefGoogle Scholar
- [33]J. D. Sánchez-Tones, E. N. Sanchez, A. G. Loukianov. Pre-defined-time stability of dynamical systems with sliding modes. In Proceedings of American Control Conference, IEEE, Chicago, USA, pp. 5842–5846, 2015. DOI: https://doi.org/10.1109/ACC.2015.7172255.Google Scholar
- [34]Z. Y. Zuo. Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, vol. 54, pp. 305–309, 2015. DOI: https://doi.org/10.1016/j.automatica.2015.01.021.MathSciNetCrossRefGoogle Scholar
- [35]Y. Huang, Y. M. Jia. Adaptive fixed-time relative position tracking and attitude synchronization control for non-co-operative target spacecraft fly-around mission. Journal of the Franklin Institute, vol. 354, no. 18, pp. 8461–8489, 2017. DOI: https://doi.org/10.1016/j.jfranklin.2017.10.006.MathSciNetCrossRefGoogle Scholar
- [36]G. W. Zhang, P. Yang, J. Wang, J. J. Sun, Y. Zhang, L. L. Chen. Fixed-time control for upper-limb exoskeleton with bounded disturbances. In Proceedings of the 24th International Conference on Automation and Computing, IEEE, Newcastle upon Tyne, UK, 2018. DOI: https://doi.org/10.23919/IConAC.2018.8748956.Google Scholar
- [37]M. Basin, C. B. Panathula, Y. Shtessel. Multivariable continuous fixed-time second-order sliding mode control: Design and convergence time estimation. IET Control Theory & Applications, vol. 11, no. 8, pp. 1104–1111, 2017. DOI: https://doi.org/10.1049/iet-cta.2016.0572.MathSciNetCrossRefGoogle Scholar
- [38]Q. Dong, Q. Zong, B. L. Tian, F. Wang. Integrated Finite-Time Disturbance Observer and Controller Design for Reusable Launch Vehicle in Reentry Phase. Journal of Aerospace Engineering, vol. 30, no. 1, Article number 04016076, 2017. DOI: https://doi.org/10.1061/(ASCE)AS.1943-5525.0000670.