Integrated Observer-based Fixed-time Control with Backstepping Method for Exoskeleton Robot

  • Gao-Wei Zhang
  • Peng Yang
  • Jie WangEmail author
  • Jian-Jun Sun
  • Yan Zhang
Research Article Special Issue on Improving Productivity through Automation and Computing


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.


Upper-limb exoskeleton sliding mode control (SMC) fixed-time control disturbance observe backstepping 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



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).


  1. [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: Scholar
  2. [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: Scholar
  3. [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: Scholar
  4. [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: Scholar
  5. [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: Scholar
  6. [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: Scholar
  7. [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: Scholar
  8. [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: Scholar
  9. [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:
  10. [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: Scholar
  11. [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: Scholar
  12. [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: Scholar
  13. [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: Scholar
  14. [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: Scholar
  15. [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: Scholar
  16. [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: Scholar
  17. [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: Scholar
  18. [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: Scholar
  19. [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: Scholar
  20. [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: Scholar
  21. [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: Scholar
  22. [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: Scholar
  23. [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: Scholar
  24. [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: Scholar
  25. [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: Scholar
  26. [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: Scholar
  27. [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: Scholar
  28. [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: Scholar
  29. [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: Scholar
  30. [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: Scholar
  31. [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: Scholar
  32. [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: Scholar
  33. [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: Scholar
  34. [34]
    Z. Y. Zuo. Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica, vol. 54, pp. 305–309, 2015. DOI: Scholar
  35. [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: Scholar
  36. [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: Scholar
  37. [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: Scholar
  38. [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:

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Artificial IntelligenceHebei University of TechnologyTianjinChina
  2. 2.Enginnering Research Center of Intelligent Rehabilitation and Detection TechnologyMinistry of EducationTianjinChina

Personalised recommendations