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Constrained control methods for lower extremity rehabilitation exoskeleton robot considering unknown perturbations

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Abstract

In this paper, trajectory tracking control is investigated for lower extremity rehabilitation exoskeleton robot. Unknown perturbations are considered in the system which are inevitable in reality. The trajectory tracking control is constructively treated as constrained control issue. To obtain the explicit equation of motion and analytical solution of lower extremity rehabilitation exoskeleton robot, Udwadia–Kalaba theory is introduced. Lagrange multipliers and pseudo-variables are not needed in Udwadia–Kalaba theory, which is more superior than Lagrange method. On the basis of Udwadia–Kalaba theory, two constrained control methods including trajectory stabilization control and adaptive robust control are proposed. Trajectory stabilization control applies Lyapunov stability theory to modify the desired trajectory constraint equations. A leakage type of adaptive law is designed to compensate unknown perturbations in adaptive robust control. Finally, comparing with nominal control and approximate constraint-following control, simulation results demonstrate the superiority of trajectory stabilization control and adaptive robust control in trajectory tracking control.

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Data availability

All data are available upon request at the authors’ email address.

Code availability

Custom code is available upon request at Liang Yuan email address.

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Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: The authors would like to thank the National Natural Science Foundation of China (U1813220, 62063033) for their support in this research.

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Authors and Affiliations

  1. School of Mechanical Engineering, Xinjiang University, 666 Shengli Road, Urumqi, 830046, China

    Jin Tian, Liang Yuan, Wendong Xiao, Teng Ran, Jianbo Zhang & Li He

  2. School of Information Science and Technology, Beijing University of Chemical Technology, 15 Beisanhuan Dong Lu, Chaoyang District, Beijing, 100029, China

    Liang Yuan

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  1. Jin Tian
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  2. Liang Yuan
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  3. Wendong Xiao
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Contributions

JT involved in writing the original draft, validation and software. LY and LH involved in writing, reviewing and editing and supervision. WX, TR and JZ took part in methodology, investigation and formal analysis.

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Correspondence to Liang Yuan.

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Tian, J., Yuan, L., Xiao, W. et al. Constrained control methods for lower extremity rehabilitation exoskeleton robot considering unknown perturbations. Nonlinear Dyn 108, 1395–1408 (2022). https://doi.org/10.1007/s11071-022-07272-2

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  • DOI: https://doi.org/10.1007/s11071-022-07272-2

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