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Zhang et al. Intell. Robot. 2025, 5(2), 333-54 Intelligence & Robotics
DOI: 10.20517/ir.2025.17

Research Article Open Access

Disturbance observer-based terminal sliding mode con-

trol for the training safety improvement in robot-assisted
rehabilitation

Yaqi Zhang, Weiyi Xie, Renjie Ma

College of Engineering, Shantou University, Shantou 515063, Guangdong, China.

Correspondence to: Yaqi Zhang, College of Engineering, Shantou University, 243 Daxue Rd., Jinping District, Shantou 515063,
Guangdong, China. E-mail: yaqizhang103@163.com
How to cite this article: Zhang, Y.; Xie, W.; Ma, R. Disturbance observer-based terminal sliding mode control for the training safety
improvement in robot-assisted rehabilitation. Intell. Robot. 2025, 5(2), 333-54. http://dx.doi.org/10.20517/ir.2025.17
Received: 11 Nov 2024 First Decision: 3 Jan 2025 Revised: 20 Feb 2025 Accepted: 25 Feb 2025 Published: 11 Apr 2025

Academic Editor: Jinhua She Copy Editor: Pei-Yun Wang Production Editor: Pei-Yun Wang

Abstract
Existing control methods for exoskeletons often face challenges in adapting to individual differences, ensuring robust-
ness in dynamic environments, and achieving real-time performance. For instance, certain approaches fail to balance
rehabilitation efficacy with wearer comfort, while others suffer from issues such as chattering and limited disturbance
rejection capabilities. This paper proposes a control framework for exoskeleton rehabilitation robots, emphasizing the
strict implementation of safety protocols to guarantee that patients in the early stages of rehabilitation can accurately
follow normal human activity postures. Firstly, an interpolating polynomial is optimized to generate the desired tra-
jectory, with consideration of the minimum jerk principle. Secondly, a motion-dependent function is proposed for
smooth switching between two modes of normal training and safe stopping. Thirdly, a non-singular fast terminal
sliding mode method based on a nonlinear disturbance observer is proposed to accurately track the desired joint an-
gles, with the objective of achieving a tracking error that tends to zero in a finite time. Furthermore, the stability of
the closed-loop system is demonstrated through the application of the Lyapunov method. Ultimately, the simulation
results demonstrate the efficacy and resilience of the proposed control framework.

Keywords: Non-singular terminal sliding mode control, disturbance observer, minimum-jerk, smooth switching, Lya-
punov methods

© The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0
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