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Wang et al. Intell Robot 2023;3(3):479-94 Intelligence & Robotics
DOI: 10.20517/ir.2023.26

Research Article Open Access

Adaptive robust control for biped walking under un-
certain external forces

Helin Wang, Qijun Chen

Department of Control Science and Engineering, Tongji University, Shanghai 201804, China.

Correspondence to: Prof. Qijun Chen, Department of Control Science and Engineering, Tongji University, No.4800 Cao’an Road
Jiading District, Shanghai 201804, China. E-mail: qjchen@tongji.edu.cn
How to cite this article: Wang H, Chen Q. Adaptive robust control for biped walking under uncertain external forces. Intell Robot
2023;3(3):479-94. http://dx.doi.org/10.20517/ir.2023.26
Received: 30 May 2023 First Decision: 8 Aug 2023 Revised: 20 Aug 2023 Accepted: 11 Sep 2023 Published: 27 Sep
2023
Academic Editor: Hongtian Chen, Simon X. Yang Copy Editor: Dan Zhang Production Editor: Dan Zhang

Abstract
Adaptability and robustness are important expressions of the intelligent walking ability of biped robots. This paper
is concerned with the problem of dynamical biped walking and robust control of biped robots under external forces.
Due to the characteristics of strong coupling and hybrid, the robotic system is modeled as a rigid kinematic chain
with Lagrange equations. A novel adaptive feedback controller is proposed based on sliding mode control (SMC)
and hybrid zero dynamics. The novelty of the proposed work lies in taking the uncertainty of upper-bound error into
consideration. The hybrid robust control is mentioned to approximate unknown dynamic functions with the adaptive
weight. The restricted Poincare return map is utilized to analyze the stability of a nonlinear impulsive system. It
ensures that the flow of the continuous subsystem can pass through the impact cross section. Finally, the simulation
results illustrate that the proposed adaptive SMC control system can favorably track the reference trajectories, even
when a fault occurs, which verifies the effectiveness of the proposed method.

Keywords: Biped walking, impulse hybrid system, adaptive sliding mode control, stability analysis

1. INTRODUCTION
Recently, intelligent robots reflect the deep integration of new-generation information technologies, such as
intelligent control and high-performance computing, and stand for major direction for the development of the
new-generation artificial intelligence strategy of the country. As the ultimate form of intelligent robots, hu-

© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0
International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, shar-
ing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you
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