FAS-Based Anti-Disturbance Stabilization Control of Nonholonomic Systems: Theory and Experiment

Abstract

This article considers the control issue for chained nonholonomic systems in the presence of disturbances and model uncertainties. The original system is a cascaded form with two subsystems. In the proposed algorithm, the first subsystem is designed to be exponentially stable, while the second is reformulated into a fully actuated system (FAS) with some states remaining unavailable. Consequently, state feedback control of the original system is transformed into output feedback control of FAS. An effective observer based on Fourier transform technique is presented to simultaneously estimate states and disturbances. Then, output feedback control and relay-switching-based control are proposed to achieve exponential or asymptotical convergence of the states. Finally, simulation and experiment results are presented to illustrate the efficacy of the proposed strategy. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Nonholonomic systems, exemplified by wheeled robots, are ubiquitous in engineering applications. This paper is motivated by the practical requirements of the stabilization control tailored to such systems. Nonholonomic systems often face complex scenarios with disturbances. For example, when a wheeled robot is parking in the snow fields, skidding and slipping may occur. Handling uncertainty and disturbance increases the challenge to the control task. Furthermore, onboard computers typically have limited computing power, thereby requiring straightforward and concise control algorithms. To meet these requirements, this paper introduces the framework of FAS, which eliminates the need for conventional recursive design procedures. Consequently, two controllers are presented: the output-feedback-based controller and the state-feedback-based controller. Both two controllers offer robustness, low complexity, and strong ability in disturbance rejection, making them suitable for practical applications. On the other hand, the controllers can not only be deployed independently to meet specific requirements, but can also be combined into a relay-switching-based strategy. This strategy is a two-stage control scheme. In the first stage, accurate parameter identification is performed while the output feedback controller maintains primary control performance. Once precise parameters are obtained, the output feedback controller seamlessly transitions to the state feedback controller, achieving higher control accuracy. Overall, this approach balances the control effectiveness with the computational efficiency, addressing the practical needs of stabilization control in nonholonomic systems.