Time-Varying RISE-Based Reinforcement Learning for Tracking Control of a Mecanum Robot

Abstract

This paper proposes a time-varying RISE-based reinforcement learning controller for trajectory tracking of a four-wheeled Mecanum mobile robot subject to center-of-mass offset, wheel slippage, and external disturbances. A sliding-variable formulation is first employed to transform the uncertain robot dynamics into a control-affine system suitable for online Actor–Critic reinforcement learning. To enhance robustness, a time-varying RISE mechanism is incorporated into the control design, where the nonlinear gains depend on the filtered tracking error and its integral. The Actor–Critic structure approximates the optimal value function and learns the control policy online, while the time-varying RISE term compensates for lumped uncertainties. Lyapunov-based analysis shows that all closed-loop signals and adaptive weight estimates remain bounded, while the tracking errors, the Actor–Critic weight mismatch, and the critic error in the regressor direction are uniformly ultimately bounded. Simulation results demonstrate that the proposed method improves tracking accuracy, disturbance rejection, and numerical learning stability compared with fixed-gain RISE-based reinforcement learning controllers. A preliminary hardware experiment with an asymmetrically mounted payload further demonstrates the real-time feasibility of the proposed controller under practical mechanical and sensing imperfections.