Nonlinear Adaptive Optimal Control Design and Implementation for Trajectory Tracking of Four-Wheeled Mecanum Mobile Robots

This study proposes a nonlinear adaptive optimal control method, the adaptive H2 control method, applied to the trajectory tracking problem of the wheeled mobile robot (WMR) with four-wheel mecanum wheels. From the perspective of solving mathematical problems, finding an analytical adaptive control solution that satisfies the adaptive H2 performance criterion for the trajectory tracking problem of the WMR with four-wheel mecanum wheels is an extremely challenging task due to the high complexity of the dynamic system. To analytically derive the control law and adaptive control law for this trajectory tracking problem, a proportional-derivative (PD) type transformation is employed to formalize the trajectory tracking error dynamics between the WMR and the desired trajectory (DT). Based on an in-depth analysis of the trajectory tracking error dynamics, a closed-form adaptive control law is analytically derived from the highly complex nonlinear dynamic system equations. This control law provides a solution to the trajectory tracking problem of the WMR while satisfying the adaptive H2 performance criterion. The proposed adaptive nonlinear control method offers a simple control structure and advantages such as improved energy efficiency. Finally, simulations and experimental implementations were conducted to verify the performance of the proposed adaptive H2 control method and the H2 control method in tracking the DT. The results demonstrate that, compared to the H2 control method, the adaptive H2 control method exhibits superior trajectory tracking performance, particularly in the presence of significant model uncertainties.