Cooperative game-oriented optimal robust control for an uncertain wheeled mobile robot with position constraints

Abstract

The trajectory tracking control performance of the wheeled mobile robot (WMR) is subject to position constraints, system uncertainties, and external disturbances. This paper explores the mechanism of the position constraints (equality and inequality) and considers the system uncertainties to be time-varying but bounded with fuzzy prescribed bounds. To solve the position constraints and uncertainties problems, a cooperative game-oriented optimal robust control method is proposed to provide high-precision, fast-response performance and robustness for WMR. First, a creative diffeomorphism transformation is proposed to convert the bounded state variables (subject to inequality constraints) into unbounded state variables. Accordingly, a restructured WMR system with the new state variables is established, which is free from inequality constraints. The uncertainties’ bound is described as a fuzzy number by employing fuzzy set theory, which builds the fuzzy dynamic system of the WMR. Second, the control goal for this study is to drive the WMR to follow the position constraints despite uncertainties. An optimal robust control is developed to guarantee that the tracking errors of the WMR converge to a predefined neighborhood of origin. Using Lyapunov stability analysis, a fuzzy performance index is constructed, including steady-state performance, time performance, and control effort. The fuzzy performance index is employed as the cost function based on the cooperative game theory. The optimal control design is formulated to seek the Pareto-optimal solution of control parameters. Finally, the stability analysis and comparative experiments demonstrate that the proposed control algorithm can ensure the WMR’s superior trajectory tracking convergence performance and strong robustness against uncertainties/disturbances.