Path Tracking Control for Underactuated Vehicles With Matched-Mismatched Uncertainties: An Uncertainty Decomposition Based Constraint-Following Approach

Abstract

This paper presents a robust path tracking control method by utilizing the ideology of constraint-following approach for uncertain underactuated autonomous vehicles. The uncertainties are bounded with an unknown boundary. They do not all fall within the range space of the input matrix. Based on kinematic relations between the desired path and vehicle, the path tracking task is transformed into an equality constraint of the vehicle lateral dynamics states. The control goal is to make the underactuated vehicle follow the constraint, thus realizing the desired tracking performance. The constraint-following robust control (CFRC) is designed in two steps. First, a servo control design for the nominal system is devised without considering uncertainty and initial constraint deviation. Second, the uncertainty is meticulously decomposed into matched and mismatched portions based on the geometric structural characteristics of the constraint dynamics system. As a result, since the mismatched uncertainty is orthogonal to the constraint-following geometric space, it “disappears” in the stability analysis. The matched uncertainty is estimated by a self-adjusting leakage type adaptive law. On this basis, a robust control is designed based on the estimated matched uncertainty. Through Lyapunov minimax analysis, the proposed control method guarantees the approximate constraint-following performance. Finally, the TruckSim–Simulink co-simulations and real vehicle experiments are presented. The results show that the proposed control can robustly realize excellent tracking performance in the presence of time-vary uncertainties.