Robust Optimal Output-Tracking Control of Constrained Mechanical Systems With Application to Autonomous Rovers

This article presents a robust optimal output-tracking control strategy for underactuated mechanical systems whose motion is restricted by mixed holonomic and nonholonomic constraints. Autonomous rovers/cars and unmanned underwater/aerial vehicles are a few examples of such systems that must often operate in harsh environments and under uncertain conditions. We present a comprehensive control analysis of this large class of nonlinear systems, including the existing studies on local reachability and static state feedback linearization. We also propose a local observability analysis of the feedback transformed input–output linearized systems. Based on the input–output linearization of the holonomically restricted nominal system, we develop a sliding mode control strategy that is robust against the projected effects of uncertainties and disturbances on the system’s output. Asymptotic stability of the output toward a bounded desired trajectory is proven using Lyapunov’s direct method, while the system’s internal stability (in the sense of boundedness) is investigated based on the notion of tracking-error zero dynamics. Time-dependent bounded matched uncertainties in the inertia parameters and disturbance forces arising in the unrestricted system are considered in this study. We propose an optimal sliding manifold according to the finite-horizon linear-quadratic regulator design problem with split boundary value conditions. The developed control strategy is implemented on a six-wheel autonomous Lunar rover in a simulation environment and its performance is compared with that of an optimal proportional–integral–derivative feedback, feedforward controller. The optimal sliding mode controller shows superior performance in trajectory tracking with acceptable control actions.