Flatness-based Robust Adaptive Tracking Control for Mobile Robot

Abstract

In this paper, we present a flatness-based robust adaptive tracking control for a mobile robot. In recent years, many cars are equipped with automatic driving systems. However, the design of control law for mobile robots is difficult because they are non-holonomic systems. To improve the safety of automatic driving, the control law considering robustness for mobile robots is required. In the conventional study for robust control, a robust adaptive tracking control is proposed for single input linear systems with matched disturbance and the simulation results shows its robustness and effectiveness. In addition, the conventional control law can be applied for nonlinear systems if the nonlinearity satisfies the matching condition. However, the conventional control law can't be applied for systems that has multiple input or its nonlinearity doesn't satisfy the matching condition. So the conventional control law can't be applied for a mobile robot because a mobile robot has two inputs and its nonlinearity don't satisfy the matching condition. Therefore, we linearize a mobile robot by flatness and regard the linear system as two single input linear subsystems. The conventional control law requires that the system matrix has the solution of Lyapnov equation, in other words, the system matrix is hurwitz. However, the system matrix obtained by flatness doesn't has the solution of Lyapnov equation. So, carefully to satisfy certain condition, we redesign a new system matrix which is hurwitz. As a result, we guarantee the stability considering robustness by dealing with the influence of the system matrix error as matched disturbance. Simulation results show the effectiveness of the proposed control law.