A two-steps robust path-following controller for wheeled robots

This paper addresses the problem of determining a feedback control law, robust with respect to localization errors, allowing a mobile robot to follow a prescribed path. The model we consider is a dynamic extension of the usual kinematic model of a car, in the sense that we define the path curvature as a new state variable. The control variables are respectively the linear velocity and the derivative of the curvature. By defining a sliding manifold we determine a stabilizing controller for the nominal system i.e. when the exact configuration is supposed to be known. Then, using Lyapunov analysis, we prove that the system remains stable when the estimated values are used for feedback instead of the exact ones, and we characterize the robustness with respect to localization and curvature estimation errors. The result is expressed by determining a compact attractive domain bounding the regulation error as the closed-loop control is performed with the estimated state values. This domain allows to compute easily a security margin for obstacle avoidance during the path-following phase. Experimental results are presented at the end of the paper.