Path-Following with a Bounded-Curvature Vehicle: a Hybrid Control Approach

In this paper, we consider the problem of stabilizing the kinematic model of a car to a path in the plane under rather general conditions. The path is subject to very mild restrictions, while the car model, although rather simplified, contains the most relevant limitations inherent in wheeled robots kinematics. Namely, the car can only move forward, its steering radius is lower bounded and a limited sensory information only provides a partial knowledge of some state parameters. In particular, we consider the case that the current distance and the heading angle error with respect to the closest point on the reference path can be measured but only the sign of the path curvature is detected. These constraints are such to make classical control techniques inefficient. As the feedback information is both continuous and discrete, the hybrid systems formalism turns out to be well appropriate to model the problem. The proposed approach is based on optimal control techniques successfully applied in a previous work for following rectilinear path. We propose here an extension to the tracking of more general paths with moderate curvature. The stability of the closed-loop system is proved by means of the hybrid system formalism and hybrid formal verification techniques. Finally, the practicality of the proposed approach, in spite of non–idealities in real-world applications, is discussed by reporting experimental results.