Hybrid Feedback Control for Path Tracking by a Bounded-Curvature Vehicle

In this paper, we consider the problem of stabilizing the kinematic model of a car to a general path in the plane, subject to very mild restrictions. The car model, although rather simplified, contains some of the most relevant limitations that make application of existing results in the literature impossible: namely, the car can only move forward, and turn with a bounded steering radius; also, only limited sensory information is available. The approach we follow to stabilization is to adapt to the present general case an optimal synthesis approach successfully applied in our previous work to tracking rectilinear paths. Due to both the nature of the problem, and the solution technique used, the analysis of the controlled system involves a rather complex switching logic. Hybrid formalism and verification techniques prove extremely useful in this context to formally proof stability of the resulting system, and are described in detail in the paper.