Exponential control law for a mobile robot: extension to path following

The authors present an exponentially stable controller for a two-degree-of-freedom robot with nonholonomic constraints. Although this system is controllable, it has been shown to be nonstabilizable via smooth state feedback. A particular class of piecewise continuous controller which exponentially stabilizes the robot about the origin was previously proposed by the authors (1991). This approach is extended to stabilize about an arbitrary position and orientation, and to track a sequence of points. This feedback law is naturally combined with path planning when the desired path to be followed can be composed of a sequence of straight lines and circle segments, i.e. shortest paths of bounded curvature in the plane