Exponential /spl epsi/-tracking and /spl epsi/-stabilization of second-order nonholonomic SE(2) vehicles using dynamic state feedback

In this paper, we address the problem of /spl epsi/-tracking and /spl epsi/-stabilization for a class of SE(2) vehicles with second-order nonholonomic constraints. We introduce a class of transformations called near-identity diffeomorphism that allow dynamic partial feedback linearization of the translational dynamics of this class of SE(2) vehicles. This allows us to achieve global exponential /spl epsi/-stabilization and /spl epsi/-tracking (in position) for the aforementioned classes of autonomous vehicles using a coordinate-independent dynamic state feedback. This feedback is only discontinuous w.r.t. the augmented state. We apply our results to /spl epsi/-stabilization and /spl epsi/-tracking for an underactuated surface vessel.