Near-identity diffeomorphisms and exponential ε-tracking and ε-stabilization of first-order nonholonomic SE(2) vehicles

In this paper, we address ε-tracking and ε-stabilization for a class of SE(2) autonomous vehicles with first-order nonholonomic constrains. We introduce a class of transformations called near-identity diffeomorphisms that allow dynamic partial feedback linearization of the translational dynamics of this planar vehicle. This allows us to achieve global exponential ε-stabilization and ε-tracking (in position) for the aforementioned class of planar vehicles using a coordinate-independent dynamic state feedback. This feedback law is only discontinuous w.r.t. the augmented state. We apply our results to ε-stabilization/tracking of a nonholonomic mobile robot.