Adaptive tracking control of a wheeled mobile robot

Abstract

The stabilization problem for nonholonomic systems has attracted considerable attention of many researchers, see the survey paper [4] and references therein. A major obstacle to the asymptotic stabilization of these systems is that there is no smooth, nor even continuous, timeinvariant state-feedback stabilizing control law since these systems fail to satisfy Brockett’s necessary condition for feedback stabilization [1]. Only recently, the from an engineering point of view very interesting tracking problem has been addressed in [2, 3] and references therein. Under appropriate assumptions, given a feasible desired trajectory xd(t) a time-varying control law has been constructed such that the trajectory of the actual system approaches the reference tracjectory, i.e. lim t!1 |x(t) x d(t)| = 0. In this talk we will consider the adaptive tracking problem for a particular example of a nonholonomic system, namely a simple kinematic model of a mobile robot: ˙ x = u1 cos( + )