Robust global stabilization of nonholonomic robots via smooth output feedback

One of the main problems when controlling a differential drive mobile robot is the nonholonomic restriction of its motion. The full-state stabilization problem resides, according to the fundamental work of R. Brockett, in the fact that the designed controller has to be either discontinuous or time-varying. In this work, we propose a novel robust position feedback controller for a class of perturbed nonholonomic robots. The controller has a rather simple to implement “proportional plus damping injection” structure that incorporates an adaptive velocity observer to exactly estimate constant external disturbances. The proposed observer is based on the well-known Immersion & Invariance technique. In order to overcome the nonholonomic restriction, the control law is time-varying. To the best of the authors' knowledge, this is the first solution to the robust output-feedback stabilization problem with a continuous time-varying controller. The formal convergence proof is established via Barbalat's lemma, and simulation results are reported to validate the performance of our method.