Robust global stabilization of nonholonomic robots via smooth output feedback

Abstract 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.