Dynamic Feedback Linearization of Nonholonomic Wheeled Mobile Robots

Abstract

Nonholonomic mechanical systems are known to be in general not stabilizable at equilibrium points by means of smooth state feedback. Nevertheless, smooth time varying laws can solve this stabilization problem. On the other hand, we show that by means of dynamic state feedback, it is possible for 3-wheeled mobile robots to track arbitrary fast trajectories not reduced to equilibrium points. Section 1 is devoted to some preliminaries about dynamical modelling of nonholonomic mechanical systems. Section 2 particularizes the case of 3-wheeled mobile robots (with free, steering or omnidirectional wheels). In Section 3 we briefly recall the idea of the dynamic extension algorithm which leads to full linearization of 3-wheeled mobile robots (with a free or steering wheel). Moreover, dynamic feedback will allow to solve the tracking problem for an omnidirectional mobile robot having less motors than degrees of freedom. This is possible by choosing “output functions” depending on the mass repartition of the robot. This result is quite analogous to the one obtained in [2] for a class of rigid manipulators having less motors than degrees of freedom.