Control of Nonholonomic Systems with Drift Terms

Abstract

In the present paper nonholonomic systems with drift terms are studied. The discussion is focused on a class of Lagrangian systems with a cyclic coordinate. We present an approach to open--loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs. A control algorithm is derived and it is applied to the planar diver. A similar algorithm is derived for the study of what states can be reached within a given time. An exponentially stabilizing feedback controller is derived for tracking of the planned trajectories. The results are illustrated with simulations. 1 Introduction Driftless nonholonomic control systems have been studied in recent years by Walsh and Sastry (1991), Teel et al. (1992), Murray and Sastry (1993), Bloch et al. (1993), Kolmanovsky and McClamroch (1995), and others. Several important results have been derived based on the structure of Lie algebras generated by the control vector fields. A dual point of ..