Planning and feedback control for mechanical systems with nonholonomic constraints

The goal of this dissertation is to present a complete strategy for controlling a class of mechanical systems with nonholonomic velocity constraints. Examples considered in this dissertation include a simple wheeled mobile robot, a front wheel drive car, a tiller truck, a satellite mounted with thrusters, and a robot with one unactuated joint called the planar acrobot. Control objectives are limited to achieving some desired configuration. Several new methods are presented to achieve these objectives in efficient ways.; The process of control is broken down into three stages. Given a large initial offset between the configuration and its desired value, first an (optimal) path planner generates an admissible trajectory connecting the initial and desired configurations. Second, an exponentially stabilizing tracking law is applied, insuring that the desired trajectory is followed closely even in the presence of disturbances and modeling errors. Finally, when the configuration variable is near the desired value, we switch to a feedback law which renders the desired configuration asymptotically stable.; The five example mechanical systems, when examined in detail, are shown to have certain structural properties in common. In particular, all except the satellite mounted with thrusters may be transformed locally into a form called the "Control Canonical Form". The planning, tracking, and regulation problems are solved for this canonical form. The results are then applied to the example systems. The satellite with thrusters, representative of a large class of mechanical systems, requires a different approach.