Nonholonomic motion planning for wheeled mobile systems using geometric phases

Abstract

In this thesis, the motion planning for wheeled mobile systems with nonholonomic constraints is studied. Such systems, in general, admit local representations in which the constraint equations are cyclic in certain variables. A nonlinear control system model describing the controlled motion of a wheeled mobile system with driving and steering inputs is first presented. State space and input space transformations are introduced to obtain a nonlinear control system in a normal form which is referred to as 'Caplygin form.' The structure of the Caplygin form equations allows identification of a 'base space', on which a set of decoupled controllable dynamics is defined. A general motion planning approach is then described. The motion planning strategy first transfers a given initial configuration to the origin of the base space and then causes the system to track a closed path in the base space that produces a desired 'geometric phase', i.e. a desired net change in the system configuration. It is shown that this motion planning approach constitutes a powerful analytic method for solving the motion planning problem associated with a large class of wheeled mobile systems including a car pulling n trailers. Results are illustrated through simulations of several examples of wheeled mobile systems.