Nonholonomic motion planning for wheeled mobile systems using geometric phases

In this paper, we consider the motion planning problem for wheeled mobile systems with nonholonomic constraints. Such systems, in general, admit local coordinate representation in which the constraints are of Caplygin form, i.e. the constraint equations are cyclic in certain variables. We first introduce a nonlinear control system model describing the motion of a wheeled mobile system with driving and steering inputs. We then describe a motion planning approach using geometric phases which have proved useful in a variety of nonholonomic control problems in the recent nonlinear control literature [1], [6]. We demonstrate that this motion planning approach provides a closed-form solution to the well-known multi-trailer problem. Results of the paper are illustrated through simulations of two examples: a front-wheel-drive car and a car pulling a trailer.