A general nonholonomic motion planning strategy for Caplygin systems

This paper studies the kinematic path planning problem for Caplygin systems, i.e. nonholonomic systems with special symmetry properties. Such systems admit local coordinate representation in which the constraint equations are cyclic in certain variables. A nonlinear control system model describing the kinematics of a Caplygin system is first introduced. An algorithm for constructing a path between specified initial and final configurations of the system is then presented. The algorithm utilizes tools from differential geometric control theory