Trajectory tracking control for maneuverable nonholonomic systems

The paper considers a motion control problem for kinematic models of nonholonomic wheeled systems. The class of maneuverable wheeled systems is defined consisting of systems that can follow any sufficiently smooth non-stop trajectory on the plane. A sufficient condition for maneuverability is obtained. The design of control law that stabilizes motion along the desired trajectory on the plane is performed in two steps. On the first step the trajectory on the configuration manifold of the system and the input function are constructed that ensure the exact reproduction of the desired trajectory on the plane. The second step is the stabilization of the constructed trajectory on the configuration manifold of the system. For this purpose a recursive procedure is used that is a version of backstepping algorithm meant for non-stationary systems nonlinearly depending on input. The procedure results in the continuous memoryless feedback that stabilizes the trajectory on the configuration manifold of the system. As an example the motion control problem for a truck with multiple trailers is considered. It is shown that the proposed control law stabilizes the desired trajectory of the vehicle on the plane for all initial states of the system from some open dense submanifold of the configuration manifold, i.e., almost globally. The statement takes place both for a truck pulling any number of trailers in a forward direction and for a truck pushing any number of trailers in a backward direction. The latter result is the solution of the intuitively hard problem of the road train reverse motion control. The effectiveness of the proposed control is demonstrated by simulation. Animated examples are presented at Sergei V. Gusev Web Page.