Global stabilization of a class of nonholonomic systems

Due to the existence of singular sets of state and input transformations, the global feedback control laws developed for nonholonomic chained systems can only locally stabilize the original nonholonomic systems, which are locally convertible to nonholonomic chained form, and the size of attractive manifold of the closed-loop system becomes very small when the desired state is near to the singular sets. The global stabilization problem of a class of nonholonomic systems locally convertible to nonholonomic chained form is investigated in this paper. Firstly, a subset of attractive manifold is derived based on the condition J that the attractive manifold is an invariant set with no intersection with the transformation singular sets. Then, an open-loop control scheme is developed to drive an arbitrary initial state te, the subset of attractive manifold. By combining the open-loop and feedback control schemes, a hybrid control strategy is finally proposed, guaranteeing that any nonsingular desired state is globally asymptotically stable. Simulation results for a two-link planar space robot show the effectiveness of the proposed hybrid control scheme.