Set stabilization of nonholonomic chained form systems

Conventional controllers for the nonholonomic systems all stabilize the closed loop system to a target point. In this paper, considering the nonholonomic chained form system, a control design approach based on set stabilization idea is proposed. The proposed control laws can asymptotically stabilize the closed loop system to a set of given target points. First, for the first-order subsystem, a state feedback control law is designed to guarantee that the state of the closed loop system is asymptotically stabilized to a set of points. Second, for the n-1th order subsystem of other states, another state feedback control law is designed to guarantee that the states of the closed loop subsystem are asymptotically stabilized. Finally, an application example, the set stabilization of periodic target points, is given. Simulation results show the effectiveness of the method.