Stabilization of a class of second-order nonholonomic systems

Stabilization problem of a class of second-order nonholonomic systems is studied. The system is shown controllable but not stabilizable by any smooth pure state feedback control law. The state and input feedback transformations are constructed explicitly to convert the system to a second-order nonholonomic chained form. A smooth time-varying control law is derived to exponentially stabilize the obtained second-order chained form. The proposed approach is applied to stabilize several underactuated robot systems.