Homogeneous stabilization of an underactuated planar PPR manipulator

A continuous time-varying feedback controller is presented for point stabilization of the second-order chained form system. The second-order chained form system can not be stabilized by means of continuous purestate feedback. Moreover, it can not be exponentially stabilized by means of smooth feedback since the linearization around any equilibrium point is uncontrollable. In this paper we provide a controller that globally ¿- exponentially stabilizes the system. The controller is derived by using a combined averaging technique for homogeneous systems and a backstepping approach. The controller is illustrated on a benchmark example of a second-order chained form system, namely an underactuated planar PPR manipulator