Variable Structure Control Based on Sliding Mode for a 2-DOF Underactuated Robot Manipulator

This paper presents a new stable sliding-mode control method for a two-link planar robot arms, with a passive rotational joint. Our idea is first to divide the underactuated system into two subsystems, and define two first-level sliding surfaces. Then we get a two-level sliding surface for the whole system and use the Lyapunov law to define the control law for the arms. The control law can drive the subsystems toward their sliding surfaces and achieve their desired values. The asymptotic stability of the sliding surfaces is established and proved theoretically in Lyapunov sense. Therefore, we get that the whole system can be drive to its sliding surface and stable. Finally the simulation results show the controller's validity and its adaptive abilities to the system parameter variations.