Model Orbit Robust Stabilization (MORS) of Pendubot with Application to Swing up Control

Orbital stabilization of a simple underactuted manipulator, namely, two-link pendulum robot (Pendubot) is under study. Since underactuated systems cannot be stabilized by means of smooth feedback, the solution to the stabilization problem is sought within switched control methods. The quasi-homogeneous control synthesis is utilized to design a switched controller that drives the Pendubot to its zero dynamics in finite time and maintains it there in sliding mode. The constructed controller is such that the Pendubot zero dynamics is generated by a modified Van der Pol oscillator, being viewed as a reference model. The closed-loop system is thus capable of moving from one orbit to another by simply changing the parameters of the proposed modification of the Van der Pol oscillator. Performance issues of the controller constructed are illustrated in a simulation study of the swing up control problem of moving the Pendubot from its stable downward position to the unstable inverted position and stabilizing it about the vertical.