Trajectory tracking control of variable length pendulum by partial energy shaping

Abstract

This paper concerns a trajectory tracking control problem for a variable length pendulum, whichis an underactuated mechanical system of two degrees of freedom with a single input of adjusting the length of the pendulum. First, we show that there exists an avoidable singular point in the controller designed by using the conventional energy-based control approach in which the total mechanical energy of the system is controlled. Second, we propose a tracking controller free of singular points by using only the kinetic energy of rotation and the potential energy of the pendulum. Third, we present a global motion analysis of the pendulum and provide some conditions on control parameters for achieving the tracking objective.