New analytical results of the energy based swinging up control of the Acrobot

This paper addresses the energy based swinging up control problem of the Acrobot, which is a typical example of underactuated mechanical systems. This paper provides a complete analysis of the convergence of the energy and the motion of the Acrobot. and illustrates clearly several unique characteristics of the closed-loop system of the Acrobot under the energy based control. Specifically, this paper shows clearly how to choose the control parameters such that starting from any initial state, the Acrobot will eventually either be swung up to an arbitrarily small neighborhood of the upright equilibrium point, or remain at the downward equilibrium point which is shown to be unstable for the closed-loop system. This proves theoretically that the energy-based control is effective for swinging up the Acrobot.