This paper addresses the energy based swinging up control problem of the Acrobot, which is a two, link underactuated planar robot. Based on the Lyapunov stability theory, this paper proposes an energy based control law, 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. Specifically, for
any initial state of the Acrobot, this paper provides a necessary and sufficient condition for non-existence of any singular point in the control law, and shows clearly how to choose the control parameters such that starting from
any initial state, the Acrobot will eventually either be swung up to any arbitrarily small neighborhood of the upright equilibrium point, or remain at the downward equilibrium point. Moreover, this paper shows that the downward equilibrium point is unstable and
hyperbolic for the closed-loop system. This proves theoretically that the proposed energy based control is effective for swinging up the Acrobot for all initial conditions except a set of zero measure. Simulation results are provided to validate the theoretical results.
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