We propose a control law to swing-up the acrobot from an initial domain to a neighbourhood of the vertically upward equilibrium position. The methodology involves reducing the system to a one degree-of-freedom system, much like a simple pendulum, evolving on a critical value of the energy level set. The system is guaranteed to converge to a neighbourhood of the upward equilibrium position about which a linear feedback controller is switched on to stabilize the system.
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