Minimum-time control of the Acrobot

The Acrobot, a two-link arm that is unactuated at the first joint, is challenging to control because it is an underactuated, nonlinear, continuous system. We describe a direct search algorithm for finding swingup trajectories for the Acrobot. The algorithm uses a lookahead search that maximizes the Acrobot's total energy in an N-step window. Because the controls are extremal and the number of switches in the window limited, the algorithm is fast. Nevertheless, the resulting trajectories are near optimal.