Nonlinear Optimal Control for Swing Up and Stabilization of the Acrobot via Stable Manifold Approach: Theory and Experiment

This paper presents a solution for the swing-up and stabilization problem for the Acrobot. The method employed is the stable manifold method for optimal control, which numerically solves Hamilton-Jacobi equations (HJEs). It is shown that the feedback controller derived from the HJE for the optimal control problem exploits an inherent motion in the Acrobot using reactions of arms effectively and, therefore, the control input is kept low. Both the simulation and the experiment confirm the effectiveness and robustness of the controller. This is the first experimental result of a swing-up control for the Acrobot with a single continuous controller. This paper also discusses the comparison with existing approaches for the same problem. It is also shown that nonunique solutions exist for the HJE and the experiment is conducted with one of those.