Swing up and stabilization of the Acrobot via nonlinear optimal control based on stable manifold method

This paper considers the problem of swing up and stabilization for the Acrobot. It is shown that stable manifold method which has been proposed for computing nonlinear optimal control is capable of designing feedback controllers for this problem. An optimal stabilization controller is obtained as a single feedback law by numerically solving a Hamilton-Jacobi equation by the stable manifold method. It is shown that unlike existing methods for Acrobot swing up such as partial feedback linearization, the resultant control is mechanically indigenous in the sense that it uses reactions of arms effectively and, as a consequence, control input is kept low. A number of simulations verify the effectiveness and robustness of the controller.