Hybrid Stabilization of Closed Orbits for a Class of Underactuated Mechanical Systems

This article presents a hybrid controller to stabilize a class of closed orbits for mechanical systems with degree of underactuation one. The controller has a hierarchical structure, whereby at the low level, a smooth feedback enforces a virtual holonomic constraint in a family, while at the high level, a supervisor selects from within the family the constraint to be enforced. To illustrate these ideas, the controller is first used to stabilize oscillations for the acrobot in a manner reminiscent of a child pumping energy on a swing and then to induce an oscillatory motion in a brachiating robot so as to make its arms bridge the gap between two consecutive handholds.