Existence and design of strongly stabilizing controller for the Acrobot

This paper concerns the strong stabilization for a typical example of underactuated robots called Acrobot, which is two-link underactuated planar robot with a single actuator driving the relative angle of two links. This paper shows the existence of strongly stabilizing controllers for the upright equilibrium point of the Acrobot by designing a specific output and employing the pole-zero relation of the linearized model around the equilibrium point. The paper presents a design method for the controllers. In terms of strong stabilization, some new features of the Acrobot are revealed and are compared with those of the cart-pendulum system. Simulation results are presented to validate the theoretical results.