The dynamical servo control problem for the Acrobot based on virtual constraints approach

This paper discusses the dynamical servo control problem for the Acrobot - a mechanics with two links while just one actuator applied to the second link. The dynamical servo control aims to access generic points in the state space not just the equilibrium points. Stabilizing of generic points is impossible and a possible way is to stabilize some periodic orbits passing through the desired points. Virtual constraints are used to generate such orbits. By analyzing the integration of the zero dynamics of the Acrobot subjected to virtual constraints, conditions of whether there is an orbit passing through the desired point and the orbit function are found. A cascade control strategy is proposed to stabilize both the virtual constraint and the orbit function which decides the system behavior. Simulation results show the effectiveness of the control law.