Stabilization of the Acrobot via iterative state steering

We present a new approach for the control of the Acrobot, an interesting example of underactuated mechanical system. In particular, our objective is to transfer the system state from the downward equilibrium to the inverted equilibrium position. The proposed method prescribes the execution of three phases. In the first two phases, the robot is preliminarily swung up using an open-loop input and then driven by a suitable feedback to the inverted equilibrium manifold. In the last phase, the Acrobot is steered along this manifold to the inverted equilibrium position, under the action of a robust feedback controller based on the iterative state steering technique. Simulation results are given to show the performance of the method.