Swing-up Control of the Acrobot Using a New Partial Linearization Controller Based on the Lyapunov Theorem

In this paper, a design of swing-up controller of an Acrobot is proposed. The Acrobot is a model of a horizontal bar gymnast, it has only one actuator at the joint of both links and is a typical example of a nonlinear underactuated system. Since the robot has a large range of motion, the Acrobot has a highly nonlinear characteristic and swing-up control of the Acrobot is a difficult problem. The Acrobot has a simple structure and its control objective is clear, hence it is used as a controlled object of not only the nonlinear underactuated control problem but also a remote network control problem recently. For swing-up control of the Acrobot, this paper proposes a controller, which uses pumping energy of the first link. In the controller, a newly proposed partial linearization is used. The nonlinear feedback is constructed based on the Lyapunov theorem. The new feature of the proposed partial linearization method is to guarantee that the linearized sub-systems track the time-variant reference function, which is not guaranteed in previous methods. Numerical simulation is performed to show the effectiveness of the proposed method