A positioning control strategy of planar Acrobot

A positioning control strategy is proposed to move the planar Acrobot with a passive first joint from any initial position to its target position. Firstly, a proportional relationship is found according to the linear approximation model at any equilibrium between angels and angular velocities. This proportional relationship can guarantee the control objective of one link is achieved by designing a control law, meanwhile, the objective of the other link can also be achieved. Then, the control process of planar Acrobot is divided into two stages based on this motion characteristics. In the first stage a Lyapunov function is constructed to design control law to drive the system satisfying the mentioned proportional relationship. In the seconde stage, another control law is designed to move one link to its desired position, and the overall control objective, which is to move the Planar Acrobot from any initial position to its target position, is realized with the coupling between system state ultimately. Finally, the simulation results demonstrate the effectiveness of the proposed strategy.