Movement Characteristics Analysis And Control Method Research Of Planar Acrobot

In this paper, a control strategy for a planar underactuated robot is proposed based on the motion states constraints by system modeling and movement characteristics analysis. The control strategy overcomes the difficult stabilization problem effectively, and provides a new way for control method of planar underactuated mechanical systems.Firstly, the dynamic model of the Planar Acrobot is obtained based on the Lagrange equation. Meanwhile, some system characteristics are analyzed for controllability, which indicate the difficulties of control.Secondly, the movement characteristics are analyzed. The angular velocity constraint and angle constraint between the two links are obtained by integrating the dynamic equation of the underactuated joint respectively. Based on the constraints, an accessibility judgment condition is proposed for any desired position. Meantime, a calculation method for the end point of the system is given, and its trajectory is obtained. The trajectory further explains that the system has usually the characteristics of any posture accessibility.Then, a control strategy is designed based on the motion states constraints. Its design procedure is divided into two steps. First step, an integer programming PSO algorithm is applied to obtain the target control angle with required precision and rapidity. Second step, a controller is designed to realize the active link posture control by using a Lyapunov function which consists of the optimal angle and the angular velocity of the active link. And the passive link can be also controlled to target position according to the motion states constraints. Therefore, the control strategy can stabilize the system at the target position.Finally, the global stability of the control strategy is guaranteed based on the largest invariant set theorem, and the simulation results prove the correctness and effectiveness of the proposed optimal algorithm and control strategy.