Trajectory Planning and Tracking Control for Positioning of Planar Three-link Underactuated Manipulator

This paper is concerned with the position control problem of the planar active-passive-active (APA) underactuated manipulator, whose dynamic constraint is mainly caused by the second-order nonholonomic constraint. First, the dynamic model of the system is established and the target angles of the three links are calculated by using differential evolution algorithm. Then, we present a trajectory planning and tracking control strategy to realize the control objective, which is to stabilize the end-point from any initial position to the target position. We plan two stage trajectories, the first of which is planned for the active links. When the the active links track the first stage trajectories, they can reach to their target angles. The second one is planned for the first active link based on the differential evolution algorithm. When the first active link tracks the second stage trajectory, it will back to its target angle eventually. Meantime, the passive link will be controlled to its target angle. Then, we design sliding mode variable structure controllers to make active links track the planned trajectories, which can make the all links reach to the their target angles. Finally, numerical simulation results illuminate the effectiveness of the proposed strategy.