A General Position Control Method for Planar Underactuated Manipulators With Second-Order Nonholonomic Constraints

The study on the stabilization of planar underactuated manipulators without gravity is well recognized as a major challenge since the system includes a second-order nonholonomic constraint when the passive link is not located at the first link. It is important to solve this difficulty for applications such as systems working in aerospace or underwater. This article presents a position control method based on bidirectional motion planning and intelligent optimization for this kind of system. The control objective is to move the end effector of the manipulator from its initial position to a given target position. The differential evolution algorithm is applied to solve the target angles of all links corresponding to the target position of the end effector. Then, bidirectional motion planning is performed, which consists of forward and backward motions. Each motion is planned by designing a trajectory for every active link based on their initial and target angles. During the forward motion, all active links except the first one are moved to their target angles, and the first active link and the passive link to the intermediate angles. For the backward motion, the first active link is moved to its target angle, the other active links remain at their target angles, and the passive link will be moved to its target angle at the same time. The planned trajectories are chosen based on the time-scaling method and differential evolution algorithm to make sure that the forward and backward planned motions can be connected smoothly. Finally, the trajectory tracking controllers for all active links are designed based on the sliding-mode control method. The proposed control method is verified on planar four-link underactuated manipulators with different passive joints. This strategy has the advantage that it works for planar underactuated manipulators with a second-order nonholonomic constraint whose passive link can be at different positions. Meanwhile, by combining intelligent optimization with bidirectional motion planning, the control process becomes simpler and more effective.