A unified and simple control strategy for a class of n-link vertical underactuated manipulator

In this paper, we propose a unified and simple trajectory planning-based control strategy for the n-link (n≥2⋂n∈Z) vertical underactuated manipulator (VUM) with an underactuated joint. The proposed method does not need to partition the entire motion space like the traditional methods, and can quickly realize the control objective of swinging the endpoint of the system up from the vertical downward starting position and stabilizing it at the vertical upward ending position. The trajectory planned for each active link includes two stages. The first stage is to make the first active link and passive link reach the intermediate states, and other active links reach the ending states. The second stage is to move the first active link and the passive link to the ending states, while other active links keep at the ending states. Considering the above targets of two stages, the trajectory of each active link is designed and the trajectory parameters are optimized via utilizing the differential evolution algorithm. Then, the tracking controllers and stabilization controllers are designed to track the two-stage trajectories and to stay the endpoint at the ending position. Finally, the numerical simulations are carried out to show the feasibility and superiority of the proposed method.