A Control Strategy Based on Trajectory Planning and Optimization for Two-Link Underactuated Manipulators in Vertical Plane

The control objective of the vertical plane underactuated manipulator (VPUM) is generally to swing up the end point (EP) from the vertical down equilibrium point (VDEP) to the vertical up equilibrium point (VUEP), and finally, to stabilize it at the VUEP. The zone control methods are usually used to achieve this control objective, but the problem of these methods is that they cannot find a unified zone range, and it is easy to appear singularity in the motion process. In this article, for two-link VPUMs, we propose a control strategy based on trajectory planning and optimization, which does not need to divide the zone range, avoids the singularity problem, and can achieve the control objective quickly and smoothly. We design the trajectory by using the time scale method for the active link according to the initial and target states. Then, we obtain the trajectory parameters by employing differential evolution algorithm to ensure that the passive link can also move from the initial states to the target states simultaneously. We design a sliding mode tracking controller to make the active link move along the designed trajectory, so the EP is moved to VUEP. Meantime, we design a sliding mode stabilization controller to ensure that the system is stable at VUEP. Finally, the universality and robustness of the proposed method are proved by simulations.