PD control with gravity compensation for 3-RPS parallel manipulator

When a 3-RPS (revolute-prismatic-spherical) parallel manipulator is working, the gravity center of its load will move with its rotation, which will deteriorate the performance of the traditional Proportional Derivative (PD) controller and introduce steady-state error. This paper proposes a dynamic gravity compensation (GC) based controller for a 3-RPS parallel manipulator to improve the dynamic performance. Specifically, this paper offers a detailed analysis of this manipulator's Jacobian matrix, through which the gravity term in the dynamic model can be separated and converted to the joint space. Then the Jacobian matrix can be used in dynamic GC for the traditional PD controller. As a result, the improved controller provides smoother motion and better control. The simulation results show that the PD controller with GC has a better control effect than the traditional one. The root mean square (RMS) values of tracking errors in three degrees of freedom under sinusoidal excitation are reduced by 49.18%, 70.25%, and 88.28%, respectively, compared to traditional PD controllers.