A Proportional Control Strategy for Stiffness Tuning of Parallel Manipulators

This article presents a control strategy for the stiffness regulation of parallel manipulators based on the implementation of a simple proportional controller. Starting from the assignment of the stiffness or compliance matrix in the task space, defined by the application-specific requirements, a proper control action is calculated by considering the translational and rotational compliances of the end effector. The proposed approach is applied in SE(2) and SE(3), addressing the analysis of the 3RRR planar parallel manipulator and the 6UPS Stewart-Gough platform. The proposed control scheme decouples the effects of the applied force and moment on the end effector displacement and rotation. Numerical examples are presented, with multibody simulations performed to verify the effectiveness of the proposed approach. The effect of friction in the active and passive joints is also investigated.