Efficient optimal force distribution method of the parallel mechanism with actuator redundancy based on geometric interpretation

Abstract

A numerically efficient force distribution method for actuator saturation avoidance is proposed, which is applicable to two different types of the mechanisms with two degrees of actuator redundancy, parallel mechanism (PM) and cable-driven parallel mechanism (CDPM). The proposed method searches the optimal force solutions based on their geometric interpretation. Each actuator force with two degrees of actuator redundancy is expressed as a plane equation with respect to two intermediate variables. Thus, the optimal forces are found by searching for both the intersections between force planes and the common intersection points among those force planes. The proposed method for each of PM and CDPM is described. Then for two different exemplary mechanisms, the 2T2R -type 4 -DOF CDPM with six actuation cables and for the 2T1R -type planar 3- DOF PM with five active joints, comparative simulations moving along the spiral trajectory are conducted, employing three different methods, the proposed method and the other two typical off-line methods, the interior point method and the linear matrix inequality method. It is confirmed from those simulation results that the computational efficiency of the proposed method in finding their desired optimal force solutions is superior to the ones of the other two typical offline optimal searching methods and also sufficiently fast enough in real time applications.