Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

In cable-driven parallel manipulators (CPMs), cables can perform only under tension, and therefore, redundant actuation, which can be provided by redundant limbs, is needed to maintain the cable tensions. By optimizing the distribution of the forces in the cables and the redundant limbs, the average size of actuators can be reduced resulting in lower cost. Optimizing the force distribution in CPMs requires consideration for the inequality constraints imposed on the cable forces as a result of the unilateral driving property of the cables. In this study, a projection method is presented to calculate optimum solutions for the actuators force distribution in CPMs. Two solutions are presented: 1) a minimum-norm solution that minimizes the 2-norm of all forces in the cables and redundant limbs and 2) a solution that minimizes the 2-norm of the forces in the cables only. The optimization problem is formulated as a projection on an intersection of convex sets and the Dykstra´s projection method is used to obtain the solutions. This method is successfully applied to a 3-DOF CPM.