Tension optimization for cable-driven parallel manipulators using gradient projection

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. Cables have unilateral driving properties so that redundant actuation is required to maintain positive cable tensions. Due to the actuation redundancy, there exists an infinite number of tension solutions for every CDPM´s pose. In this paper, a gradient projection method is employed for tension optimization of CDPMs. This optimization process minimizes a performance criterion which is a function of the cable tensions and the tension limits. The steepest descent direction of the performance criterion is projected onto the null space of the structure matrix to provide the direction towards the local minimum. Global optimal tension solution is found by repeating this process. A factor is introduced to adjust the tension solution towards the upper or lower tension limits. Simulation results show that the algorithm produces tension solutions that are continuous and smooth.