Iterative-analytic redundancy resolution scheme for a cable-driven redundant parallel manipulator

In this paper, redundancy resolution of a cable-driven parallel manipulator is solved by an iterative-analytic scheme. The method can be applied to all kind of redundant manipulators either parallel or serial with constraint caused through their dynamics. However, for sake of simulation the proposed method is implemented on a cable-driven redundant parallel manipulator (CDRPM). The redundancy resolution problem is formulated as a convex optimization with equality and non-equality constraints caused by manipulator structure and cables dynamics. Karush-Kuhn-Tucker theorem is used to analyze the optimization problem and to find an analytic solution. Subsequently, a tractable and iterative search algorithm is proposed to solve the redundancy resolution of such redundant mechanisms. Furthermore, it is shown through the simulation that, the elapsed time required to implement the analytical redundancy resolution scheme in a closed-loop structure is considerably less than that of other numerical optimization methods.