On the determination of the maximal inscribed ellipsoid in the Wrench-Feasible Workspace of the cable-driven parallel robots

Abstract

This paper deals with determining the maximal regions within the Wrench-Feasible Workspace (WFW) of cable-driven parallel robots using convex optimization. In this regard, an approach is proposed in order to obtain the maximal-area ellipse and the maximal-volume ellipsoid within the wrench feasible workspace of the planar and spatial cable-driven parallel robots respectively, using convex optimization. The main contribution of this paper consists in relaxing the equations of the workspace boundaries by using Weierstrass and Chebyshev approximation theorems, which are approximated to the higher-order workspace equations with second-order polynomials. Then, an algorithm to solve the obtained quadratic programming problem is introduced. Finally, a pseudo-code for the proposed procedure is presented and the obtained results are illustrated.