Direct method for tension feasible region calculation in multi-redundant cable-driven parallel robots using computational geometry

Abstract

With a low moving inertia, high payload-to-weight ratio, and large workspace, cable-driven parallel robots (CDPRs) are relevant in many applications, especially redundant CDPRs. As there exist an infinite number of tension distributions, this paper presents a novel computational geometry-based method to calculate a tension feasible region (TFR)—a preimage of tension distribution—for multi-redundant CDPRs. The proposed TFR algorithm overcomes some of the limitations of conventional iterative and vertices search methods. The TFR is first interpreted as a convex intersection of multiple boundary-parallel spaces, where its dimension is equal to redundancy r. To obtain the centroid of TFR, the vertices coordinates and order for r = 2 and 3 only need to be determined on surface. Static simulations with 6 degrees-of-freedom using 8-cable and 9-cable CDPRs are employed to demonstrate the algorithmic accuracy. Additionally, to illustrate that the optimal tension distribution has continuity, motion trajectories for the same CDPRs are calculated. Furthermore, the proposed algorithm minimizes computational time when compared to the performance of existing algorithms. Thus, the proposed method could rapidly establish the optimal tension distribution.