A Versatile Tension Distribution Algorithm for $n$ -DOF Parallel Robots Driven by $n+2$ Cables

Redundancy resolution of redundantly actuated cable-driven parallel robots (CDPRs) requires the computation of feasible and continuous cable tension distributions along a trajectory. This paper focuses on n-DOF CDPRs driven by n + 2 cables, since, for n = 6, these redundantly actuated CDPRs are relevant in many applications. The set of feasible cable tensions of n-DOF (n + 2)-cable CDPRs is a 2-D convex polygon. An algorithm that determines the vertices of this polygon in a clockwise or counterclockwise order is first introduced. This algorithm is efficient and can deal with infeasibility. It is then pointed out that straightforward modifications of this algorithm allow the determination of various (optimal) cable tension distributions. A self-contained and versatile tension distribution algorithm is thereby obtained. Moreover, the worst-case maximum number of iterations of this algorithm is established. Based on this result, its computational cost is analyzed in detail, showing that the algorithm is efficient and real-time compatible even in the worst case. Finally, experiments on two six-degree-of-freedom eight-cable CDPR prototypes are reported.