On the robustness of cable configurations of suspended cable-driven parallel robots

Cable-driven parallel robot (CDPR) are parallel robots that use coilable cables as legs. We are interested here in suspended CDPR for which there is no cable that exert a downward force on the platform. If we assume that the cables are mass-less and not elastic it has been shown that at a given pose whatever is the number m > 6 of cables there will always be at most 6 cables under tension simultaneously. A cable configuration (CC) at a given pose is the set of cables number that are under tension and usually there are several possible CC for the same pose. These CC are not equivalent in terms of cable tensions, sensitivity to measurement errors and therefore it make sense from a control viewpoint to enforce the ”best” CC to obtain the optimal robot configuration, which can be done by controlling the length of the cables that are not members of the CC so that we are sure that they are slack. Hence we are interested in ranking the different CC in term of robustness. We propose several ranking indices for a CC and algorithms to calculate these indices at a pose, on a trajectory or when the robot moves on a surface and we show examples for a CDPR with 8 cables.