Force-distribution sensitivity to cable-tension errors in overconstrained cable-driven parallel robots

Cable-driven parallel robots (CDPRs) employ extendable cables to move their end-effectors (EEs) throughout the workspace. Since cables can only sustain tensile stresses, the EE is often overconstrained to keep cable tensions within positive limits during motion. In this case, to control the overall cable-tension distribution, one can force-control a particular set of cables, and length-control the others. This work aims at evaluating the maximum value of tension error caused on the length-controlled cables, while force-controlling a chosen cable set, by computing a performance index called force-distribution sensitivity to cable-tension errors. This index informs about the maximum expected cable-tension error on the length-controlled cables, if a unitary tension error is committed on a specific set of force-controlled cables, and allows one to determine which set of cables are best to be force-controlled, to ensure the lowest error in the overall tension distribution. The force-distribution sensitivity is derived for a generic overconstrained CDPR, with arbitrary geometry and number of cables. As an application example, its minimum value is computed to characterize the workspace of three exemplifying overconstrained CDPRs.