A New Performance Index for Underactuated Cable-Driven Parallel Robots

Cable-driven parallel robots (CDPRs) equipped with less cables than the end-effector (EE) degrees of freedom (DoFs) are underactued and underconstrained by design. These characteristics imply that only a subset of the EE DoFs can be assigned for planning purposes, and that the EE can freely move when actuators are locked. The performance of this class of manipulators has yet to be fully analyzed, since common performance indices for fully or redundantly actuated robots may not directly apply. In this paper, a novel index is proposed, which is tailored for suspended underactuated CDPRs. This index analyses cable-tension sensitivity to cable-length variation, and aims at determining if a static equilibrium configuration is attainable under bounded cable-length control errors. When 4- or 5-cable UACDPRs have to perform positioning tasks, the optimization of such an index may be used to determine the safest EE orientation with respect to actuation errors.