Static workspace computation for underactuated cable-driven parallel robots

Cable-Driven Parallel Robots (CDPRs) move an end-effector (EE) using cables arranged in a parallel fashion. If a CDPR employs fewer cables than its EE degrees of freedom (DoFs), the robot is generally underactuated and underconstrained. Consequently, only a subset of the EE DoFs can be assigned for trajectory planning purposes, and the EE pose cannot be inferred by only relying on forward kinematics. Consequently, it is not trivial to assess the robot workspace (WS), even though WS computation is of paramount importance in analyzing the robot's performance. This paper introduces a novel algorithm for the computation of the reachable static WS of generic underactuated CDPRs, namely the set of EE positions that are statically attainable with at least one orientation and characterized by positive and bounded cable tensions. The algorithm leverages a novel geometrico-static problem, which, given a candidate EE position, seeks an orientation satisfying a stable static equilibrium characterized by a desired tension distribution.