Underconstrained planar cable-direct-driven robots: A trajectory planning method ensuring positive and bounded cable tensions

A major open issue in the design and operation of cable-direct-driven-robots (CDDRs) is ensuring tensile cable forces for any admissible motion of the CDDR. Such a problem is particularly challenging when underconstrained and non-redundant CDDR configurations are considered. In this paper a new and general trajectory planning method is introduced, which has been specifically developed to ensure always positive and bounded cable tensions in underconstrained planar two-degree-of-freedom translational CDDRs. The proposed method translates the typical bilateral force constraints of the cables (i.e. positive and bounded tensions) into constraints on the velocity and acceleration of the CDDR end-effector along the path. Such constraints are computed making use of the robot dynamic model and are then incorporated in a suitable trajectory planning algorithm also yielding the minimum traversal time. The method is explained and validated numerically by applying it to a novel concept of underconstrained hybrid (serial/parallel) CDDR. The results achieved prove that the proposed method may a priori ensure positive and bounded cable tensions along any straight line and circular path.