Time-Optimal Trajectory Planning of Cable-Driven Parallel Mechanisms for Fully-Specified Paths With G¹ Discontinuities

Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully-specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is adapted for use with cable-driven parallel robots, which exhibit the additional constraint that all cable tensions remain positive along a path to be followed. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the minimum-tension constraint is imposed directly and is fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. This approach is relevant for cable-driven mechanism applications that involve high accelerations, particularly in the vertical direction.