Beyond-the-static-workspace point-to-point trajectory planning of a 6-DoF cable-suspended mechanism using oscillating SLERP

Abstract

This paper presents a general framework for the planning of point-to-point motions that extend beyond the static workspace of six-degree-of-freedom cable-suspended parallel mechanisms. The proposed translational trajectories are based on a generalization of the hypocycloidal motion previously introduced for cable-suspended robots. Also, the concept of ideal kinematic state is used to maximize the chances of obtaining feasible trajectories, i.e., trajectories in which tension is maintained in the cables. The rotational component of the trajectories is based on the use of spherical linear interpolation. A novel formulation is proposed to connect two arbitrary orientations through oscillations going through the reference orientation. It is shown that the impact of the translational trajectories on the tension constraints is largely dominant, compared to that of the rotational trajectories. A procedure is presented for the determination of the trajectory parameters in order to ensure the continuity of the trajectories. Trajectory feasibility is verified, including mechanical interferences and singularity detection. Finally, a natural cylindrical coordinate frame is proposed that yields a very intuitive description of the trajectories and simulation results are given to illustrate the effectiveness of the proposed approach.