Dynamic trajectory planning for a spatial 3-DoF cable-suspended parallel robot

This paper deals with continuous path motion planning of a spatial 3-DoF cable-suspended parallel robot considering the robot's dynamic constraints. First, based on the analysis of the algebraic and geometric properties of cable tension constraints, we present the sufficient and necessary conditions for the end-effector to pass through parallel singularities along straight line paths. Then, a piecewise linear interpolation method is introduced, showing that any target points above cable exit points can be connected in sequence via some intermediate points in the static workspace of the mechanism. The intermediate points are properly selected to avoid collisions between cables and obstacles, and the resulting trajectory is modified using quintic polynomials to enhance the performance. Afterwards, conditions for a general planar curve determined by three points to be feasible are given, and a general curve interpolation method is presented. Finally, three types of periodic trajectories are designed. Using the proposed trajectory planning method, not only can the positive cable tension constraints be satisfied, but the safety and the continuity of tensions can also be ensured. The effectiveness of the method is examined through simulations and experiments.