Global Planning of Dynamically Feasible Trajectories for Three-DOF Spatial Cable-Suspended Parallel Robots

Abstract

This paper addresses the dynamic trajectory planning of three-DOF spatial cable-suspended parallel robots. Based on a dynamic model of the suspended robot, a set of algebraic inequalities is obtained that represents the constraints on the cable tensions. Dynamic feasibility is then established using interval arithmetics on the latter inequalities in order to obtain global conditions on the trajectory parameters that can guarantee that the cable tensions remain positive throughout the trajectory. Such conditions are obtained for a variety of parametric trajectories. When periodic functions are used in the design of the trajectories, it is shown that special frequencies arise that are akin to natural frequencies of pendulum-type systems. These special frequencies can be used in practice to greatly simplify the trajectory planning. An experimental implementation on a three-dof cable-suspended prototype is presented. As demonstrated, the proposed trajectory planning approach can be used to plan dynamic trajectories that go beyond the static workspace of the mechanism, thereby opening novel applications and possibilities for cable-suspended robots.