Geometry-Based Trajectory Planning of a 3-3 Cable-Suspended Parallel Robot

Abstract

This paper addresses the dynamic trajectory planning of a spatial cable-suspended parallel robot with three cables and three-degree-of-freedom. A new $s-\ddot{s}$ plane ( $s$ is the path parameter) method is presented to devise dynamically feasible point-to-point trajectories and periodic trajectories that are not fully located in the static workspace (SW) of the robot. First, the unilateral cable tension constraints are explicitly converted into geometry constraints in the $s-\ddot{s}$ plane. Then, a set of reachable workspaces is defined, which can be obtained analytically and the volumes of which are all much larger than the volume of the SW. By designing dynamic point-to-point trajectories directly in the $s-\ddot{s}$ plane, any points in the reachable workspaces can be reached in sequence via some intermediate points in the SW. The $s-\ddot{s}$ plane method also offers insights into planning periodic circular trajectory and transition trajectory for oscillations along a straight line, which is considered to be more efficient than the algebraic method provided in the literature. The proposed method always guarantees positive and continuous cable tensions and yields analytical results. The performance of the method is evaluated through numerical simulations and experiments.