Smooth Trajectory Planning Based on Direct Collocation Method for Cable-Driven Parallel Robots with Central Spine

摘要

An important characteristic of cable robots as a new type of parallel robots is well known as cables can be only driven by positive tension. Cables tensions in the cable-driven parallel robots make trajectory planning more challenging than rigid-link parallel robots. This paper offers a direct collocation technique to solve the point-to-point trajectory planning to minimize the jerk cost function. This hybrid structure includes a 3-cable robot and a central linear actuator which cancels the end-effector’s weight while improving the tensionability condition. First, the kinematics and dynamics of the cable-driven parallel robot are formulated. Then the direct collocation approach is addressed through the sequential quadratic programming algorithm, while the computation time is considerably diminished via the linear initial guess and defining sparse structure for Jacobian of constraints. The offered method is then compared with the standard MATLAB software package GPOPS-II to develop trajectories with smooth profiles. Using the proposed planning algorithm with a constraint on the cable forces, the sudden tension change in all cables can be conveniently eliminated, which leads to a harmonized distribution of tensions. Simulation results demonstrate that the presented algorithm has remarkable benefits, proposing an effective solution to generate smooth trajectories with a short execution time.