Time Optimal Trajectory Tracking of Redundant Planar Cable-Suspended Robots Considering Both Tension and Velocity Constraints

In this paper, time optimal trajectory tracking of redundant planar cable-suspended robots is investigated. The equations of motion of these cable robots are obtained as a system of second order differential equation in terms of path parameter $s$ using the specified path. Besides, the bounds on the cable tensions and cable velocities are transformed into the bounds on the acceleration and velocity along the path. Assuming bang-bang control, the switching points in $ṡ2−s$ plane are obtained. Then the cable tensions are found in terms of path parameter and, subsequently, versus time. The proposed approach is validated and the effect of the number of superfluous cables on the value of minimum time is studied. The next notable challenges include time optimal path planning of cable-suspended robots. By developing a hybrid genetic algorithm and bang-bang control approach, the minimum motion time from initial state to final one and also the corresponding path can be found. The optimum path is the one that minimizes traveling time from initial state to final one, while not exceeding the cable tensions and cable velocities limits, without collision with any obstacles.