Time-Energy Optimal Trajectory Planning of Cable-Suspended Manipulators

This paper addresses the problem of time-energy optimal control of cable robot with the trajectory planning as the overall mission. The final dynamic equations were organized in a closed form similar to serial manipulator equations. Thus, employing the Pontryagin maximum principle, it was verified that the optimal motions are all bang–bang controls with bounded control torque on the winches. This consists of minimizing a cost function, considering dynamic equations of motion as well as bounds on joint torques. Here, the cost function was chosen as a weighted balance of traveling time and mechanical energy of the actuators. The approaches of solving concrete optimal control laws based on Two-Point Boundary Value Problems were provided in this paper and the algorithm was tested in simulation yielding acceptable results.