Timescale separate optimal control of tethered space-Tug systems for space-debris removal

A computationally efficient algorithm was developed with an acceptable accuracy to solve an optimal-control problem of tethered space tug (TST) systems during the propulsion stage of a Hohmann transfer that remove space debris or dysfunction satellites from a geostationary orbit to the graveyard orbit. The purpose of the optimal control is to stabilize the TST system in the orbital transfer with minimum fuel consumption by controlling the acceleration of tether length, the control torque on the tug, and the orientation of the propulsion force. The computational efficiency is achieved by timescale separation of state and control input variables. Furthermore, a two-stage control strategy is proposed by using a sliding-mode closed-loop controller to track the optimal trajectory. The numerical simulation demonstrates the proposed timescale-separation scheme is effective in reducing the computational burden of the optimal control by 26% with an acceptable control accuracy.