Dynamic control of tug-debris tethered system after the capturing of the debris

This paper focuses on the problem of control of the tug-debris space tether system for debris De-orbiting. The motion of the tether system is considered when the space tug and tethered debris have an initial relative velocity, which can affect the tether tension. We investigate two stages of the space tether motion: tether elongation stage and tether retraction stage. Two control laws for the tether length are proposed for the each stage. The control law for the first stage is based on the measurement of the tether tension and is intended to decrease the relative velocity between the space tug and debris object. The control law for the second stage retracts the tether and decrease the distance between the space tug and debris assisting to the process of the docking of the space tug with debris. The proposed control laws are demonstrated by numerical simulations.