Abstract: A method of towing space debris to the grave orbit by constant tension is proposed for the problem of precise control during orbit transfer. In this paper, the dynamics model of a tethered space-tug (TST) system is firstly formulated by the Newton-Euler method. Then the system stability is proved by the Lyapunov method. The attitude nutation of space debris is restrained by using the constant tension switching control law, and the control law based on the phase plane control principle is proposed to stabilize the in-plane and out-plane swing of the tethered combination, thus preventing the collision between the tug spacecraft and debris as well as the twine and breakage of the tether, and ensuring the safety of the towing process. The numerical simulation shows the effectiveness of the above control methods．

Key words: Space debris, Tether system, Newton-Euler method, Constant tension, Phase plane principle