Relative Distance Control of Uncooperative Tethered Debris

An increasing concern for space-based missions is the potential of collisions with space debris. Long-term mitigation of this risk can be achieved by removing large debris from orbit, as, in particular, collisions involving these can significantly increase the number of smaller debris in orbit. One method of removal involves an active craft capturing and towing a large piece of debris from orbit using a tether. To ensure a successful mission, collisions and tether winding about the target must be avoided. This work proposes relative distance proportional-integral-derivative (PID) and proportional-derivative (PD) controllers to regulate the distance between the chaser and target for a post-capture tethered satellite model. The performances of both controllers are compared to each other and to the performance of an open loop thrust to understand their impact on the system dynamics. The simulation results indicate that PID control is unsuitable for scenarios where the tether is initially slack, as it induces significant angular motion on the target, which could potentially lead to tether winding. However, PD control was found to induce safe angular motion both with an initially slack and an initially taut tether. A sensitivity study found PD control to be robust to the initial chaser-target relative distance and target inertia properties; however, similarly to PID control, it cannot control the angular motion of the target. As such, it is recommended to apply the PD controller after detumbling has been performed or when the debris angular motion is sufficiently small.