Hybrid tension control method for tethered satellite systems during large tumbling space debris removal

Large space debris in the valuable orbit is an inevitable and serious problem which increases the risk of fatal collisions. The use of space tether is a promising method for de-orbiting large debris safely at low cost and low energy consumption. However, the risk of winding is increasing because of variations in sway motion due to underactuativity, high nonlinearity, and the strong coupling of the tethered system. Hence, in this paper, a hybrid tension control method is proposed to stabilise satellite system tethered to large space debris. The dynamic equations of a tethered satellite system are formulated with an analysis of the impact of the variation in sway motion on tether winding. Following this, the optimal commands of sway motion are planned using the Gauss pseudospectral method to preliminarily avoid the tether winding with the target. To further reduce the risk of winding, a fuzzy adaptive proportion differentiation (PD) controller is designed to stabilise the relative attitude of the tether and the large debris. And the control tension is considered as a time-varying parameter and is added using a hierarchical sliding-mode controller (HSMC), which is used to control the in-plane angle and the relative distance to implement the hybrid control of the overall tethered satellite system. Several simulations were implemented to verify the effectiveness of the proposed tension control method.