Detumbling of Underactuated Tethered Satellite System Based on Hierarchical Sliding Mode Control

Millions of space debris pose a significant risk to operational spacecraft, making active debris removal (ADR) missions an urgent priority. Net capturing is a promising method to remove space debris objects due to its multiple advantages. However, once a target has been captured, a combined tethered system comprising the chaser, the target, and the tethers is formed, which requires effective stabilization. In this paper, stabilization of the entire postcapture system is realized by solely controlling the active chaser satellite. Such a control strategy can attenuate system hardware facilities compared with those by applying additional tether control such as using a winding mechanism, which were mostly discussed in the literature. Further, for the first time, considering the uncertainties during the capture process, including inaccurate target parameters, initial attitude error of the target, and external disturbances, a hierarchical sliding mode controller (HSMC) with two sublayers is developed to detumble this underactuated system. Additionally, a hybrid position controller is proposed to eliminate the undesired swing motion within the system. Numerical simulations demonstrate that HSMC method delivers better performance over the proportionalderivative controller in efficiency and robustness for postcapture stabilization of the combined tethered system. Overall, our proposed control strategy offers a promising solution for future ADR missions, contributing to a safer and more sustainable space environment.