Disturbance observer-based fixed-time control for space tether system with prescribed performance after capturing debris

This paper studies the dynamic and control problems of space tether system (STS) after capturing space debris. The fully integrated system post-capture is referred to as space tether debris-assembly (STDA), while the system comprising the capture device and debris is termed the debris assembly. A significant challenge in stabilizing STS after debris capture lies in the residual angular momentum of the debris, which, if unmitigated, coupled with the relative angular velocity difference between the debris and the tether, can lead to detrimental effects such as tether entanglement and system destabilization. Furthermore, STDA system experiences unknown mass parameter variations that exacerbate control difficulties. To address these challenges, this paper proposes a nonlinear control strategy designed to rapidly stabilize the attitude motion of the end body, despite uncertainties in mass parameters and boundary constraints. A dynamic model of STDA system, encompassing the host spacecraft, tether, capture device, and space debris, is formulated based on Lagrangian equation. This model accounts for the relative attitude motion between the debris-assembly and the tether, as well as the attitude dynamics of the tether itself, thereby enabling an analysis of disturbances arising from unknown mass parameters and collision-induced angular motion. To mitigate these disturbances, a sliding mode disturbance observer is developed to compensate for dynamic uncertainties associated with the space debris’ unknown mass. Furthermore, an error transformation is performed, and a prescribed performance controller is designed to ensure that the system remains within predefined boundaries during stabilization. The effectiveness of the proposed method is validated through numerical simulations.