Optimal commands based multi-stage drag de-orbit design for a tethered system during large space debris removal

There is a serious challenge to the safe operation of orbiting satellites as the number of space debris increases for its high risks and the possible crippling effects of collisions. Consequently, the active removal scenario of space debris has drawn wide attention in recent years, and a tethered system is considered to be a promising method for its large operating distance and low power consumption. However, the flexible tether of the system will bring the coupling of the orbit motion, the sway motion and the variation of large debris attitude, which brings about great danger in de-orbiting phase and a huge challenge in later control. Hence, aiming to de-orbit large space debris safely with a tethered system, a multi-stage horizontal drag de-orbit strategy that consists of two stages is designed. At the first stage, the orbit altitude is rose with a tug thrust whose direction is consistent with the tether, which does not provoke the in-plane oscillation of the tethered system. At the second stage, the orbit is circularized by changing the size and direction of the tug thrust. Especially, optimal commands based on the minimum of tangling risks are planned using Gauss pseudospectral method to avoid target tangling and achieve decoupling of the orbit motion, the sway motion and the variation of the target attitude. Then, the stable attitude control of the tethered system is achieved by designing a hybrid fuzzy adaptive proportion differentiation (PD) with hierarchical sliding-mode controller (HSMC) in the de-orbit process. Finally, numerical simulation is implemented to verify the effectiveness of the proposed de-orbit design.