Station-keeping strategy for tethered drag sail-based transverse formation

During general 2-satellite formation, the relative baseline between satellites periodically changes, resulting in limited time for interferometric imaging and poor observation quality. This study incorporates a drag sail into the tethered satellite system, where the chief satellite moves in a low Earth orbit (LEO) and connected deputy drag sail is in a non-Keplerian displaced orbit. Given the free-molecule flow property of the atmosphere in LEO, the drag sail can simultaneously provide normal pressure and tangential stress. By adjusting its attitude appropriately, the sail can move synchronously with the chief satellite with respect to a fixed relative position, during which a fixed baseline for formation flying can be achieved. Because the component of the baseline perpendicular to the ground tracks of the satellite is constant, the proposed system is denoted as a transverse formation. To better investigate the system, the nonlinear characteristics are analyzed for the controlled dynamical models. Considering the complexity of aerodynamic force based on rarefied gas dynamics, feasible formation configurations are investigated from the perspective of the control force direction. Then, a control strategy is provided to maintain the formation configuration based on the linear quadratic regulator (LQR) control framework. The parameter optimization of LQR control considers the coupling degree of modals, control force, and error. The attitude of the sail is inversely computed based on the Taylor expansion, and the results show that the proposed maintenance strategy is successfully realized with the smooth rotation of the drag sail.