Spacecraft fast fly-around formations design using the bi-teardrop configuration

This paper investigates the feasibility, description, design, and control of fast fly-around formations around a chief spacecraft for rapid on-orbit servicing missions. The forming mechanics of two kinds of fast fly-around orbits is analyzed through an explicit geometrical demonstration in both inertial and relative coordinates. Then, relative motion equations based on relative orbit elements are presented to design the bielliptic and bi-teardrop formations, which provides intuitive geometric insight of relative motion in contrast to Cartesian position and velocity variables. The degree of urgency, fly-around distance, and relative view angle are chosen to describe the configuration of the in-plane and the out-of-plane formations. A detailed design process for the fast fly-around formations is proposed. Impulsive control strategies for the fast fly-around formations establishment and reconfiguration are derived. The design method and control strategies are validated through several numerical simulations. The effect of fly-around parameters on fuel consumption and payload performance are analyzed.