A Novel Analytical Approach for Spacecraft Fly-Around Formation Design with a Low-Thrust Maneuver

This paper investigates the fly-around formation between the servicer spacecraft and the target spacecraft. Inspired by the spacecraft orbital motion under the Earth’s gravity, an intuitive, analytical guidance law for spatial fly-around formation design with the low-thrust maneuver is proposed. Beginning with the relative translational dynamics based on relative position and velocity, the control input of the guidance law is designed to contain two parts. The first part is the feed-forward term, which makes the relative dynamics a second-order integration model. The second part is the artificial gravity term, which has similar expressions to the Earth’s gravity, and includes the artificial gravitational coefficient and the vector of the artificial gravity center. The above two parameters can be designed to determine the size, shape, and period of the fly-around trajectory. Specifically, three kinds of fly-around trajectories are discussed in detail. The first two are the spatial ellipses with the target spacecraft locating at the focus and the center of the ellipses, respectively. The third is the spatial circle. The proposed method can be easily extended to the design of planar fly-around formation, which is very systematic and comprehensive, and the fuel consumption of the control input is specifically discussed. Numerical simulations are conducted to demonstrate the efficiency of the proposed method.