Bounded relative motions for formation flying in displaced orbits by low-thrust propulsion

This paper discusses a numerical searching approach for the relative motion of formation flying in displaced orbits by spacecraft with low-thrust propulsion. The nonlinear dynamical model of spacecraft is established in a two-body rotating reference frame with arbitrary polar component of momentum and thrust-induced acceleration. Motions near the stable equilibria are distinguished from each other by means of five-dimensional variables, which can then be compressed uniquely into two-dimensional mapping images characterized by the crossing interval and the angle drifts. The surjective but not injective mapping makes the generation of three configurations of the relative motions possible. The corresponding relative orbits for three kinds of two-spacecraft formation flying are searched and exemplified based on the formation conditions formulized as functions of the crossing interval and the angle drifts. Furthermore, based on the assignment of displaced relative orbits to five-dimensional vector, the working orbit of the deputy for a specific chief can also be searched via the optimization algorithm to generate the bounded relative motion with the minimum thrust acceleration magnitude, which is of certain significance in reducing fuel consumption of formations.