Practical maintenance strategies for teardrop hovering formation relative to elliptical orbit

Hovering technology, as one of the core technologies in on-orbit service (OOS) missions, enables the relative position between an active spacecraft and chief spacecraft to be maintained within a given range, and it has received widespread attention in recent years. In this study, for an elliptical reference orbit, we proposed a series of control strategies to maintain a teardrop hovering formation with a J2 perturbation. First, we formulated a mathematical model of the teardrop hovering formation maintained by the impulse control and presented a rapid method based on a relative-position correction method. Based on the sensitivity matrix, a strategy for maintaining a hovering formation using constant-thrust control was obtained. Furthermore, based on the proposed fast iterative method, an improved strategy was developed to satisfy a magnitude constraint. Finally, we analyzed the influence of the reference orbital elements and formation parameters on the hovering formation using numerical simulations, which demonstrated the efficiency of the proposed method. This provides a reference for the preliminary design of hovering formations.