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In this study, the formation flying of two spacecraft in near-circular orbits under the influence of a J2 perturbation is considered to obtain a control strategy for maintaining formation flying while minimizing fuel usage. This study utilizes a state transition matrix that describes the relative motion of a deputy spacecraft with respect to a chief spacecraft in terms of the argument of latitude of the chief spacecraft. Owing to the J2 perturbing force, the actual position of the deputy with respect to the chief deviates from the nominal position. The abovementioned state transition matrix enables the analytical calculation of the secular terms of the deviation, providing the strategy for optimized fuel position maintenance. In this study, a two impulsive control is considered to compensate for the secular terms of the position error. Additionally, the conditions for the chief spacecraft's argument of latitude that minimize the velocity increments for the two impulsive controls are derived. The velocity increments are effectively reduced by adjusting the chief spacecraft's argument of latitude while taking the influence of the J2 perturbation into account.

Fuel-Optimal Control of Formation Flying in Near-Circular Orbits