Fuel optimization schemes for formation reconfiguration in satellite formation flying

We study the satellite formation reconfiguration within a fixed orbit transfer time and aim to minimize or balance its fuel consumption. In this study, the formation will end up with an in-plane formation regardless of its initial state. We take consideration of the constraints of relative motion equation, initial and terminal states, collision avoidance, and maximum thrust. We attach an unknown offset in the terminal state of the formation and adapt a convex-programming-based iterative approach to jointly optimize the fuel usage and the offset of the formations. The proposed algorithms clearly outperform benchmarks in all the numerically tested situations with respect to both minimization of the total fuel consumption and minimization of the maximum fuel usages across all the satellites of the formation.