Optimal target states for satellite cluster flight control on near-circular orbits

One of the methods for maintaining a cluster of satellites in long-term bounded relative distances is keeping the satellites on near-circular orbits having the same mean semimajor axes and mean inclinations. This approach allows some freedom in determining the reference mean semimajor axis and reference mean inclination for the cluster. In this paper, this freedom is used to find the optimal target values of the mean semimajor axis and mean inclination, with the optimization criteria being either the total propellant consumption of the cluster or the fuel consumption differences among satellites. The optimization problems are solved analytically, assuming that a fixed-magnitude thruster is used for closed-loop orbit control, and new results are presented, providing simple closed-form expressions for the optimal target states. Simulations are used for validating the results, showing that much propellant can be saved by properly setting the cluster reference orbit.