Analytical fuel-optimal impulsive reconfiguration of formation-flying satellites

This paper investigates fuel‐optimal impulsive reconfiguration of formation‐flying satellites near circular reference orbit. First, the general reconfiguration is transformed into reconfiguration that should be accomplished during multiple orbital periods of the chief. Then, based on the primer vector analysis, multiple‐impulse fuel‐optimal analytical solutions for the transformed reconfiguration are derived. It is shown that multiple‐impulse fuel‐optimal analytical solutions appear conjugated and the corresponding reconfiguration trajectories are symmetric about the chief. Furthermore, for fuel‐optimal analytical solution with three or more impulses, the associated impulse magnitudes may have many combinations, which would yield different reconfiguration trajectories but with the same fuel cost. Finally, numerical examples for three typical formation reconfiguration maneuvers, including resizing, reorientation, and reassignment, are given to illustrate and validate the obtained results.