Fuel optimization for constrained rotation of spacecraft formations

The problem of reorienting a constellation of spacecraft, such that the fuel distributed across the constellation is both conserved and expended uniformly, is considered. Results are derived for constellations with an arbitrary number of spacecraft, assuming that the constellation is in free space, that the spacecraft mass is time invariant, and that the thrusters can produce thrust in any direction. an open-loop control algorithm is derived by minimizing a cost function that trades off total fuel minimization and fuel equalization. The associated optimization problem is shown to be amenable to standard algorithms, simulation results using a four-spacecraft constellation are given.