Optimal Reconfiguration of Formation Flying Satellites

We employ a recently developed new technique for the numerical treatment of optimal control problems for mechanical systems in order to compute optimal open loop control laws for the reconfiguration of a group of formation flying satellites. The method is based on a direct discretization of a variational formulation of the dynamical constraints. We extend the method by linearizing around a given nominal trajectory and incorporate certain collision avoidance strategies. We numerically illustrate the approach for a certain reconfiguration maneuver in the context of future formation flying missions and compare our method to a standard finite difference approach.