Optimal Fuel-Balanced Impulsive Formationkeeping for Perturbed Spacecraft Orbits

This paper develops an impulsive spacecraft formation-flying control algorithm using relative-orbital-element corrections. This formalism introduces an inherent freedom that is used for deriving an optimal formationkeeping law, balancing the fuel consumption among the spacecraft based on the impulsive Gauss variational equations. The main idea is that formulating the problem of formationkeeping in terms of relative-orbital-element corrections leaves the final values of the orbital elements unconstrained, thus allowing the spacecraft to create a natural energy-balanced formation. The freedom rendered by this modeling is used to find optimal impulsive maneuvers, minimizing the squared 12-norm of the velocity-correction vector, which can be used for formation initialization and control. The optimization is solved using the least-squares method. The optimal formationkeeping method is designed to accommodate the effects of oblateness and drag. Based on graph theory, it is shown that the spacecraft will naturally form a stable energy-balanced formation and that the optimal formationkeeping strategy is invariant to the spanning tree. The algorithm is illustrated by simulating the motion of a formation of spacecraft possessing different ballistic coefficients subject to oblateness and drag.