N-Impulse Formation Flying Feedback Control Using Nonsingular Element Description

An N-impulse feedback control strategy is developed to mitigate errors in a set of nonsingular orbit element differences between a chief and deputy spacecraft. Although suitable for general, elliptic chief orbits, this strategy is motivated by relative orbit control in the geostationary regime, in which nonsingular element descriptions are especially convenient. The Gauss variational equations for this nonsingular set are developed as a basis for the N-impulse feedback control strategy, which assumes piecewise constant element errors evaluated once per orbit. The N corrective impulses are applied at uniform intervals in true anomaly, and the magnitudes thereof are determined with a swift numerical method. Two examples demonstrate that this method is proficient in helping to detect fuel-optimal burn locations for general formation and element difference corrections.