Stability of an impulsive control scheme for spacecraft formations in eccentric orbits

An N-impulse control scheme for spacecraft formations in elliptical orbits is developed to regulate the differential elements of the deputy spacecraft in the presence of the J(2) perturbation. The presented control scheme is an extension of an existing circular-orbit formation control scheme and is shown to perform well at large eccentricities where the circular control scheme fails. For the case of two impulses being applied at arbitrary firing times, a discrete-time approach for ascertaining the stability of the controlled spacecraft formation, under the assumption of small impulsive thrusts, is presented. It is found that stability is guaranteed for the majority of firing time pairs; however, the requisite V can be prohibitive for some firing time pairs. The control scheme and stability predictions for formations in high eccentricity orbits are validated in numerical simulation.