Impulsive feedback control to establish specific mean orbit elements of spacecraft formations

An impulsive feedback control is developed to establish specific relative orbits for spacecraft formation flying, The relative orbit tracking errors are expressed in terms of mean orbit elements. The feedback control. based on Gauss's variational equations of motion, allows specific orbit elements or orbit element sets to be controlled with minimal impact on the remaining osculating orbit elements. This is advantageous when J(2)-invariant orbits are to be controlled, where only the argument of perigee and mean anomaly will drift apart at equal and opposite rates. The advantage of this impulsive feedback control, compared to optimal control solutions, is that it can operate with little computational effort and in a near-optimal manner, while requiring only a marginal penalty in fuel cost. When applied to the spacecraft formation flying problem, this control could also be used to perform general orbit corrections. Formulas are developed providing accurate estimates of the sensitivities of the mean semimajor axis and mean eccentricity with respect to the osculating inclination angle, with these sensitivities, the tracking error in semimajor axis, eccentricity, and inclination angle can be canceled within one orbit.