An impulsive control scheme 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 control scheme, based on Gauss' 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 control scheme allows only these two parameters to be corrected without affecting the other four orbit elements. Formulas are developed providing accurate estimates of the sensitivities of the mean semi-major axis and mean eccentricity with respect to the osculating inclination angle. With these sensitivities, the tracking error in semi-major axis, eccentricity and inclination angle can be cancelled within one orbit.
展开▼
