Impulsive control for near round reference orbit satellites formation

For a satellite flying on a round orbit, there exists a singularity problem when the Gauss perturbation is used to describe the satellite's argument of perigee and mean anomaly. Aiming at this situation, satellite motion was described by nonsingular orbit elements and the corresponding impulsive control model for a near round reference satellite formation is derived. Based on this model, first, the inclination and right ascension error is corrected by exerting an impulsive control effort along the normal direction. After that, suppose other elements error is corrected by exerting impulsive control efforts at two positions and at each position, impulsive control efforts are exerted along tangent and radial directions simultaneously, and then the conclusion can be drawn that a complex nonlinear problem is induced by exerting tangent impulsive control at the first position. Taking this situation into account, a two impulsive control algorithm that only exerts control effort along radial direction at the first position and only exerts control effort along tangent direction at the second one is put forward. The fuel consumption of the given algorithm is analyzed. In the end, the simplicity and effectiveness of the given algorithm is verified by mathematical simulation results.