Optimal collision avoidance maneuver for formation flying satellites using relative orbital elements

The safety of the formation flying satellites in the cross-track plane is investigated. It is important to ensure a minimum separation in the cross-track plane due to the uncertainty of the along-track drift. Once the satellite is within the avoidance region, the collision avoidance maneuver with optimization is planned to reach a safe ellipse, which remains out of the avoidance region. Firstly, the formation configuration is described based on the relative orbital elements. Secondly, formulas of the parameters of the ellipse in the cross-track plane are proposed and the formation control strategy based on the Gauss perturbation equations is put forward. Finally, the energy of the collision avoidance maneuver is expressed by the rotating angle of the safe ellipse in the cross-track plane, which is optimized by the Newton method. The simulation results indicate the simplicity and effectiveness of the presented method.