Long-time stable formation optimal design method for satellite formation

To design a long time stable satellite formation for saving fuel is very important work, so an optimization method to design a long time stable satellite formation under various perturbations is derived. Firstly the constraints between relative positions and velocities in Hill frame according to the specific mission are developed by using the Hill s equation. Secondly using the free relative positions or velocities as optimization variables, the optimization cost function is the sum of the relative mean orbit elements drift velocities under J₂ perturbation. The optimal algorithm used above is the modified genetic algorithm. The genetic algorithm can find the global optimal values compared to other optimal methods, while the genetic algorithm also has some drawbacks such as prematurity and evolution stagnancy in solving some difficult problems. So a modified genetic algorithm is derived to overcome the drawbacks mentioned above. The simulation results show that the satellite formation designed by the optimization method under various perturbations can keep stable for a long time without any control.