Hybrid planning for LEO long-duration multi-spacecraft rendezvous mission

For the low-earth-orbit （LEO） long-duration multi-spacecraft rendezvous mission, a mixed integer nonlinear programming （MINLP） model is built with consideration of the , perturbation and the time window constraints based on lighting condition. A two-level hybrid optimization approach is proposed. The up-level problem uses the visiting sequence, the orbital transfer duration and the service time after each rendezvous as design variables, and employs the mix-coded genetic algorithm to search the optimal solution; the low-level problem uses the maneuver time and impulses in each rendezvous as design vari- ables, and employs the downhill simplex method to search the optimal solution. To improve the solving efficiency of the low-level problem, a linear dynamic model with J~ perturbation is derived, and the approximate strategy of the low-level prob- lem is then proposed. The proposed method has been applied to several numerical problems. The results lead to three major conclusions： （1） The MINLP model for LEO long-duration multi-spacecraft rendezvous mission is effective, and the proposed hybrid optimization strategy can obtain good solutions that satisfy time window constraints; （2） The derived linear dynamic equations are good first-order approximation to the long-duration rendezvous trajectory under ,J2 perturbation; （3） Under J2 perturbation, the long-duration rendezvous problem has multiple local minimums either in the duration of multiple orbits or in a single orbit, and it agrees with the problem＇s characteristic to use the mix-coded genetic algorithm.