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 J (2) 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 variables, 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 (2) perturbation is derived, and the approximate strategy of the low-level problem 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 J (2) perturbation; (3) Under J (2) 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.