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 J2 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 J2 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.