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.
A circumlunar free return orbit design model that satisfies manned lunar mission constraints is established. By combining analytical method with numerical method,a serial orbit design strategy from initial value design to precision solution is proposed. A simulation example is given,and the conclusion indicates that the method has excellent convergence performance and precision. According to a great deal of simulation results solved by the method,the free return orbit characters such as accessible moon orbit parameters,return orbit parameters,transfer delta velocity,etc. are analyzed,which can supply references to constitute manned lunar mission orbit scheme.
