Statistical fuel budgets for impulsive guidance to earth-moon l1 halo orbits

An impulsive guidance scheme is introduced to mitigate the effects of thrust magnitude and direction errors for manifold-based transfers from LEO or GEO to an Earth-Moon L1 halo orbit. The trajectory is determined from a genetic algorithm combined with primer vector theory. The timing of the impulsive burns are found by solving for the maximum Lyapunov exponents of the stable manifold. To numerically obtain the required statisti- cal fuel budget for this guidance scheme, Monte Carlo simulations are performed for the guided transfer with Gaussian thrust error dispersions assumed in the orbit departure burn, manifold injection burn and the individual trajectory correction maneuvers (TCMs). The robustness of the guidance scheme is demonstrated by implementing TCMs while travelling along the stable manifold and reducing the resulting miss distance compared to previous results. The resulting TCM _V statistics are compared with the generalized analytical DV99 statistical fuel budget (SFB). The SFB estimate is shown to accurately match the fuel budget range from the Monte Carlo simulations.