Impulsive guidance for optimal manifold-based transfers to earth-moon L1 halo orbits

An impulsive guidance scheme is presented which maintains the spacecraft on the stable manifold of a L1 halo orbit in the Earth-Moon system in the presence of thrust errors in the manifold injection maneuver for a 2-impulse ballistic transfer from LEO to the halo orbit. A Monte Carlo analysis is shown for the unguided case using Gaussian input dispersions in burn magnitude and direction to demonstrate the need of impulsive guidance. Two strategies based on the state transition matrix are presented, one using single burns that only target the manifold, and full burn pairs that target the manifold at t1 and correct velocity errors at t2. Both strategies effectively reduce the halo orbit insertion miss distances; however, the single burn strategy has lower ΔV costs for guidance. Lyapunov Exponents (Les) of the stable manifold are then obtained and used to determine the best locations to perform the TCMs, which also include similar thrust errors in the final simulations.