Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds: A preliminary study

Two optimization methods are presented for designing fuel-optimal impulsive transfers from low earth orbit to the Earth-Moon libration points L₁ and L₃ using the stable manifolds found in the Circular Restricted Three Body Problem. The two methods used are a grid search and a genetic algorithm. All transfers require one maneuver to leave LEO and a second to transfer onto the stable manifold. The trajectories discussed have total changes in velocity between 3.48 km/s and 3.72 km/s. An LQR based guidance scheme is presented which maintains the spacecraft on the stable manifold in the presence of injection errors in burn magnitude and direction. Monte Carlo analyses are conducted to further demonstrate effectiveness of the guidance scheme. The total ΔV costs to use the guidance scheme average 12.34 m/s and 10.88 m/s for L₁ and L₃ libration point transfers, respectively, when a thrust magnitude Gaussian dispersion with 1σ = 1% error is combined with in-plane and out-of-plane thrust direction Gaussian dispersions with 1σ = 1 degree error.