Optimal impulsive manifold-based transfers with guidance to Earth-Moon L₁ halo orbits

An optimization method combining genetic algorithms, differential correction, and primer vector theory is employed for designing fuel optimal 2-impulse transfers from low earth orbit or geostationary orbit to a halo orbit about the Earth-Moon L₁ libration point using the stable manifold of the halo orbit. All transfers require one maneuver to leave LEO or GEO and a second maneuver to transfer onto the stable manifold. The trajectories obtained have total ΔV's of 3.61 and 1.14 km/s respectively. 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 using a variable low continuous thrust engine. Monte Carlo analyses are conducted to further demonstrate the effectiveness of the guidance scheme. The total ΔV costs to use the guidance scheme averages 14.385 m/s for transfers from LEO and 6.54 m/s for transfers from GEO, when a thrust magnitude Gaussian dispersion with 1σ = 1% is combined with in-plane and out-of-plane thrust direction Gaussian dispersions with 1σ = 1 degree error. The guidance is also implemented assuming a limit to the continuous thrust.