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

Annie Larsen, William Anthony, Thomas Critz, Morad Nazari, Masoud Deilami, Eric Butcher, George Born, Jay MacMahon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Title of host publicationAIAA/AAS Astrodynamics Specialist Conference 2012
DOIs
StatePublished - 2012
Externally publishedYes
EventAIAA/AAS Astrodynamics Specialist Conference 2012 - Minneapolis, MN, United States
Duration: Aug 13 2012Aug 16 2012

Other

OtherAIAA/AAS Astrodynamics Specialist Conference 2012
CountryUnited States
CityMinneapolis, MN
Period8/13/128/16/12

Fingerprint

libration
Moon
natural satellites
Earth (planet)
low Earth orbits
thrust
Electronic guidance systems
linear quadratic regulator
Dispersions
Spacecraft
three body problem
maneuvers
Orbits
moon
Genetic algorithms
Trajectories
genetic algorithms
spacecraft
grids
trajectories

ASJC Scopus subject areas

  • Aerospace Engineering
  • Astronomy and Astrophysics

Cite this

Larsen, A., Anthony, W., Critz, T., Nazari, M., Deilami, M., Butcher, E., ... MacMahon, J. (2012). Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds: A preliminary study. In AIAA/AAS Astrodynamics Specialist Conference 2012 https://doi.org/10.2514/6.2012-4667

Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds : A preliminary study. / Larsen, Annie; Anthony, William; Critz, Thomas; Nazari, Morad; Deilami, Masoud; Butcher, Eric; Born, George; MacMahon, Jay.

AIAA/AAS Astrodynamics Specialist Conference 2012. 2012.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Larsen, A, Anthony, W, Critz, T, Nazari, M, Deilami, M, Butcher, E, Born, G & MacMahon, J 2012, Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds: A preliminary study. in AIAA/AAS Astrodynamics Specialist Conference 2012. AIAA/AAS Astrodynamics Specialist Conference 2012, Minneapolis, MN, United States, 8/13/12. https://doi.org/10.2514/6.2012-4667
Larsen A, Anthony W, Critz T, Nazari M, Deilami M, Butcher E et al. Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds: A preliminary study. In AIAA/AAS Astrodynamics Specialist Conference 2012. 2012 https://doi.org/10.2514/6.2012-4667
Larsen, Annie ; Anthony, William ; Critz, Thomas ; Nazari, Morad ; Deilami, Masoud ; Butcher, Eric ; Born, George ; MacMahon, Jay. / Optimal transfers with guidance to the earth-moon L1 and L3 libration points using invariant manifolds : A preliminary study. AIAA/AAS Astrodynamics Specialist Conference 2012. 2012.
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