1 / 23

Andrew Abraham Lehigh University

Optimization of Preliminary Low-Thrust Trajectories From GEO-Energy Orbits To Earth-Moon, L 1 , Lagrange Point Orbits Using Particle Swarm Optimization . Andrew Abraham Lehigh University. Introduction: The Importance of Lagrange Points. L 2. L 1. Applications of Earth-Moon L 1 Orbits:

shawn
Download Presentation

Andrew Abraham Lehigh University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Optimization of Preliminary Low-Thrust Trajectories From GEO-Energy Orbits To Earth-Moon, L1, Lagrange Point Orbits Using Particle Swarm Optimization Andrew Abraham Lehigh University

  2. Introduction:The Importance of Lagrange Points L2 L1 • Applications of Earth-Moon L1 Orbits: • Communications relay • Navigation Aid • Observation & Surveillance of Earth and/or Moon • Magnetotail Measurements (ARTIMIS mission) • Parking Orbits for Space Stations or Spacecraft

  3. Introduction:The Importance of Low-Thrust • Advantages of Low-Thrust Dynamics: • Low fuel consumption • Better Isp (order of magnitude) • High payload fraction delivered to target • Power source arrives at target

  4. CR3B Problem Setup • Assume: • m1 & m2 orbit their barycenter in perfectly circular orbits • m1≥m2>>m3 Define: Synodic Reference Frame

  5. CR3BP Low-Thrust Equations of Motion

  6. Lagrange Points

  7. L-Point Orbits and Their Manifolds Pick a point on the orbit, X0 Integrate the EOM and STM for 1 period. The STM = Monodromy Matrix Calculate the Eigenvalues (λ) and Eigenvectors (υ) of the Monodromy Matrix Find the stable Eigenvector/value Perturb the original state by a small amount along the stable Eigenvector and propagate that perturbation backwards in time to generate a trajectory Repeat steps 1-5 for multiple points along the nominal orbit X0

  8. Overview A L2 L1 C B ?- Low Thrust Patch Point Goal: Get From GEO (A) to a L1 Halo (C) via some trajectory (B)

  9. Mingotti et al. A L2 L1 C B ?- Low Thrust Mingotti’s Technique* Begin with a reasonable guess trajectory Trajectory will join a low-thrust arc with the invariant stable manifold Use Non-Linear Programming (NLP) with Direct Transcription and Collocation Fast algorithm with reasonable convergence Shortcomings: Requires a reasonable guess solution to converge Prone to locating local minima instead of global minima *G. Mingottiet al, “Combined Optimal Low-Thrust and Stable-Manifold Trajectories to the Earth-Moon Halo Orbits,” AIP Conference Proceedings, 2007

  10. New Approach • Select a “Patch Point” on the Stable Manifold • Propagate a low-thrust trajectory backwards in time from that point • Use a “tangential thrust” control law to steer the spacecraft • Instantaneous 3-body velocity of the spacecraft • This control law is the most fuel and time efficient law because it maximizes the Jacobi Energy • Stop propagation once Jacobi Energy of the spacecraft is equal to a GEO orbit • Repeat steps 1-4 for a new Patch Point • Find the Patch Point that minimizes some cost/fitness/performance function

  11. Fitness Function = eccentricity of GEO-energy Earth orbit = fuel consumed during low-thrust transfer = time of flight from GEO to the nominal L-point orbit = a patch point on the stable manifold

  12. How to Find the Optimal Patch Point? τs.m. = -21.56 k = 583+ τs.m. = -18.31 τs.m. = -17.71 Patch Point k = 610+

  13. Particle Swarm Optimization (PSO) = Inertial Weight = Cognitive Weight = Social Weight = 0.15 * = 1.5 * = 1.5 * (1) (2) = Number of Particles = Position of Particle iduring the jth iteration = Velocity of Particle iduring the jthiteration = “Global Best” value for any Particle = “Personal Best” value for Particle iduring the jthiteration = Random number with range zero to one and uniform distribution *Pontani and Conway, “Particle Swarm Optimization Applied to Space Trajectories,” Journal of Guidance, Navigation, Control, and Dynamics, Vol. 33, Sep.-Oct. 2010

  14. Application of PSO: Nominal Orbit k = 1 Earth-Moon L1 Northern Halo Orbit: Defined by… k = N k = 2 k = 3 = … k = … k = N/2

  15. Study A: c1=1, c2=c3=0

  16. Optimal Trajectory Optimal Patch Point: k=610+, τs.m.=-18.101[tu], eGEO = 0.000930

  17. Study B: c1=1, c2=10-3, c3=0

  18. Study C: c1=1, c2=10-3, c3=10-4

  19. Future Work Repeat Study… hope is to further reduce run-time by using less particles

  20. Thank You!

  21. Study A: c1=1, c2=c3=0

More Related