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Trajectory Design Leveraging Low-Thrust, Multi-Body Equilibria and their Manifolds

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Abstract

A key challenge in low-thrust trajectory design is generating preliminary solutions that simultaneously specify the spacecraft position and velocity vectors, as well as the thrust history. To mitigate this difficulty, dynamical structures within a combined low-thrust circular restricted 3-body problem (CR3BP) are investigated as candidate solutions to seed initial low-thrust trajectory designs. The addition of a low-thrust force to the CR3BP modifies the locations and stability of the equilibria, offering novel geometries for mission applications. Transfers between these novel equilibria are constructed by leveraging the associated stable and unstable manifolds and insights from the low-thrust CR3BP.

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Notes

  1. See the Deep Space 1 Asteroid Flyby press kit, https://www.jpl.nasa.gov/news/press_kits/ds1asteroid.pdf

References

  1. Anderson, R.: Low-Thrust Trajectory Design for Resonant Flybys and Captures Using Invariant Manifolds. Ph.d. Dissertation, University of Colorado at Boulde, Boulder (2005)

  2. Bokelmann, K.A., Russell, R.P., Lantoine, G.: Periodic orbits and equilibria near jovian moons using an electrodynamic tether. J. Guid. Control. Dyn. 38(1). https://doi.org/10.2514/1.G000428 (2015)

  3. Cox, A.D.: Transfers to a Sun-Earth Saddle Point: An Extended Mission Design for Lisa Pathfinder. Master’s Thesis, Purdue University, West Lafayette (2016)

  4. Cox, A.D., Howell, K.C., Folta, D.C.: Dynamical Structures in a Combined Low-Thrust Multi-Body Environment In: AAS/AIAA Astrodynamics Specialist Conference. Columbia River Gorge, Stevenson (2017)

  5. Cox, A.D., Howell, K.C., Folta, D.C.: Dynamical structures in a low-thrust, multi-body model with applications to trajectory design. Celest. Mech. Dyn. Astron. 131(12). . Available Online (2019)

  6. Das-Stuart, A., Howell, K.C., Folta, D.C.: A Rapid Trajectory Design Strategy for Complex Environments Leveraging Attainable Regions and Low-Thrust Capabilities. In: 68Th International Astronautical Congress. Adelaide, Australia (2017)

  7. Farrés, A.: Transfer orbits to l4 with a solar sail in the earth-sun system. Acta Astronaut. 137, 78–90 (2017). https://doi.org/10.1016/j.actaastro.2017.04.010

    Article  Google Scholar 

  8. Farrés, A., Jorba, À.: Solar sail surfing along families of equilibrium points. Acta Astronaut. 63, 249–257 (2008). https://doi.org/10.1016/j.actaastro.2007.12.021

    Article  Google Scholar 

  9. Farrés, A., Jorba, À.: Periodic and quasi-periodic motions of a solar sail close to sl1 in the earth-sun system. Celest. Mech. Dyn. Astron. 107(1-2), 233–253 (2010). https://doi.org/10.1007/s10569-010-9268-4

    Article  Google Scholar 

  10. Gómez, G., Koon, W., Lo, M., Marsden, J., Masdemont, J., Ross, S.: Connecting orbits and invariant manifolds in the spatial restricted three-body problem. Nonlinearity 17(5), 1571–1606 (2004). https://doi.org/10.1088/0951-7715/17/5/002

    Article  MathSciNet  Google Scholar 

  11. Grebow, D., Ozimek, M., Howell, K.: Design of optimal low-thrust lunar pole-sitter missions. J. Astronaut. Sci. 58 (1), 55–79 (2011). https://doi.org/10.1007/BF03321159

    Article  Google Scholar 

  12. Hernandez, S.: Low-Thrust Trajectory Design Techniques with a Focus on Maintaining Constant Energy. Ph.D. Thesis, University of Texas at Austin, Austin (2014)

  13. Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Dynamical Systems, the Three-Body Problem and Space Mission Design. Springer, New York (2011). http://www.cds.caltech.edu/~marsden/volume/missiondesign/KoLoMaRo_DMissionBook_2011-04-25.pdf

    MATH  Google Scholar 

  14. Lo, M.W., Williams, B.G., Bollman, W.E., Han, D., Hahn, Y., Bell, J.L., Hirst, E.A., Corwin, R.A., Hong, P.E., Howell, K.C., Barden, B.T., Wilson, R.S.: Genesis mission design. J. Astronaut. Sci. 49(1), 169–184 (2001)

    Google Scholar 

  15. McInnes, C.R., McDonald, A.J.C., Simmons, J.F.L., MacDonald, E.W.: Solar sail parking in restricted three-body systems. J. Guid. Control Dyn. 17(2). https://doi.org/10.2514/3.21211 (1994)

  16. Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Combined Optimal Low-Thrust and Stable-Manifold Trajectories to the Earth-Moon Halo Orbits. In: AIP Conference Proceedings. https://doi.org/10.1063/1.2710047 (2007)

  17. Mingotti, G., Topputo, F., Bernelli-Zazzera, F.: Optimal low-thrust invariant manifold trajectories via attainable sets. J. Guid. Control Dyn. 34(6), 1644–1656 (2011). https://doi.org/10.2514/1.52493

    Article  Google Scholar 

  18. Moore, A., Ober-Blöbaum, S., Marsden, J.: Trajectory design combining invariant manifolds with discrete mechanics and optimal control. J. Guid. Control Dyn. 35(5), 1507–1525 (2012). https://doi.org/10.2514/1.55426

    Article  Google Scholar 

  19. Petropoulous, A., Sims, J.: A review of some exact solutions to the planar equations of motion of a thrusting spacecraft. In: 2nd International Symposium on Low Thrust Trajectories, Toulouse. https://trs.jpl.nasa.gov/bitstream/handle/2014/8673/02-1211.pdf (2002)

  20. Pritchett, R., Zimovan, E., Howell, K.C.: Impulsive and Low-Thrust Transfer Design between Stable and Nearly Stable Periodic Orbits in the Restricted Problem. In: AIAA Scitech Forum, Kissimmee (2018)

  21. Stuart, J.: A Hybrid Systems Strategy for Automated Spacecraft Tour Design and Optimization. Ph.D. Thesis, Purdue University, West Lafayette (2014)

  22. Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967)

    MATH  Google Scholar 

  23. Topputo, F.: Low-Thrust Non-Keplerian Orbits: Analysis, Design, and Control. Ph.D. thesis, Plitecnico di Milano (2005)

  24. Topputo, F., Vasile, M., Bernelli-Zazzera, F.: Low energy interplanetary transfers exploiting invariant manifolds of the restricted three-body problem. J. Astronaut. Sci. 53(4), 353–372 (2005)

    MathSciNet  Google Scholar 

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Acknowledgements

The authors thank the Purdue University School of Aeronautics and Astronautics for the facilities and support, including access to the Rune and Barbara Eliasen Visualization Laboratory. Additionally, many thanks to the Purdue Multi-Body Dynamics Research Group, the JPL Mission Design and Navigation branch, and Dr. Dan Grebow for interesting discussions and ideas. This research is supported by a National Aeronautics and Space Administration (NASA) Space Technology Research Fellowship, NASA Grant NNX16AM40H. The authors are grateful to the reviewers for providing thorough and insightful feedback on this paper; it has certainly been improved as a result.

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Correspondence to Andrew D. Cox.

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The original version of this paper was presented during the AAS/AIAA Astrodynamics Specialist Conference in Snowbird, Utah in August 2018. This work is supported by a NASA Space Technology Research Fellowship, NASA Grant NNX16AM40H

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Cox, A.D., Howell, K.C. & Folta, D.C. Trajectory Design Leveraging Low-Thrust, Multi-Body Equilibria and their Manifolds. J Astronaut Sci 67, 977–1001 (2020). https://doi.org/10.1007/s40295-020-00211-6

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