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Bayesian Shape Reconstruction and Optimal Guidance for Autonomous Landing on Asteroids

Abstract

Construction of the precise shape of an asteroid is critical for spacecraft operations as the gravitational potential is determined by spatial mass distribution. The typical approach to shape determination requires a prolonged “mapping” phase of the mission over which extensive measurements are collected and transmitted for Earth-based processing. This paper presents a set of approaches to explore an unknown asteroid with onboard calculations, and to land on its surface area selected in an optimal fashion. The main motivation is to avoid the extended period of mapping or preliminary ground observations that are commonly required in spacecraft missions around asteroids. First, range measurements from the spacecraft to the surface are used to incrementally correct an initial shape estimate according to the Bayesian framework. Then, an optimal guidance scheme is proposed to control the vantage point of the range sensor to construct a complete 3D model of the asteroid shape. This shape model is then used in a nonlinear controller to track a desired trajectory about the asteroid. Finally, a multi resolution approach is presented to construct a higher fidelity shape representation in a specified location while avoiding the inherent burdens of a uniformly high resolution mesh. This approach enables for an accurate shape determination around a potential landing site. We demonstrate this approach using several radar shape models of asteroids and provide a full dynamical simulation about asteroid 4769 Castalia.

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References

  1. Scheeres, D.: Orbital mechanics about small bodies. Acta Astronaut. 72, 1–14 (2012). https://doi.org/10.1016/j.actaastro.2011.10.021

    Article  Google Scholar 

  2. Rubincam, D.P.: Radiative spin-up and spin-down of small asteroids. Icarus 148(1), 2–11 (2000). https://doi.org/10.1006/icar.2000.6485

    Article  Google Scholar 

  3. Hughes, P.: Spacecraft Attitude Dynamics. Dover Publications, New York (2004)

    Google Scholar 

  4. Elmasri, H.M., McClamroch, N.H.: Dynamics and control properties for an asymmetric dumbbell spacecraft. In: Proceedings of 2005 IEEE Conference on Control Applications, 2005. pp 364–369 (2005)

  5. Sanyal, A.K., Shen, J., McClamroch, N.H.: Control of a dumbbell spacecraft using attitude and shape control inputs only. In: Proceedings of the IEEE American Control Conference, vol. 2, pp. 1014–1018 (2004)

  6. Misra, G., Sanyal, A.K.: Analysis of orbit-attitude coupling of spacecraft near small bodies. In: AIAA/AAS Astrodynamics Specialist Conference (2015)

  7. Werner, R.A., Scheeres, D.J.: Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celest. Mech. Dyn. Astron. 65(3), 313–344 (1996). https://doi.org/10.1007/BF00053511

    MATH  Google Scholar 

  8. Hudson, R.S.: Shape of asteroid 4769 Castalia (1989 PB). Science 263, 18 (1994)

    Article  Google Scholar 

  9. Busch, M.W., Ostro, S.J., Benner, L.A., Brozovic, M., Giorgini, J.D., Jao, J.S., Scheeres, D.J., Magri, C., Nolan, M.C., Howell, E.S., Taylor, P.A., Margot, J.-L., Brisken, W.: Radar observations and the shape of near-Earth asteroid 2008EV5. Icarus 212(2)649–660 (2011) https://doi.org/10.1016/j.icarus.2011.01.013

  10. Greenberg, A.H., Margot, J.-L.: Improved algorithms for radar-based reconstruction of asteroid shapes. Astron. J. 150(4), 114 (2015). https://doi.org/10.1088/0004-6256/150/4/114

    Article  Google Scholar 

  11. Williams, B., Antreasian, P., Carranza, E., Jackman, C., Leonard, J., Nelson, D., Page, B., Stanbridge, D., Wibben, D., Williams, K., Moreau, M., Berry, K., Getzandanner, K., Liounis, A., Mashiku, A., Highsmith, D., Sutter, B., Lauretta, D.S.: OSIRIS-REx flight dynamics and navigation design. Space Sci. Rev. 214(4), 69 (2018). https://doi.org/10.1007/s11214-018-0501-x

    Article  Google Scholar 

  12. Kubota, T., Hashimoto, T., Sawai, S., Kawaguchi, J., Ninomiya, K., Uo, M., Baba, K.: An autonomous navigation and guidance system for MUSES-C asteroid landing. Acta Astronaut. 52(2), 125–131 (2003). https://doi.org/10.1016/S0094-5765(02)00147-9

    Article  Google Scholar 

  13. Cole, T.D.: Near laser rangefinder: A tool for the mapping and toplogic study of asteroid 433 Eros. Johns Hopkins APL Techn. Dig. 19(2) (1998)

  14. Kulumani, S., Takami, K., Lee, T.: Geometric control for autonomous landing on asteroid itokawa using visual localization. In: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Stevenson, Washington (2017)

  15. Lee, T., McClamroch, N.H., Leok, M.: Optimal control of a rigid body using geometrically exact computations on se (3). In: 2006 45th IEEE conference on decision and control, pp. 2710–2715. IEEE (2006)

  16. Lee, T., Leok, M., McClamroch, N.H.: Lie group variational integrators for the full body problem. Comput. Methods Appl. Mech. Eng. 196(29), 2907–2924 (2007). https://doi.org/10.1016/j.cma.2007.01.017

    MathSciNet  Article  Google Scholar 

  17. Greenwood, D.T.: Principles of Dynamics. Prentice-Hall Upper Saddle River, NJ (1988)

    Google Scholar 

  18. Werner, R.A.: The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celest. Mech. Dyn. Astron. 59(3), 253–278 (1994). https://doi.org/10.1007/BF00692875

    Article  Google Scholar 

  19. Zuber, M.T., Smith, D.E., Cheng, A.F., Cole, T.D.: The near laser ranging investigation. J. Geophys. Res. 102(E10), 23761–23773 (1997). https://doi.org/10.1029/97JE00890

    Article  Google Scholar 

  20. Zuber, M.T., Smith, D.E., Cheng, A.F., Garvin, J.B., Aharonson, O., Cole, T.D., Dunn, P.J., Guo, Y., Lemoine, F.G., Neumann, G.A., et al.: The shape of 433 Eros from the NEAR-Shoemaker Laser Rangefinder. Science 289(5487), 2097–2101 (2000). https://doi.org/10.1126/science.289.5487.2097

    Article  Google Scholar 

  21. Lauretta, D.S., Balram-Knutson, S.S., Beshore, E., Boynton, W.V., Drouet d’Aubigny, C., DellaGiustina, D.N., Enos, H.L., Golish, D.R., Hergenrother, C.W., Howell, E.S., Bennett, C.A., Morton, E.T., Nolan, M.C., Rizk, B., Roper, H.L., Bartels, A.E., Bos, B.J., Dworkin, J.P., Highsmith, D.E., Lorenz, D.A., Lim, L.F., Mink, R., Moreau, M.C., Nuth, J.A., Reuter, D.C., Simon, A.A., Bierhaus, E.B., Bryan, B.H., Ballouz, R., Barnouin, O.S., Binzel, R.P., Bottke, W.F., Hamilton, V.E., Walsh, K.J., Chesley, S.R., Christensen, P.R., Clark, B.E., Connolly, H.C., Crombie, M.K., Daly, M.G., Emery, J.P., McCoy, T.J., McMahon, J.W., Scheeres, D.J., Messenger, S., Nakamura-Messenger, K., Righter, K., Sandford, S.A.: OSIRIS-REx: Sample return from asteroid (101955) Bennu. Space Sci. Rev. 212(1), 925–984 (2017). https://doi.org/10.1007/s11214-017-0405-1

    Article  Google Scholar 

  22. Daly, M.G., Barnouin, O.S., Dickinson, C., Seabrook, J., Johnson, C.L., Cunningham, G., Haltigin, T., Gaudreau, D., Brunet, C., Aslam, I., Taylor, A., Bierhaus, E.B., Boynton, W., Nolan, M., Lauretta, D.S.: The OSIRIS-REx Laser Altimeter (OLA) investigation and instrument. Space Sci. Rev. 212(1), 899–924 (2017). https://doi.org/10.1007/s11214-017-0375-3

    Article  Google Scholar 

  23. Gaskell, R.W., Barnouin-jha, O.S., Scheeres, D.J., Konopliv, A.S., Mukai, T., Abe, S., Saito, J., Ishiguro, M., Kubota, T., Hashimoto, T., Kawaguchi, J., Yoshikawa, M., Shirakawa, K., Kominato, T., Hirata, N., Demura, H.: Characterizing and navigating small bodies with imaging data. Meteor. Planet. Sci. 43(6), 1049–1061 (2008). https://doi.org/10.1111/j.1945-5100.2008.tb00692.x

    Article  Google Scholar 

  24. de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry. Springer, Berlin Heidelberg (2008)

    Book  Google Scholar 

  25. O’Rourke, J.: Computational Geometry in C, 2nd edn. Cambridge University Press, Cambridge (1998)

    Book  Google Scholar 

  26. Thrun, S., Burgard, W., Fox, D.: Probabilistic robotics. MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  27. Gade, K.: A non-singular horizontal position representation. J. Navig. 63(3), 395–417 (2010)

    Article  Google Scholar 

  28. Bishop, C.: Pattern Recognition and Machine Learning, Springer, New York (2006)

    MATH  Google Scholar 

  29. Neese, C.: Small body radar shape models v2.0 EAR-A-5-DDR-RADARSHAPE-MODELS-V2.0 (2004). http://sbn.psi.edu/pds/resource/rshape.html

  30. Chen, C.-L.: A systematic approach for solving the great circle track problems based on vector algebra. Polish Marit. Res. 23(2), 3–13 (2016). https://doi.org/10.1515/pomr-2016-0014

    Article  Google Scholar 

  31. Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments, Springer, Berlin (2012)

    Book  Google Scholar 

  32. Kulumani, S., Lee, T.: Constrained geometric attitude control on \(\sf SO(3)\). Int. J. Control Autom. Syst. 15(6) (2017) https://doi.org/10.1007/s12555-016-0607-4

  33. Scheeres, D.J., Ostro, S.J., Hudson, R., Werner, R.A.: Orbits close to asteroid 4769 Castalia. Icarus 121(1), 67–87 (1996). https://doi.org/10.1006/icar.1996.0072

    Article  Google Scholar 

  34. Botsch, M., Kobbelt, L., Pauly, M., Alliez, P., Lévy, B.: Polygon Mesh Processing. CRC Press, Boca Raton (2010)

    Book  Google Scholar 

  35. McMahon, J.W.: Improved gravity model performance by using mixed fidelity shape models for irregularly shaped small bodies. In: Proceedings of AAS/AIAA Astrodynamics Specialist Conference, Stevenson, Washington (2017)

  36. The CGAL Project, CGAL User and Reference Manual, 4.12 ed. CGAL Editorial Board, (2018). Available: https://doc.cgal.org/4.12/Manual/packages.html

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Correspondence to Shankar Kulumani.

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Kulumani, S., Lee, T. Bayesian Shape Reconstruction and Optimal Guidance for Autonomous Landing on Asteroids. J Astronaut Sci 69, 335–367 (2022). https://doi.org/10.1007/s40295-022-00310-6

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  • DOI: https://doi.org/10.1007/s40295-022-00310-6

Keywords

  • Asteroids
  • Shape construction
  • Guidance
  • Optimization