Stochastic Motion Planning for Hopping Rovers on Small Solar System Bodies

  • Benjamin HockmanEmail author
  • Marco Pavone
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 10)


Hopping rovers have emerged as a promising platform for the future surface exploration of small Solar System bodies, such as asteroids and comets. However, hopping dynamics are governed by nonlinear gravity fields and stochastic bouncing on highly irregular surfaces, which pose several challenges for traditional motion planning methods. This paper presents the first ever discussion of motion planning for hopping rovers that explicitly accounts for various sources of uncertainty. We first address the problem of planning a single hopping trajectory by developing (1) an algorithm for robustly solving Lambert’s orbital boundary value problems in irregular gravity fields, and (2) a method for computing landing distributions by propagating control and model uncertainties—from which, a time/energy-optimal hop can be selected using a (myopic) policy gradient. We then cast the sequential planning problem as a Markov decision process and apply a sample-efficient, off-line, off-policy reinforcement learning algorithm—namely, a variant of least squares policy iteration (LSPI)—to derive approximately optimal control policies that are safe, efficient, and amenable to real-time implementation on computationally-constrained rover hardware. These policies are demonstrated in simulation to be robust to modelling errors and outperform previous heuristics.


Space robotics Planning under uncertainty Reinforcement learning 



This work is supported by NASA under the Innovative Advanced Concepts program.


  1. 1.
    Castillo, J., Pavone, M., Nesnas, I., Hoffman, J.A.: Expected science return of spatially-extended in-situ exploration at small Solar System bodies. In: IEEE Aerospace Conference (2012)Google Scholar
  2. 2.
    Ambrose, R., Nesnas, I.A.D., Chandler, F., Allen, B.D., Fong, T., Matthies, L., Mueller, R.: NASA technology roadmaps: TA 4: robotics and autonomous systems. Technical report, NASA (2015)Google Scholar
  3. 3.
    Dietze, C., Herrmann, F., Kuß, S., Lange, C., Scharringhausen, M., Witte, L., van Zoest, T., Yano, H.: Landing and mobility concept for the small asteroid lander MASCOT on asteroid 1999 JU3. In: International Astronautical Congress (2010)Google Scholar
  4. 4.
    Yoshimitsu, T., Kubota, T., Nakatani, I., Adachi, T., Saito, H.: Micro-hopping robot for asteroid exploration. Acta Astronaut. 52(2–6), 441–446 (2003)CrossRefGoogle Scholar
  5. 5.
    Abercromby, A.F.J., Gernhardt, M.L., Chappell, S.P., Lee, D.E., Howe, A.S.: Human exploration of phobos. In: IEEE Aerospace Conference (2015)Google Scholar
  6. 6.
    Allen, R., Pavone, M., McQuin, C., Nesnas, I.A., Castillo-Rogez, J.C., Nguyen, T.N., Hoffman, J.A.: Internally-actuated rovers for all-access surface mobility: theory and experimentation. In: Proceedings IEEE Conference on Robotics and Automation (2013)Google Scholar
  7. 7.
    Reid, R.G., Roveda, L., Nesnas, I.A.D., Pavone, M.: Contact dynamics of internally-actuated platforms for the exploration of small solar system bodies. In: Proceedings of i-SAIRAS (2014)Google Scholar
  8. 8.
    Hockman, B., Frick, A., Nesnas, I.A.D., Pavone, M.: Design, control, and experimentation of internally-actuated rovers for the exploration of low-gravity planetary bodies. J. Field Robot. 34(1), 5–24 (2016)CrossRefGoogle Scholar
  9. 9.
    Hockman, B., Reid, R.G., Nesnas, I.A.D., Pavone, M.: Experimental methods for mobility and surface operations of microgravity robots. In: International Symposium on Experimental Robotics (2016)Google Scholar
  10. 10.
    Bajracharya, M., Maimone, M.W., Helmick, D.: Autonomy for mars rovers: past, present, and future. IEEE Comput. 41(12), 44–50 (2008)CrossRefGoogle Scholar
  11. 11.
    Higo, S. Nakatani, I., Yoshimitsu, T.: Localization over small body surface by radio ranging. In: Proceedings of Space Sciences and Technology Conference (2005)Google Scholar
  12. 12.
    So, E.W.Y., Yoshimitsu, T., Kubota, T.: Relative localization of a hopping rover on an asteroid surface using optical flow. In: SICE Anual Conference (2008)Google Scholar
  13. 13.
    Scheeres, D.J.: Orbit mechanics about asteroids and comets. AIAA J. Guid. Control. Dyn. 35(3), 987–997 (2012)CrossRefGoogle Scholar
  14. 14.
    Tardivel, S., Scheeres, D.J., Michel, P., Van wal, S., Ánchez, P.S.: Contact motion on surface of asteroid. AIAA J. Spacecr. Rocket. 51(6), 1857–1871 (2014)Google Scholar
  15. 15.
    Van wal, S., Tardivel, S., Scheeres, D.J.: High-fidelity small body lander simulations. In: International Conference on Astrodynamics Tools and Techniques (2016)Google Scholar
  16. 16.
    Bellerose, J., Scheeres, D.J.: Dynamics and control for surface exploration of small bodies. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit (2008)Google Scholar
  17. 17.
    Klesh, A., Bellerose, J., Kubota, T.: Guidance and control of hoppers for small body exploration. In: International Astronautical Congress (2010)Google Scholar
  18. 18.
    Hand, E.: Philae probe makes bumpy touchdown on a comet. Science 346(6212), 900–901 (2014)CrossRefGoogle Scholar
  19. 19.
    Sharma, I., Burns, J.A., Hui, C.-Y.: Nutational damping times in solids of revolution. Mon. Not. R. Astron. Soc. 359(1), 79–92 (2005)CrossRefGoogle Scholar
  20. 20.
    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)zbMATHGoogle Scholar
  21. 21.
    Murdoch, N., Martinez, I.A., Sunday, C., Zenou, E., Cherrier, O., Cadu, A., Gourinat, Y.: An experimental study of low-velocity impacts into granular material in reduced gravity. Mon. Not. R. Astron. Soc. 468(2), 1259–1272 (2017)Google Scholar
  22. 22.
    Gooding, R.H.: A procedure for the solution of lambert’s orbital boundary-value problem. Celest. Mech. Dyn. Astron. 48(2), 145–165 (1990)zbMATHGoogle Scholar
  23. 23.
    Woollands, R.M., Younes, A.B., Junkins, J.L.: New solutions for the perturbed lambert problem using regularization and picard iteration. AIAA J. Guid. Control. Dyn. 38(9), 1548–1562 (2015)CrossRefGoogle Scholar
  24. 24.
    Lagoudakis, M.G. Parr, R.: Least-squares policy iteration. J. Mach. Learn. Res. 4(Dec), 1107–1149 (2003)Google Scholar
  25. 25.
    Konidaris, G., Osentoski, S., Thomas, P.: Value function approximation in reinforcement learning using the Fourier basis. In: Proceedings AAAI Conference on Artificial Intelligence (2011)Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Robotic Mobility GroupJet Propulsion Laboratory, California Institute of TechnologyPasadenaUSA
  2. 2.Department of Aeronautics and AstronauticsStanford UniversityStanfordUSA

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