Bayesian Optimisation for Safe Navigation Under Localisation Uncertainty

  • Rafael OliveiraEmail author
  • Lionel Ott
  • Vitor Guizilini
  • Fabio Ramos
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 10)


In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.


Bayesian optimisation Gaussian processes Uncertain inputs Traversability mapping Mobile robotics 



This work was supported by CAPES, Brazil (scholarship BEX 13224/13-1), and by Data61/CSIRO, Australia.


  1. 1.
    Brochu, E., Cora, V.M., de Freitas, N.: A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. Technical report, University of British Columbia (2010)Google Scholar
  2. 2.
    Dallaire, P., Besse, C., Chaib-Draa, B.: An approximate inference with Gaussian process to latent functions from uncertain data. Neurocomputing 74, 1945–1955 (2011)CrossRefGoogle Scholar
  3. 3.
    Damianou, A.C., Titsias, M.K., Lawrence, N.D.: Variational inference for latent variables and uncertain inputs in Gaussian processes. J. Mach. Learn. Res. 17(1), 1–62 (2016)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Girard, A.: Approximate methods for propagation of uncertainty with Gaussian process models. University of Glasgow, Ph.D (2004)Google Scholar
  5. 5.
    Hennig, P., Schuler, C.J.: Entropy search for information-efficient global optimization. J. Mach. Learn. Res. (JMLR) 13, 1809–1837 (2012)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Ho, K., Peynot, T., Sukkarieh, S.: Traversability estimation for a planetary rover via experimental kernel learning in a Gaussian process framework. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 3475–3482. IEEE, Karlsruhe, Germany (2013)Google Scholar
  7. 7.
    Komma, P., Weiss, C., Zell, A.: Adaptive Bayesian filtering for vibration-based terrain classification. In: Proceedings - IEEE International Conference on Robotics and Automation, pp. 3307–3313. IEEE, Kobe, Japan (2009)Google Scholar
  8. 8.
    Lang, T., Plagemann, C., Burgard, W.: Adaptive non-stationary kernel regression for terrain modelling. In: Burgard, W., Brock, O., Stachniss, C. (eds.) Proceedings of the Robotics: Science and Systems Conference (RSS). Atlanta, GA (2007)Google Scholar
  9. 9.
    Maekawa, T., Noda, T., Tamura, S., Ozaki, T., Machida, K.I.: Curvature continuous path generation for autonomous vehicle using B-spline curves. Comput.-Aided Des. 42(4), 350–359 (2010)Google Scholar
  10. 10.
    Marchant, R., Ramos, F.: Bayesian optimisation for intelligent environmental monitoring. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE (2012)Google Scholar
  11. 11.
    Marchant, R., Ramos, F.: Bayesian optimisation for informative continuous path planning. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 6136–6143 (2014)Google Scholar
  12. 12.
    Martin, S., Murphy, L., Corke, P.: Building large scale traversability maps using vehicle experience. In: The 13th International Symposium on Experimental Robotics (ISER), vol. 88, pp. 891–905. Springer (2013)Google Scholar
  13. 13.
    Mchutchon, A., Rasmussen, C.E.: Gaussian process training with input noise. In: Advances in Neural Information Processing Systems, pp. 1341–1349 (2011)Google Scholar
  14. 14.
    Moore, T., Stouch, D.: A generalized extended Kalman filter implementation for the robot operating system. In: Proceedings of the 13th International Conference on Intelligent Autonomous Systems (IAS-13). Springer (2014)Google Scholar
  15. 15.
    Nogueira, J., Martinez-Cantin, R., Bernardino, A., Jamone, L.: Unscented Bayesian optimization for safe robot grasping. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 1967–1972. Daejeon, Korea (2016)Google Scholar
  16. 16.
    Nordin, P.: Mobile robot traversability mapping. Licentiate thesis, Linköping University (2012)Google Scholar
  17. 17.
    O’Callaghan, S.T., Ramos, F.T.: Gaussian process occupancy maps. Int. J. Robot. Res. (IJRR) 31(1), 42–62 (2012)CrossRefGoogle Scholar
  18. 18.
    Oliveira, R., Ott, L., Ramos, F.: Active perception for modelling energy consumption in off-road navigation. In: Australasian Conference on Robotics and Automation (ACRA). Brisbane, QLD, Australia (2016)Google Scholar
  19. 19.
    Powell, M.: A View of Algorithms for Optimization Without Derivatives. Technical report, Cambridge University DAMTP, Cambridge, United Kingdom (2007)Google Scholar
  20. 20.
    Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press, Cambridge, MA (2006)zbMATHGoogle Scholar
  21. 21.
    Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2002)Google Scholar
  22. 22.
    Snoek, J., Larochelle, H., Adams, R.P.: Practical Bayesian optimization of machine learning algorithms. In: Pereira, F., Burges, C.J.C., Bottou, L., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems, vol. 25, pp. 2951–2959. Curran Associates, Inc. (2012)Google Scholar
  23. 23.
    Souza, J.R., Marchant, R., Ott, L., Wolf, D.F., Ramos, F.: Bayesian optimisation for active perception and smooth navigation. In: IEEE International Conference on Robotics and Automation (ICRA) (2014)Google Scholar
  24. 24.
    Srinivas, N., Krause, A., Kakade, S.M., Seeger, M.W.: Information-theoretic regret bounds for Gaussian process optimization in the bandit setting. IEEE Trans. Inf. Theory 58(5), 1–16 (2012)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Underwood, J., Wendel, A., Schofield, B., McMurray, L., Kimber, R.: Efficient in-field plant phenomics for row-crops with an autonomous ground vehicle. J. Field Robot. 34, 1061–1083 (2017)Google Scholar
  26. 26.
    Wan, E.A., van der Merwe, R.: The unscented Kalman filter for nonlinear estimation. In: Adaptive Systems for Signal Processing, Communications, and Control Symposium (AS-SPCC), pp. 153–158 (2000)Google Scholar
  27. 27.
    Wilson, A., Fern, A., Tadepalli, P.: Using trajectory data to improve Bayesian optimization for reinforcement learning. J. Mach. Learn. Res. 15, 253–282 (2014)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Rafael Oliveira
    • 1
    Email author
  • Lionel Ott
    • 1
  • Vitor Guizilini
    • 1
  • Fabio Ramos
    • 1
  1. 1.School of Computer ScienceThe University of SydneySydneyAustralia

Personalised recommendations