Bayesian Maps: Probabilistic and Hierarchical Models for Mobile Robot Navigation

  • Julien Diard
  • Pierre Bessière
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 46)


Imagine yourself lying in your bed at night. Now try to answer these questions: Is your body parallel or not to the sofa that is two rooms away from your bedroom? What is the distance between your bed and the sofa? Except for some special cases (like rotating beds, people who actually sleep on their sofas, or tiny apartments), these questions are usually nontrivial, and answering them requires abstract thought. If pressed to answer quickly, so as to forbid the use of abstract geometry learned in high school, the reader will very probably give wrong answers.

However, if people had the same representations of their environment that roboticians usually provide to their robots, answering these questions would be very easy. The answers would come quickly, and they would certainly be correct. Indeed, robotic representations of space are usually based on large-scale, accurate, metric Cartesian maps. This enables judgment of parallelism and estimations of distances to be straightforward.


Mobile Robot Markov Decision Process Navigation Task Mobile Robot Navigation Abstraction Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Attias, H.: Planning by probabilistic inference. In: Ninth International Workshop on Artificial Intelligence and Statistics Proceedings (2003)Google Scholar
  2. Berthoz, A.: The Brain’s Sense of Movement. Harvard University Press, Cambridge (2000)Google Scholar
  3. Bessière, P., Dedieu, E., Lebeltel, O., Mazer, E., Mekhnacha, K.: Interprétation vs. description I: Proposition pour une théorie probabiliste des systèmes cognitifs sensori-moteurs. Intellectica 26-27, 257–311 (1998)Google Scholar
  4. Boutilier, C., Dean, T., Hanks, S.: Decision theoretic planning: Structural assumptions and computational leverage. Journal of Artificial Intelligence Research 10, 1–94 (1999)MathSciNetGoogle Scholar
  5. Burgard, W., Cremers, A.B., Fox, D., Hähnel, D., Lakemeyer, G., Schultz, D., Steiner, W., Thrun, S.: Experiences with an interactive museum tour-guide robot. Artificial Intelligence 114, 3–55 (1999)zbMATHCrossRefGoogle Scholar
  6. Diard, J.: La carte bayésienne – Un modèle probabiliste hiérarchique pour la navigation en robotique mobile. Thèse de doctorat, Institut National Polytechnique de Grenoble, Grenoble, France (January 2003)Google Scholar
  7. Diard, J., Bessière, P., Mazer, E.: A survey of probabilistic models, using the bayesian programming methodology as a unifying framework. In: The Second Int. Conf. on Computational Intelligence, Robotics and Autonomous Systems (CIRAS), Singapore (December 2003)Google Scholar
  8. Diard, J., Bessière, P., Mazer, E.: Merging probabilistic models of navigation: the bayesian map and the superposition operator. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), pp. 668–673 (2005)Google Scholar
  9. Fox, D., Burgard, W., Dellaert, F., Thrun, S.: Monte Carlo localization: Efficient position estimation for mobile robots. In: Proceedings of the AAAI National Conference on Artificial Intelligence, Orlando, FL (1999)Google Scholar
  10. Franz, M., Mallot, H.: Biomimetic robot navigation. Robotics and Autonomous Systems 30, 133–153 (2000)CrossRefGoogle Scholar
  11. Gothard, K., Skaggs, W., Moore, K., McNaughton, B.: Binding of hippocampal CA1 neural activity to multiple reference frames in a landmark-based navigation task. Journal of Neuroscience 16(2), 823–835 (1996)Google Scholar
  12. Hartley, T., Burgess, N.: Encyclopedia of Cognitive Science. chapter Models of spatial cognition, p. 369. Macmillan, Basingstoke (in press, 2002)Google Scholar
  13. Hauskrecht, M., Meuleau, N., Kaelbling, L.P., Dean, T., Boutilier, C.: Hierarchical solution of Markov decision processes using macro-actions. In: Cooper, G.F., Moral, S. (eds.) Proceedings of the 14th Conf. on Uncertainty in Artificial Intelligence (UAI-1998), July 24–26, 1998, pp. 220–229. Morgan Kaufmann, San Francisco (1998)Google Scholar
  14. Jacobs, L.F.: The evolution of the cognitive map. Brain, behavior and evolution 62, 128–139 (2003)CrossRefGoogle Scholar
  15. Jacobs, L.F., Schenk, F.: Unpacking the cognitive map: the parallel map theory of hippocampal function. Psychological Review 110(2), 285–315 (2003)CrossRefGoogle Scholar
  16. Jaynes, E.T.: Probability Theory: The Logic of Science, June 2003. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  17. Kaelbling, L., Littman, M., Cassandra, A.: Planning and acting in partially observable stochastic domains. Artificial Intelligence 101(1-2), 99–134 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  18. Kavraki, L., Svestka, P., Latombe, J.-C., Overmars, M.: Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Trans. on Robotics and Automation 12(4), 566–580 (1996)CrossRefGoogle Scholar
  19. Kuipers, B.J.: The spatial semantic hierarchy. Artificial Intelligence 119(1–2), 191–233 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  20. Kuipers, B.J.: A hierarchy of qualitative representations for space. In: Working Papers of the Tenth International Workshop on Qualitative Reasoning (QR-1996) (1996)Google Scholar
  21. Lambrinos, D., Möller, R., Labhart, T., Pfeifer, R., Wehner, R.: A mobile robot employing insect strategies for navigation. Robotics and Autonomous Systems (Special issue on Biomimetic Robotics) 30, 39–64 (2000)CrossRefGoogle Scholar
  22. Lane, T., Kaelbling, L.P.: Toward hierarchical decomposition for planning in uncertain environments. In: Proceedings of the 2001 IJCAI Workshop on Planning under Uncertainty and Incomplete Information, Seattle, WA, August 2001, AAAI Press, Menlo Park (2001)Google Scholar
  23. Lane, T., Kaelbling, L.P.: Nearly deterministic abstractions of markov decision processes. In: 18th Nat. Conf. on Artificial Intelligence (2002)Google Scholar
  24. Latombe, J.-C.: Robot Motion Planning. Kluwer Academic Publishers, Boston (1991)Google Scholar
  25. Lebeltel, O., Bessière, P., Diard, J., Mazer, E.: Bayesian robot programming. Autonomous Robots 16(1) (in press, 2004)Google Scholar
  26. Leonard, J., Durrant-Whyte, H., Cox, I.: Dynamic map-building for an autonomous mobile robot. The International Journal of Robotics Research 11(4), 286–298 (1992)CrossRefGoogle Scholar
  27. Leonard, J.J., Durrant-Whyte, H.F.: Mobile robot localization by tracking geometric beacons. IEEE Transactions on Robotics and Automation 7(3), 376–382 (1991)CrossRefGoogle Scholar
  28. Levitt, T.S., Lawton, D.T.: Qualitative navigation for mobile robots. Artificial Intelligence 44(3), 305–360 (1990)CrossRefGoogle Scholar
  29. Mazer, E., Ahuactzin, J.-M., Bessière, P.: The Ariadne’s clew algorithm. Journal of Artificial Intelligence Research (JAIR) 9, 231–295 (1998)Google Scholar
  30. Murphy, K.: Dynamic Bayesian Networks: Representation, Inference and Learning. Ph.D. thesis, University of California, Berkeley, Berkeley, CA (July 2002)Google Scholar
  31. Pineau, J., Thrun, S.: An integrated approach to hierarchy and abstraction for POMDPs. Technical Report CMU-RI-TR-02-21, Carnegie Mellon University (August 2002)Google Scholar
  32. Rabiner, L.R., Juang, B.-H.: Fundamentals of Speech Recognition. chapter Theory and implementation of Hidden Markov Models, pp. 321–389. Prentice-Hall, Englewood Cliffs (1993)Google Scholar
  33. Redish, A.D., Touretzky, D.S.: Cognitive maps beyond the hippocampus. Hippocampus 7(1), 15–35 (1997)CrossRefGoogle Scholar
  34. Roweis, S., Ghahramani, Z.: A unifying review of linear gaussian models. Neural Computation 11(2), 305–345 (1999)CrossRefGoogle Scholar
  35. Simonin, É., Diard, J., Bessière, P.: Learning Bayesian models of sensorimotor interaction: from random exploration toward the discovery of new behaviors. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), pp. 1226–1231 (2005)Google Scholar
  36. Smyth, P., Heckerman, D., Jordan, M.I.: Probabilistic independence networks for hidden markov probability models. Neural Computation 9(2), 227–269 (1997)zbMATHCrossRefGoogle Scholar
  37. Stackman, R., Herbert, A.: Rats with lesions of the vestibular system require a visual landmark for spatial navigation. Behavioural Brain Research 128, 27–40 (2002)CrossRefGoogle Scholar
  38. Stackman, R., Clark, A., Taube, J.: Hippocampal representations require vestibular input. Hippocampus 12, 291–303 (2002)CrossRefGoogle Scholar
  39. Svestka, P., Overmars, M.: Probabilistic path planning. In: Laumond, J.-P. (ed.). Lecture Notes in Control and Information Sciences, vol. 229, Springer, Heidelberg (1998)Google Scholar
  40. Thrun, S.: Probabilistic algorithms in robotics. AI Magazine 21(4), 93–109 (2000)Google Scholar
  41. Thrun, S.: Robotic mapping: A survey. Technical Report CMU-CS-02-111, Carnegie Mellon University (February 2002)Google Scholar
  42. Thrun, S.: Learning metric-topological maps for indoor mobile robot navigation. Artificial Intelligence 99(1), 21–71 (1998)zbMATHCrossRefGoogle Scholar
  43. Thrun, S., Bücken, A., Burgard, W., Fox, D., Fröhlinghaus, T., Hennig, D., Hofmann, T., Krell, M., Schmidt, T.: Map learning and high-speed navigation in RHINO. In: Kortenkamp, D., Bonasso, R., Murphy, R. (eds.) AI-based Mobile Robots: Case Studies of Successful Robot Systems, pp. 580–586. MIT Press, Cambridge (1998)Google Scholar
  44. Thrun, S., Bennewitz, M., Burgard, W., Cremers, A.B., Dellaert, F., Fox, D., Hähnel, D., Rosenberg, C., Roy, N., Schulte, J., Schulz, D.: MINERVA: A second generation mobile tour-guide robot. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (1999a)Google Scholar
  45. Thrun, S., Bennewitz, M., Burgard, W., Cremers, A.B., Dellaert, F., Fox, D., Hähnel, D., Rosenberg, C., Roy, N., Schulte, J., Schulz, D.: MINERVA: A tour-guide robot that learns. In: Burgard, W., Christaller, T., Cremers, A.B. (eds.) KI 1999. LNCS (LNAI), vol. 1701, pp. 14–26. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  46. Tolman, E.: Cognitive maps in rats and men. Psychol. Rev. 55, 189–208 (1948)CrossRefGoogle Scholar
  47. Tomatis, N., Nourbakhsh, I., Arras, K., Siegwart, R.: A hybrid approach for robust and precise mobile robot navigation with compact environment modeling. In: Proceedings of the 2001 IEEE International Conference on Robotics and Automation (ICRA 2001), pp. 1111–1116 (2001)Google Scholar
  48. Tomatis, N., Nourbakhsh, I., Siegwart, R.: Hybrid simultaneous localization and map building: a natural integration of topological and metric. Robotics and Autonomous Systems 44, 3–14 (2003)CrossRefGoogle Scholar
  49. Touretzky, D.S., Redish, A.D.: A theory of rodent navigation based on interacting representations of space. Hippocampus 6, 247–270 (1996)CrossRefGoogle Scholar
  50. Trullier, O., Wiener, S., Berthoz, A., Meyer, J.-A.: Biologically-based artificial navigation systems: Review and prospects. Progress in Neurobiology 51, 483–544 (1997)CrossRefGoogle Scholar
  51. Victorino, A.C., Rives, P.: An hybrid representation well-adapted to the exploration of large scale indoors environments. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2004), New Orleans, LA, USA, pp. 2930–2935 (2004)Google Scholar
  52. Wang, R.F., Spelke, E.S.: Updating egocentric representations in human navigation. Cognition, 215–250 (2000)Google Scholar
  53. Wang, R.F., Spelke, E.S.: Human spatial representation: insights from animals. TRENDS in Cognitive Science 6(9), 376–382 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Julien Diard
    • 1
  • Pierre Bessière
    • 2
  1. 1.Laboratoire de Psychologie et NeuroCognition CNRS UMR 5105Université Pierre Mendès France, BSHM 
  2. 2.CNRS - Grenoble Université 

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