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Efficient Wayfinding in Hierarchically Regionalized Spatial Environments

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Spatial Cognition VI. Learning, Reasoning, and Talking about Space (Spatial Cognition 2008)

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Abstract

Humans utilize region-based hierarchical representations in the context of navigation. We propose a computational model for representing region hierarchies and define criteria for automatically generating them. We devise a cognitively plausible online wayfinding algorithm exploiting the hierarchical decomposition given by regions. The algorithm allows an agent to derive plans with decreasing detail level along paths, enabling the agent to obtain the next action in logarithmic time and complete solutions in almost linear time. The resulting paths are reasonable approximations of optimal shortest paths.

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References

  1. Thrun, S.: Robotic mapping: A survey (2002)

    Google Scholar 

  2. Werner, S., Krieg-Brückner, B., Herrmann, T.: Modelling navigational knowledge by route graphs. In: Habel, C., Brauer, W., Freksa, C., Wender, K.F. (eds.) Spatial Cognition II 2000. LNCS (LNAI), vol. 1849, pp. 295–317. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  3. Kuipers, B.: The spatial semantic hierarchy. Technical Report AI99-281 (29, 1999)

    Google Scholar 

  4. Car, A., Frank, A.: General principles of hierarchical reasoning - the case of wayfinding. In: SDH 1994, Sixth Int. Symposium on Spatial Data Handling, Edinburgh, Scotland (September 1994)

    Google Scholar 

  5. Botea, A., Müller, M., Schaeffer, J.: Near optimal hierarchical path-finding. Journal of Game Development 1(1), 7–28 (2004)

    Google Scholar 

  6. Cagigas, D.: Hierarchical D* algorithm with materialization of costs for robot path planning. Robotics and Autonomous Systems 52(2-3), 190–208 (2005)

    Article  Google Scholar 

  7. Graham, S., Joshi, A., Pizlo, Z.: The traveling salesman problem: a hierarchical model. Memory & Cognition 28(7), 1191–1204 (2000)

    Google Scholar 

  8. Pizlo, Z., Stefanov, E., Saalweachter, J., Li, Z., Haxhimusa, Y., Kropatsch, W.: Traveling salesman problem: a foveating pyramid model. Journal of Problem Solving 1, 83–101 (2006)

    Google Scholar 

  9. Tomko, M., Winter, S.: Recursive construction of granular route directions. Journal of Spatial Science 51(1), 101–115 (2006)

    Google Scholar 

  10. Stevens, A., Coupe, P.: Distortions in judged spatial relations. Cognitive Psychology 10, 526–550 (1978)

    Article  Google Scholar 

  11. Hirtle, S.C., Jonides, J.: Evidence of hierarchies in cognitive maps. Memory and Cognition 13(3), 208–217 (1985)

    Google Scholar 

  12. McNamara, T.P.: Mental representations of spatial relations. Cognitive Psychology 18, 87–121 (1986)

    Article  Google Scholar 

  13. Wiener, J., Mallot, H.: ’Fine-to-coarse’ route planning and navigation in regionalized environments. Spatial Cognition and Computation 3(4), 331–358 (2003)

    Article  Google Scholar 

  14. Wiener, J., Schnee, A., Mallot, H.: Navigation strategies in regionalized environments. Technical Report 121 (January 2004)

    Google Scholar 

  15. Voicu, H.: Hierarchical cognitive maps. Neural Networks 16(5-6), 569–576 (2003)

    Article  Google Scholar 

  16. Thomas, R., Donikian, S.: A model of hierarchical cognitive map and human memory designed for reactive and planned navigation. In: 4th International Space Syntax Symposium, Londres (June 2003)

    Google Scholar 

  17. Gadzicki, K., Gerkensmeyer, T., Hünecke, H., Jäger, J., Reineking, T., Schult, N., Zhong, Y., et al.: Project MazeXplorer. Technical report, University of Bremen (2007)

    Google Scholar 

  18. Schill, K., Zetzsche, C., Wolter, J.: Hybrid architecture for the sensorimotor representation of spatial configurations. Cognitive Processing 7, 90–92 (2006)

    Article  Google Scholar 

  19. Schill, K., Umkehrer, E., Beinlich, S., Krieger, G., Zetzsche, C.: Scene analysis with saccadic eye movements: Top-down and bottom-up modeling. Journal of Electronic Imaging 10(1), 152–160 (2001)

    Article  Google Scholar 

  20. Montello, D.R., Goodchild, M.F., Gottsegen, J., Fohl, P.: Where’s downtown?: Behavioral methods for determining referents of vague spatial queries. Spatial Cognition & Computation 3(2-3), 185–204 (2003)

    Article  Google Scholar 

  21. Han, J., Kamber, M., Tung, A.K.H.: Spatial clustering methods in data mining. In: Geographic Data Mining and Knowledge Discovery, pp. 188–217. Taylor & Francis, Inc., Bristol (2001)

    Google Scholar 

  22. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1(1), 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  23. Barbehenn, M.: A note on the complexity of dijkstra’s algorithm for graphs with weighted vertices. IEEE Trans. Comput. 47(2), 263 (1998)

    Article  MathSciNet  Google Scholar 

  24. Junghanns, A.: Pushing the limits: new developments in single-agent search. PhD thesis, University of Alberta (1999)

    Google Scholar 

  25. Papadias, D., Egenhofer, M.J., Sharma, J.: Hierarchical reasoning about direction relations. In: GIS 1996: Proceedings of the 4th ACM international workshop on Advances in geographic information systems, pp. 105–112. ACM, New York (1996)

    Chapter  Google Scholar 

  26. Maaß, W.: From vision to multimodal communication: Incremental route descriptions. Artificial Intelligence Review 8(2), 159–174 (1994)

    Article  Google Scholar 

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Christian Freksa Nora S. Newcombe Peter Gärdenfors Stefan Wölfl

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© 2008 Springer-Verlag Berlin Heidelberg

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Reineking, T., Kohlhagen, C., Zetzsche, C. (2008). Efficient Wayfinding in Hierarchically Regionalized Spatial Environments. In: Freksa, C., Newcombe, N.S., Gärdenfors, P., Wölfl, S. (eds) Spatial Cognition VI. Learning, Reasoning, and Talking about Space. Spatial Cognition 2008. Lecture Notes in Computer Science(), vol 5248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87601-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-87601-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87600-7

  • Online ISBN: 978-3-540-87601-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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