Skip to main content
SpringerLink
Log in

Autonomous Construction of Hierarchical Voronoi-Based Route Graph Representations

  • Conference paper
Spatial Cognition IV. Reasoning, Action, Interaction (Spatial Cognition 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3343))

Included in the following conference series:

Abstract

A route graph as proposed in Werner et al. (2000) is a spatial representation of the environment that focuses on integrating qualitatively different routes an agent can use for navigation. In this paper we describe how a route graph based on the generalized Voronoi diagram (GVD) of the environment can be used for mobile robot mapping and navigation tasks in an office-like indoor environment. We propose a hierarchical organization of the graph structure resulting in more abstract layers that represent the environment at coarser levels of granularity. For this purpose, we define relevance measures to weight the meet points in the GVD based on how significant they are for navigation and present an algorithm that utilizes these weights to generate the coarser route graph layers. Computation of the relevance values from either complete or incomplete information about the environment is considered. Besides robot navigation, the techniques developed can be employed for other tasks in which abstract route graph representations are advantageous, e.g. automatically generating route descriptions from floor plans.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aurenhammer, F.: Voronoi diagrams - A survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)

    Article  Google Scholar 

  2. Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, pp. 362–380. MIT Press, Cambridge (1967)

    Google Scholar 

  3. Choset, H., Burdick, J.: Sensor based exploration: The Hierarchical Generalized Voronoi Graph. The International Journal of Robotics Research 19(2), 96–125 (2000)

    Article  Google Scholar 

  4. Choset, H., Konukseven, I., Burdick, J.: Mobile robot navigation: Issues in implementing the generalized Voronoi graph in the plane. In: 1996 IEEE/SICE/RSJ International Conference on Multisensor Fusion and Integration for Intelligent Systems, New York, NY, USA, pp. 241–248. IEEE, Los Alamitos (1996)

    Google Scholar 

  5. Cohn, A.G.: Qualitative spatial representation and reasoning techniques. In: Brewka, G., Habel, C., Nebel, B. (eds.) KI 1997. LNCS, vol. 1303, pp. 1–30. Springer, Heidelberg (1997)

    Google Scholar 

  6. Crowley, J.: World modeling and position estimation for a mobile robot using ultrasonic ranging. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 674–680 (1989)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Elfes, A.: Using occupancy grids for mobile robot perception and navigation. Computer 22(6), 46–57 (1989)

    Article  Google Scholar 

  9. Hähnel, D., Fox, D., Burgard, W., Thrun, S.: A highly efficient FastSLAM algorithm for generating cyclic maps of large-scale environments from raw laser range measurements. In: Proceedings of the Conference on Intelligent Robots and Systems, IROS (2003)

    Google Scholar 

  10. Kirkpatrick, D.G.: Efficient computation of continuous skeletons. In: 20th Annual Symposium on Foundations of Computer Science, pp. 18–27. IEEE, Los Alamitos (1979)

    Google Scholar 

  11. Kortenkamp, D., Weymouth, T., Chown, E., Kaplan, S.: A scene-based, multi-level representation for mobile robot spatial mapping and navigation. Technical Report CSE-TR-119-92, Computer Science and Engineering Division, University of Michigan (1992)

    Google Scholar 

  12. Krieg-Brückner, B., Frese, U., Lüttich, K., Mandel, C., Mossakowski, T., Ross, R.: Specification of an ontology for route graphs. In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds.) Spatial Cognition IV - Reasoning, Action, Interaction. Springer, Berlin (this volume)

    Google Scholar 

  13. Kuipers, B.: The spatial semantic hierarchy. Artificial Intelligence 119, 191–233 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kuipers, B.J., Byun, Y.-T.: A robust, qualitative method for robot spatial learning. In: AAAI 1988. Seventh National Conference on Artificial Intelligence, pp. 774–779 (1988)

    Google Scholar 

  15. Latombe, J.-C.: Robot Motion Planning. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  16. Lee, D.T., Drysdale III, R.L.: Generalization of Voronoi diagrams in the plane. SIAM Journal on Computing 10(1), 269–271 (1981)

    Article  MathSciNet  Google Scholar 

  17. Leonard, J.J., Durrant-Whyte, H.F.: Simultaneous map building and localization for an autonomous mobile robot. In: Proceedings of IEEE/RSJ International Workshop on Intelligent Robots and Systems, pp. 1442–1447 (1991)

    Google Scholar 

  18. Lu, F., Milios, E.: Robot pose estimation in unknown environments by matching 2D scans. In: IEEE Computer Vision and Pattern Recognition Conference, CVPR (1994)

    Google Scholar 

  19. Mayya, N., Rajan, V.T.: Voronoi diagrams of polygons: A framework for shape representation. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 638–643 (1994)

    Google Scholar 

  20. Montemerlo, M., Thrun, S., Koller, D., Wegbreit, B.: FastSLAM: A factored solution to the simultaneous localization and mapping problem. In: Proceedings of the AAAI National Conference on Artificial Intelligence, Edmonton, Canada. AAAI, Menlo Park (2002)

    Google Scholar 

  21. Moratz, R., Wallgrün, J.O.: Spatial reasoning about relative orientation and distance for robot exploration. In: Kuhn, W., Worboys, M.F., Timpf, S. (eds.) COSIT 2003. LNCS, vol. 2825, pp. 61–74. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. Moratz, R., Wallgrün, J.O.: Propagation of distance and orientation intervals. In: Proceedings of 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 3245–3250 (2003)

    Google Scholar 

  23. Moravec, H.P.: Certainty grids for sensor fusion in mobile robots. AI Magazine 9(2), 61–77 (1988)

    Google Scholar 

  24. Ó’Dúnlaing, C., Yap, C.K.: A retraction method for planning the motion of a disc. Journal of Algorithms 6, 104–111 (1982)

    Article  Google Scholar 

  25. Ogniewicz, R.L., Kübler, O.: Hierarchic Voronoi skeletons. Pattern Recognition 28(3), 343–359 (1995)

    Article  Google Scholar 

  26. Ross, R.J., Shi, H., Vierhuff, T., Krieg-Brückner, B., Bateman, J.A.: Towards dialogue based shared control of navigating robots. In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds.) Spatial Cognition IV. LNCS (LNAI), vol. 3343, pp. 478–499. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  27. Siddiqi, K., Kimia, B.B.: Toward a shock grammar for recognition. In: IEEE Conference on Computer Vision and Pattern Recognition (1996)

    Google Scholar 

  28. Thrun, S.: Learning metric-topological maps for indoor mobile robot navigation. Artificial Intelligence 99(1), 21–71 (1998)

    Article  MATH  Google Scholar 

  29. Thrun, S., Fox, D., Burgard, W.: A probabilistic approach to concurrent mapping and localization for mobile robots. Machine Learning 31, 29–53 (1998); also appeared in Autonomous Robots 5, 253–271 (joint issue)

    Article  MATH  Google Scholar 

  30. Wallgrün, J.O.: Exploration und Pfadplanung für mobile Roboter basierend auf Generalisierten Voronoi-Graphen. Diploma thesis, Fachbereich Informatik, Universität Hamburg (2002)

    Google Scholar 

  31. 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 2000. LNCS (LNAI), vol. 1849, pp. 295–316. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  32. Wolter, D., Latecki, L.J.: Shape matching for robot mapping. In: Zhang, C., Guesgen, H.W., Yeap, W.K. (eds.) Proceedings of 8th Pacific Rim International Conference on Artificial Intelligence, Auckland, New Zealand (August 2004)

    Google Scholar 

  33. Yeap, W.K., Jefferies, M.E.: Computing a representation of the local environment. Aritificial Intelligence 107, 265–301 (1999)

    Article  MATH  Google Scholar 

  34. van Zwynsvoorde, D., Simeon, T., Alami, R.: Building topological models for navigation in large scale environments. In: 2001 IEEE International Conference on Robotics and Automation (ICRA 2001), pp. 4256–4261 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Universität Bremen, Bibliothekstr. 1, 28359, Bremen, Germany

    Jan Oliver Wallgrün

Authors
  1. Jan Oliver Wallgrün
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. SFB/TR 8 Spatial Cognition, Universität Bremen, Bibliothekstr. 1, 28359, Bremen, Germany

    Christian Freksa

  2. Center for Cognitive Science, Friedrichstraße 50, 79098, Freiburg, Germany

    Markus Knauff

  3. Universität Bremen and DFKI-Lab Bremen, P.O. Box, Germany

    Bernd Krieg-Brückner

  4. Institut für Informatik, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

    Bernhard Nebel

  5. SFB/TR 8 Spatial Cognition, Universität Bremen, Germany

    Thomas Barkowsky

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wallgrün, J.O. (2005). Autonomous Construction of Hierarchical Voronoi-Based Route Graph Representations. In: Freksa, C., Knauff, M., Krieg-Brückner, B., Nebel, B., Barkowsky, T. (eds) Spatial Cognition IV. Reasoning, Action, Interaction. Spatial Cognition 2004. Lecture Notes in Computer Science(), vol 3343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32255-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-32255-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25048-7

  • Online ISBN: 978-3-540-32255-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation