Localization on Discrete Grid Graphs

  • Anna Gorbenko
  • Vladimir Popov
  • Andrey Sheka
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 107)


Grid graphs are popular testbeds for planning with incomplete information. In particular, it is studied a fundamental planning problem, localization, to investigate whether gridworlds make good testbeds for planning with incomplete information. It is found empirically that greedy planning methods that interleave planning and plan execution can localize robots very quickly on random gridworlds or mazes. Thus, they may not provide adequately challenging testbeds. On the other hand, it is showed that finding localization plans that are within a log factor of optimal is NP-hard. Thus there are instances of gridworlds on which all greedy planning methods perform very poorly. These theoretical results help empirical researchers to select appropriate planning methods for planning with incomplete information as well as testbeds to demonstrate them. However, for practical application of difficult instances we need a method for their fast decision. In this paper we describe an approach to solve localization problem. This approach is based on constructing a logical model for the problem.


Localization Grid graph Genetic algorithm 


  1. 1.
    Hanks S, Pollack M, Cohen P (1993) AI Mag 14:17Google Scholar
  2. 2.
    Gupta N, Nau D (1992) Artif Intell 56:223Google Scholar
  3. 3.
    Koenig S, Simmons R (1996) In: Proceedings of the national conference on artificial intelligence, p 279Google Scholar
  4. 4.
    Reinefeld A (1993) In: Proceedings of the international joint conference on artificial intelligence, p 248Google Scholar
  5. 5.
    Slaney J, Thiebaux S (1996) In: Proceedings of the national conference on artificial intelligence planningGoogle Scholar
  6. 6.
    Tovey C, Koenig S (2000) In: Proceedings of the AAAI conference on artificial intelligence, p 819Google Scholar
  7. 7.
    Koenig S, Likhachev M (2005) Fast replanning for navigation in unknown terrain. IEEE Trans Robot 21:354Google Scholar
  8. 8.
    Koenig S, Smirnov Y, Tovey C (2003) Performance bounds for planning in unknown terrain. J Artif Intell 147:253Google Scholar
  9. 9.
    Mudgal A, Tovey C, Koenig S (2004) In: Proceedings of the international symposium on artificial intelligence and mathematicsGoogle Scholar
  10. 10.
    Tovey C, Koenig S (2010) IEEE Trans Robot 26:320Google Scholar
  11. 11.
  12. 12.
  13. 13.
    Nourbakhsh I (1996) In: Proceedings of the AAAI-96 spring symposium on planning with incomplete information for robot problems, p 86Google Scholar
  14. 14.
    Information on
  15. 15.
  16. 16.
    Filliat D (2008) In: IEEE/RSJ international conference on intelligent robots and systems. IEEE computer society press, New York, p 248Google Scholar
  17. 17.
    Park IP, Kender JR (1995) Topological direction-giving and visual navigation in large environments. Artif Intell 78:355Google Scholar
  18. 18.
    Santos-Victor J, Vassallo R, Schneebeli H (1999) In: Christensen HI (ed) Proceedings of the first international conference on computer vision systems. Springer, London, UK, p 21Google Scholar
  19. 19.

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Ural State UniversityEkaterinburgRussia

Personalised recommendations