How Simple Robots Benefit from Looking Back

  • Jérémie Chalopin
  • Shantanu Das
  • Yann Disser
  • Matúš Mihalák
  • Peter Widmayer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6078)

Abstract

We study the sensor and movement capabilities that simple robots need in order to create a map of an unknown polygon of size n, and to meet. We consider robots that can move from vertex to vertex, can backtrack movements, and see distant vertices in counter-clockwise order but have no means of visibly identifying them. We show that such robots can always solve the weak rendezvous problem and reconstruct the visibility graph, given an upper bound on n. Our results are tight: The strong rendezvous problem, in which robots need to gather at a common location, cannot be solved in general, and without a bound on n, not even n can be determined. In terms of mobile agents exploring a graph, our result implies that they can reconstruct any graph that is the visibility graph of a simple polygon. This is in contrast to the known result that the reconstruction of arbitrary graphs is impossible in general, even if n is known.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation 15(5), 818–828 (1999)CrossRefGoogle Scholar
  2. 2.
    Bilò, D., Disser, Y., Mihalák, M., Suri, S., Vicari, E., Widmayer, P.: Reconstructing visibility graphs with simple robots. In: Proceedings of the 16th International Colloquium on Structural Information and Communication Complexity, pp. 87–99 (2009)Google Scholar
  3. 3.
    Brunner, J., Mihalák, M., Suri, S., Vicari, E., Widmayer, P.: Simple robots in polygonal environments: A hierarchy. In: Fekete, S.P. (ed.) ALGOSENSORS 2008. LNCS, vol. 5389, pp. 111–124. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Chalopin, J., Godard, E., Métivier, Y., Ossamy, R.: Mobile agent algorithms versus message passing algorithms. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 187–201. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors and movements. SIAM Journal of Computing 38(1), 276–302 (2008)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Ganguli, A., Cortés, J., Bullo, F.: Distributed deployment of asynchronous guards in art galleries. In: Proceedings of the 2006 American Control Conference, pp. 1416–1421 (2006)Google Scholar
  7. 7.
    Ghosh, S.K.: Visibility Algorithms in the Plane. Cambridge University Press, Cambridge (2007)CrossRefMATHGoogle Scholar
  8. 8.
    Norris, N.: Universal covers of graphs: isomorphism to depth n − 1 implies isomorphism to all depths. Discrete Applied Mathematics 56(1), 61–74 (1995)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Suri, S., Vicari, E., Widmayer, P.: Simple robots with minimal sensing: From local visibility to global geometry. International Journal of Robotics Research 27(9), 1055–1067 (2008)CrossRefGoogle Scholar
  10. 10.
    Yamashita, M., Kameda, T.: Computing on anonymous networks: Part I – characterizing the solvable cases. IEEE Transactions on Parallel and Distributed Systems 7(1), 69–89 (1996)CrossRefGoogle Scholar
  11. 11.
    Yershova, A., Tovar, B., Ghrist, R., LaValle, S.M.: Bitbots: Simple robots solving complex tasks. In: Proceedings of the 20th National Conference on Artificial intelligence, vol. 3, pp. 1336–1341 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jérémie Chalopin
    • 1
  • Shantanu Das
    • 1
  • Yann Disser
    • 2
  • Matúš Mihalák
    • 2
  • Peter Widmayer
    • 2
  1. 1.LIF, CNRS & Aix-Marseille UniversitéFrance
  2. 2.Institute of Theoretical Computer ScienceETH ZürichSwitzerland

Personalised recommendations