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.
Most of this work was carried out while the first two authors were at ETH Zürich.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
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)
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)
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)
Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors and movements. SIAM Journal of Computing 38(1), 276–302 (2008)
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)
Ghosh, S.K.: Visibility Algorithms in the Plane. Cambridge University Press, Cambridge (2007)
Norris, N.: Universal covers of graphs: isomorphism to depth n − 1 implies isomorphism to all depths. Discrete Applied Mathematics 56(1), 61–74 (1995)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chalopin, J., Das, S., Disser, Y., Mihalák, M., Widmayer, P. (2010). How Simple Robots Benefit from Looking Back. In: Calamoneri, T., Diaz, J. (eds) Algorithms and Complexity. CIAC 2010. Lecture Notes in Computer Science, vol 6078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13073-1_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-13073-1_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13072-4
Online ISBN: 978-3-642-13073-1
eBook Packages: Computer ScienceComputer Science (R0)