Abstract
A (new) geometric pattern formation problem by a set of oblivious, anonymous, asynchronous (i.e., CORDA) robots is investigated in this paper. The conventional pattern formation problem assumes that the target pattern is given as a set of the positions by their coordinates in the global coordinate system, under the assumption that the robots are not aware of it. In the pattern formation problem we discuss in this paper, the points comprising the pattern are assumed to be “visible” to all robots, like landmarks. However, the robots still cannot obtain their positions in the global coordinate system. This paper shows that this pattern formation problem is solvable by oblivious asynchronous robots through the optimum matching between the robots and the pattern’s points.
Our study is partly motivated by the state-of-arts of the conventional pattern formation problem by oblivious asynchronous robots; description and correctness proof of a formation algorithm is usually complicated and ambiguous, because of the oblivious and asynchronous natures of the robots. A modular method is thus looked for to describe and prove algorithm in a clearer and more concrete way. Our pattern formation problem and the formation algorithm based on the optimum matching are used as a primitive building block in the modular method.
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.
References
Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM Journal on Computing 36, 56–82 (2006)
Bouzid, Z., Potop-Butucaru, M.G., Tixéuil, S.: Optimal Byzantine resilient convergence in asynchronous robot networks. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 165–179. Springer, Heidelberg (2009)
Bouzid, Z., Potop-Butucaru, M.G., Tixéuil, S.: Byzantine-resilient convergence in oblivious robot networks: The price of asynchrony. In: Garg, V., Wattenhofer, R., Kothapalli, K. (eds.) ICDCN 2009. LNCS, vol. 5408, pp. 275–280. Springer, Heidelberg (2009)
Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors. SIAM Journal on Computing 38, 276–302 (2008)
Dieudonné, Y., Petit, F., Villain, V.: Leader election problem versus pattern formation problem. In: Lynch, N.A., Shvartsman, A.A. (eds.) Distributed Computing. LNCS, vol. 6343, pp. 267–281. Springer, Heidelberg (2010)
Diestel, R.: Graph Theory, 2nd edn. Springer, Heidelberg (2000)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous mobile robots with limited visibility. Theoretical Computer Science 337, 147–168 (2005)
Izumi, T., Samia, S., Katayama, Y., Inuzuka, N., Défago, X., Wada, K., Yamashita, M.: The Gathering Problem for Two Oblivious Robots with Unreliable Compasses (to appear)
Katayama, Y., Tomida, Y., Imazu, H., Inuzuka, N., Wada, K.: Dynamic compass models and gathering algorithms for autonomous mobile robots. In: Prencipe, G., Zaks, S. (eds.) SIROCCO 2007. LNCS, vol. 4474, pp. 274–288. Springer, Heidelberg (2007)
Lovasz, L., Plummer, M.: Matching Theory. AMS Chelsea Publishing, Providence (2009)
Nagamochi, H., Yamashita, M., Ibaraki, T.: Distributed algorithms for cooperative controlling of anonymous mobile robots. Technical Reports of IEICE, COMP95-24, pp. 31–40 (1995) (in Japanese)
Prencipe, G.: Distributed coordination of a set of autonomous mobile robots. PhD Thesis, Universita di Pisa (2002)
Souissi, S., Défago, X., Yamashita, M.: Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. ACM Trans. Autonomous and Adaptive Systems 4 (2009)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing 28, 1347–1363 (1999)
Yamamoto, K., Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: Convergence of mobile robots with uniformly-inaccurate sensors. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 320–333. Springer, Heidelberg (2009)
Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theoretical Computer Science 411, 2433–2453 (2010)
Zhang, H., Zhang, F.: Plane elementary bipartite graphs. Discrete Applied Mathematics 105, 291–311 (2000)
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
Fujinaga, N., Ono, H., Kijima, S., Yamashita, M. (2010). Pattern Formation through Optimum Matching by Oblivious CORDA Robots. In: Lu, C., Masuzawa, T., Mosbah, M. (eds) Principles of Distributed Systems. OPODIS 2010. Lecture Notes in Computer Science, vol 6490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17653-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-17653-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17652-4
Online ISBN: 978-3-642-17653-1
eBook Packages: Computer ScienceComputer Science (R0)