Abstract
We study the computational power of distributed systems consisting of simple autonomous robots moving on the plane. The robots are endowed with visual perception, allowing them to see each other, but they do not have any means of explicit communication with each other. Further the robots are oblivious, meaning that they always act based on their current perception of the environment, and they have no memory of the past. Such system of simple robots have been studied extensively with the objective of achieving coordinated tasks e.g. arranging the robots in a line or a circle. In fact it has been shown that obliviousness is not a limiting factor to form a single geometric pattern, however arbitrary. This paper aims to understand the computational limits imposed by the obliviousness of the robots by studying the formation of a series of geometric patterns instead of a single pattern. If such a series of patterns could be formed this would create some form of memory in an otherwise memory-less system. We show that, under particular conditions, oblivious robot systems can indeed form a given series of geometric patterns starting from any arbitrary configuration. More precisely, we characterize the series of patterns that can be formed by oblivious robot systems under various additional restrictions such as anonymity, asynchrony and lack of common orientation. These results provide strong indications that oblivious solutions may be obtained also for tasks that intuitively seem to require memory.
Similar content being viewed by others
Notes
This models any deviations in sensory apparatus used by a robot in between two steps, specially when the robot physically moves across the plane.
The robots themselves are not aware of this global coordinate system.
unlike the definition of views in [26].
References
Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput. 36(1), 56–82 (2006)
Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: A distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robotics Autom. 15(5), 818–828 (1999)
Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: IEEE Symposium on Intelligent Control, pp. 453–460 (1995)
Asahiro, Y., Fujita, S., Suzuki, I., Yamashita, M.: A self-stabilizing marching algorithm for a group of oblivious robots. In: 12th International Conference on Principles of Distributed Systems (OPODIS), pp. 125–144 (2008)
Bouzid, Z., Lamani, A.: Robot networks with homonyms: the case of patterns formation. arXiv, Report, 1105.5817 (2011)
Bullo, F., Cortés, J., Martínez, S.: Distrib. Control Robotic Netw. Princeton University Press, Princeton (2009)
Chatzigiannakis, I., Markou, M., Nikoletseas, S. E.: Distributed circle formation for anonymous oblivious robots. In: 3rd Workshop on Efficient and Experimental Algorithms (WEA), pp. 159–174 (2004)
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)
Cohen, R., Peleg, D.: Local spreading algorithms for autonomous robot systems. Theor. Comput. Sci. 399(1–2), 71–82 (2008)
Défago, X., Souissi, S.: Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity. Theor. Comput. Sci. 396(1–3), 97–112 (2008)
Dieudonné, Y., Dolev, S., Petit, F., Segal, M.: Deaf, dumb, and chatting asynchronous robots. In 13th International Conference on Principles of Distributed Systems (OPODIS), pp. 71–85 (2009)
Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. ACM Trans. Auton. Adapt. Syst. 3(4), 16:1–16:20 (2008)
Efrima, A., Peleg, D.: Distributed models and algorithms for mobile robot systems. In: 33rd Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), pp. 70–87 (2007)
Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool, San Rafael (2012)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337(1–3), 147–168 (2005)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci. 407(1–3), 412–447 (2008)
Fujinaga, N., Ono, H., Kijima, S., Yamashita, M.: Pattern formation through optimum matching by oblivious corda robots. In: 14th International Conference on Principles of Distributed Systems (OPODIS), pp. 1–15 (2010)
Fujinaga, N., Yamauchi, Y., Kijima, S., Yamashita, M.: Asynchronous pattern formation by anonymous oblivious mobile robots. In: Proceedings of the 26th International Symposium on Distributed Computing (DISC), pp. 312–325 (2012)
Gervasi, V., Prencipe, G.: Coordination without communication: the case of the flocking problem. Discret. Appl. Math. 144(3), 324–344 (2004)
Gordon, N., Wagner, I. A., Bruckstein, A. M.: Discrete bee dance algorithms for pattern formation on a grid. In: IEEE/WIC International Conference on Intelligent Agent Technology (IAT), pp. 545–549 (2003)
Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Feasibility of polynomial-time randomized gathering for oblivious mobile robots. IEEE Trans. Parallel Distrib. Syst. 24(4), 716–723 (2013)
Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: Gathering autonomous mobile robots with dynamic compasses: an optimal result. In: 21st International Symposium on Distributed Computing (DISC), pp. 298–312 (2007)
Lin, J., Morse, A.S., Anderson, B.D.O.: The multi-agent rendezvous problem. Parts 1 and 2. SIAM J. Control Optim. 46(6), 2120–2147 (2007)
Souissi, S., Izumi, T., Wada, K.: Oracle-based flocking of mobile robots in crash-recovery model. Theor. Comput. Sci. 412(33), 4350–4360 (2011)
Sugihara, K., Suzuki, I.: Distributed algorithms for formation of geometric patterns with many mobile robots. J. Robotics Syst. 13, 127–139 (1996)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)
Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411(26–28), 2433–2453 (2010)
Yamauchi, Y., Yamashita, M.: Pattern formation by mobile robots with limited visibility. In: 20th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp. 201–212 (2013)
Acknowledgments
This research has been supported in part by the Natural Sciences and Engineering Research Council (Canada) under the Discovery Grant program, by Prof. Flocchini’s University Research Chair, and by the Scientific Grant in Aid by the Ministry of Education, Sports, Culture and Technology of Japan.
Author information
Authors and Affiliations
Corresponding author
Additional information
A preliminary version of this paper has been presented at the 29th ACM Symposium on Principles of Distributed Computing, 2010.
Rights and permissions
About this article
Cite this article
Das, S., Flocchini, P., Santoro, N. et al. Forming sequences of geometric patterns with oblivious mobile robots. Distrib. Comput. 28, 131–145 (2015). https://doi.org/10.1007/s00446-014-0220-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00446-014-0220-9