Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots
The Arbitrary Pattern Formation problem asks to design a distributed algorithm that allows a set of autonomous mobile robots to form any specific but arbitrary geometric pattern given as input. The problem has been extensively studied in literature in continuous domains. This paper investigates a discrete version of the problem where the robots are operating on a two dimensional infinite grid. The robots are assumed to be autonomous, identical, anonymous and oblivious. They operate in Look-Compute-Move cycles under a fully asynchronous scheduler. The robots do not agree on any common global coordinate system or chirality. We have shown that a set of robots can form any arbitrary pattern, if their starting configuration is asymmetric.
KeywordsDistributed algorithm Autonomous robots Arbitrary Pattern Formation Grid Asynchronous Look-Compute-Move cycle
The first three authors are supported by NBHM, DAE, Govt. of India, CSIR, Govt. of India and UGC, Govt. of India respectively. We would like to thank the anonymous reviewers for their valuable comments which helped us improve the quality and presentation of this paper.
- 1.Adhikary, R., Bose, K., Kundu, M.K., Sau, B.: Mutual visibility by asynchronous robots on infinite grid. In: 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS 2018), Helsinki, Finland, 23–24 August 2018 (Forthcoming)Google Scholar
- 2.Bose, K., Adhikary, R., Kundu, M.K., Sau, B.: Arbitrary pattern formation on infinite grid by asynchronous oblivious robots. CoRR abs/1811.00834 (2018). http://arxiv.org/abs/1811.00834
- 3.Bramas, Q., Tixeuil, S.: Brief announcement: probabilistic asynchronous arbitrary pattern formation. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, PODC 2016, Chicago, IL, USA, pp. 443–445, 25–28 July 2016. https://doi.org/10.1145/2933057.2933074
- 4.Cicerone, S., Di Stefano, G., Navarra, A.: Asynchronous arbitrary pattern formation: the effects of a rigorous approach. Distrib. Comput., 1–42 (2018) https://doi.org/10.1007/s00446-018-0325-7
- 5.Cicerone, S., Di Stefano, G., Navarra, A.: Embedded pattern formation by asynchronous robots without chirality. Distrib. Comput., 1–25 (2018). https://doi.org/10.1007/s00446-018-0333-7
- 7.Dieudonné, Y., Petit, F., Villain, V.: Leader election problem versus pattern formation problem. CoRR abs/0902.2851 (2009). http://arxiv.org/abs/0902.2851
- 13.Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots. In: SIROCCO 1996, The 3rd International Colloquium on Structural Information & Communication Complexity, Siena, Italy, pp. 313–330, 6–8 June 1996Google Scholar