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Pattern Formation by Robots with Inaccurate Movements

Authors Kaustav Bose , Archak Das , Buddhadeb Sau

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Author Details

Kaustav Bose
  • Advanced Computing and Microelectronics Unit, Indian Statistical Institute, Kolkata, India
Archak Das
  • Department of Mathematics, Jadavpur University, Kolkata, India
Buddhadeb Sau
  • Department of Mathematics, Jadavpur University, Kolkata, India


We would like to thank the anonymous reviewers for their comments and suggestions which helped us to improve the presentation of the paper.

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Kaustav Bose, Archak Das, and Buddhadeb Sau. Pattern Formation by Robots with Inaccurate Movements. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 10:1-10:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Arbitrary Pattern Formation is a fundamental problem in autonomous mobile robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any arbitrary pattern F given as input. In this paper, we study the problem for robots whose movements can be inaccurate. Our movement model assumes errors in both direction and extent of the intended movement. Forming the given pattern exactly is not possible in this setting. So we require that the robots must form a configuration which is close to the given pattern F. We call this the Approximate Arbitrary Pattern Formation problem. With no agreement in coordinate system, the problem is unsolvable, even by fully synchronous robots, if the initial configuration 1) has rotational symmetry and there is no robot at the center of rotation or 2) has reflectional symmetry and there is no robot on the reflection axis. From all other initial configurations, we solve the problem by 1) oblivious, silent and semi-synchronous robots and 2) oblivious, asynchronous robots that can communicate using externally visible lights.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Computational geometry
  • Computing methodologies → Distributed algorithms
  • Computing methodologies → Robotic planning
  • Distributed Algorithm
  • Mobile Robots
  • Movement Error
  • Approximate Arbitrary Pattern Formation
  • Look-Compute-Move
  • Minimum Enclosing Circle


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  1. Kaustav Bose, Ranendu Adhikary, Manash Kumar Kundu, and Buddhadeb Sau. Positional encoding by robots with non-rigid movements. In Proc. of 26th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2019, L'Aquila, Italy, volume 11639 of LNCS, pages 94-108. Springer, 2019. URL:
  2. Kaustav Bose, Ranendu Adhikary, Manash Kumar Kundu, and Buddhadeb Sau. Arbitrary pattern formation on infinite grid by asynchronous oblivious robots. Theor. Comput. Sci., 815:213-227, 2020. URL:
  3. Kaustav Bose, Archak Das, and Buddhadeb Sau. Pattern formation by robots with inaccurate movements. arXiv, abs/2010.09667, 2020. URL:
  4. Kaustav Bose, Manash Kumar Kundu, Ranendu Adhikary, and Buddhadeb Sau. Arbitrary pattern formation by asynchronous opaque robots with lights. Theor. Comput. Sci., 849:138-158, 2021. URL:
  5. Quentin Bramas and Sébastien Tixeuil. Brief announcement: Probabilistic asynchronous arbitrary pattern formation. In Proc. of the 2016 ACM Symposium on Principles of Distributed Computing, PODC 2016, Chicago, IL, USA, pages 443-445, 2016. URL:
  6. Serafino Cicerone, Gabriele Di Stefano, and Alfredo Navarra. Asynchronous arbitrary pattern formation: the effects of a rigorous approach. Distributed Computing, pages 1-42, 2018. doi: URL: 10.1007/s00446-018-0325-7.
  7. Reuven Cohen and David Peleg. Convergence of autonomous mobile robots with inaccurate sensors and movements. SIAM J. Comput., 38(1):276-302, 2008. URL:
  8. Yoann Dieudonné, Franck Petit, and Vincent Villain. Leader election problem versus pattern formation problem. In Proc. of 24th International Symposium on Distributed Computing, DISC 2010, Cambridge, MA, USA, pages 267-281, 2010. URL:
  9. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, and Peter Widmayer. Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci., 407(1-3):412-447, 2008. URL:
  10. Nao Fujinaga, Yukiko Yamauchi, Hirotaka Ono, Shuji Kijima, and Masafumi Yamashita. Pattern formation by oblivious asynchronous mobile robots. SIAM J. Comput., 44(3):740-785, 2015. URL:
  11. Giuseppe Antonio Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, and Masafumi Yamashita. Meeting in a polygon by anonymous oblivious robots. Distributed Comput., 33(5):445-469, 2020. URL:
  12. Ichiro Suzuki and Masafumi Yamashita. Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. Comput., 28(4):1347-1363, 1999. URL:
  13. Ramachandran Vaidyanathan, Gokarna Sharma, and Jerry L. Trahan. On fast pattern formation by autonomous robots. In Proc. of 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2018, Tokyo, Japan, pages 203-220, 2018. URL:
  14. Masafumi Yamashita and Ichiro Suzuki. Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci., 411(26-28):2433-2453, 2010. URL:
  15. Yukiko Yamauchi and Masafumi Yamashita. Randomized pattern formation algorithm for asynchronous oblivious mobile robots. In Proc. of 28th International Symposium on Distributed Computing, DISC 2014, Austin, TX, USA, pages 137-151, 2014. URL:
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