Gathering Asynchronous Mobile Robots with Inaccurate Compasses

  • Samia Souissi
  • Xavier Défago
  • Masafumi Yamashita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4305)


This paper considers a system of asynchronous autonomous mobile robots that can move freely in a two-dimensional plane with no agreement on a common coordinate system. Starting from any initial configuration, the robots are required to eventually gather at a single point, not fixed in advance (gathering problem).

Prior work has shown that gathering oblivious (i.e., stateless) robots cannot be achieved deterministically without additional assumptions. In particular, if robots can detect multiplicity (i.e., count robots that share the same location) gathering is possible for three or more robots. Similarly, gathering of any number of robots is possible if they share a common direction, as given by compasses, with no errors.

Our work is motivated by the pragmatic standpoint that (1) compasses are error-prone devices in reality, and (2) multiplicity detection, while being easy to achieve, allows for gathering in situations with more than two robots. Consequently, this paper focusses on gathering two asynchronous mobile robots equipped with inaccurate compasses. In particular, we provide a self-stabilizing algorithm to gather, in a finite time, two oblivious robots equipped with compasses that can differ by as much as π/4.


Mobile Robot Obtuse Angle Autonomous Mobile Robot Common Coordinate System Deadlock Situation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. In: Proc. 15th Annual ACM-SIAM Symp. on Discrete Algorithms (SODA 2004), Philadelphia, PA, USA, pp. 1070–1078 (2004)Google Scholar
  2. 2.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. on Robotics and Automation 15(5), 818–828 (1999)CrossRefGoogle Scholar
  3. 3.
    Cieliebak, M.: Gathering non-oblivious mobile robots. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 577–588. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the robots gathering problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1181–1196. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Cohen, R., Peleg, D.: Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 549–560. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Défago, X., Gradinariu, M., Messika, S., Raipin-Parvédy, P.: Fault-tolerant and self-stabilizing mobile robots gathering. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 46–60. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Dolev, S.: Self-Stabilization. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  8. 8.
    Fisher, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)CrossRefGoogle Scholar
  9. 9.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337(1–3), 147–168 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Imazu, H., Itoh, N., Katayama, Y., Inuzuka, N., Wada, K.: A Gathering Problem for Autonomous Mobile Robots with Disagreement in Compasses. In: 1st Workshop on Theoretical Computer Science in Izumo, Japan, pp. 43–46 (2005) (in Japanese)Google Scholar
  11. 11.
    Prencipe, G.: Instantaneous Actions vs. Full Asynchronicity: Controlling and Coordinating a Set of Autonomous Mobile Robots. In: Restivo, A., Ronchi Della Rocca, S., Roversi, L. (eds.) ICTCS 2001. LNCS, vol. 2202, pp. 154–171. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Prencipe, G.: CORDA: Distributed coordination of a set of autonomous mobile robots. In: Proc. 4th European Research Seminar on Advances in Distributed Systems (ERSADS 2001), Bertinoro, Italy, pp. 185–190 (2001)Google Scholar
  13. 13.
    Prencipe, G.: On the feasibility of gathering by autonomous mobile robots. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 246–261. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Schneider, M.: Self-stabilization. ACM Computing Surveys 25(1), 45–67 (1993)CrossRefGoogle Scholar
  15. 15.
    Souissi, S., Défago, X., Yamashita, M.: Using Eventually Consistent Compasses to Gather Oblivious Mobile Robots with Limited Visibility. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 484–500. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Souissi, S., Défago, X., Yamashita, M.: Gathering Asynchronous Mobile Robots with Inaccurate Compasses. Research Report (JAIST), IS-RR-2006-014, Hokuriku, Japan (2006)Google Scholar
  17. 17.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing 28(4), 1347–1363 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Samia Souissi
    • 1
  • Xavier Défago
    • 1
  • Masafumi Yamashita
    • 2
  1. 1.School of Information ScienceJapan Advanced Institute of Science and Technology (JAIST)IshikawaJapan
  2. 2.Department of Computer Science and Communication EngineeringKyushu UniversityFukuokaJapan

Personalised recommendations