Fault-Tolerant Mobile Robots

  • Xavier Défago
  • Maria Potop-ButucaruEmail author
  • Sébastien Tixeuil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)


This chapter surveys crash tolerance, self-stabilization, Byzantine fault-tolereance, and resilience to inaccuracies for the main building blocks in mobile robots networks: gathering, convergence, scattering, leader election, and flocking.


Fault-tolerant Mobile robots Distributed algorithms 


  1. 1.
    Abraham, I., Amit, Y., Dolev, D.: Optimal resilience asynchronous approximate agreement. In: Higashino, T. (ed.) OPODIS 2004. LNCS, vol. 3544, pp. 229–239. Springer, Heidelberg (2005). Scholar
  2. 2.
    Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. SIAM J. Comput. 36(1), 56–82 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Auger, C., Bouzid, Z., Courtieu, P., Tixeuil, S., Urbain, X.: Certified impossibility results for Byzantine-tolerant mobile robots. In: Higashino, T., Katayama, Y., Masuzawa, T., Potop-Butucaru, M., Yamashita, M. (eds.) SSS 2013. LNCS, vol. 8255, pp. 178–190. Springer, Cham (2013). Scholar
  4. 4.
    Aurenhammer, F.: Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Comput. Surv. 23(3), 345–405 (1991)CrossRefGoogle Scholar
  5. 5.
    Balabonski, T., Delga, A., Rieg, L., Tixeuil, S., Urbain, X.: Synchronous gathering without multiplicity detection: a certified algorithm. In: Bonakdarpour, B., Petit, F. (eds.) SSS 2016. LNCS, vol. 10083, pp. 7–19. Springer, Cham (2016). Scholar
  6. 6.
    Bhagat, S., Gan Chaudhuri, S., Mukhopadhyaya, K.: Fault-tolerant gathering of asynchronous oblivious mobile robots under one-axis agreement. In: Rahman, M.S., Tomita, E. (eds.) WALCOM 2015. LNCS, vol. 8973, pp. 149–160. Springer, Cham (2015). Scholar
  7. 7.
    Bhagat, S., Mukhopadhyaya, K.: Fault-tolerant gathering of semi-synchronous robots. In: Proceedings of 18th International Conference on Distributed Computing and Networking (ICDCN), Hyderabad, India, p. 6, January 2017Google Scholar
  8. 8.
    Borowsky, E., Gafni, E., Lynch, N.A., Rajsbaum, S.: The BG distributed simulation algorithm. Distrib. Comput. 14(3), 127–146 (2001)CrossRefGoogle Scholar
  9. 9.
    Bouzid, Z., Das, S., Tixeuil, S.: Gathering of mobile robots tolerating multiple crash faults. In: Proceedings of 33rd IEEE International Conference on Distributed Computing Systems (ICDCS), Philadelphia, PA, USA, pp. 337–346, July 2013Google Scholar
  10. 10.
    Bouzid, Z., Gradinariu Potop-Butucaru, M., Tixeuil, S.: Byzantine convergence in robot networks: the price of asynchrony. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 54–70. Springer, Heidelberg (2009). Scholar
  11. 11.
    Bouzid, Z., Potop-Butucaru, M.G., Tixeuil, S.: Optimal Byzantine-resilient convergence in uni-dimensional robot networks. Theoret. Comput. Sci. 411(34–36), 3154–3168 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Bramas, Q., Tixeuil, S.: Wait-free gathering without chirality. In: Scheideler, C. (ed.) Structural Information and Communication Complexity. LNCS, vol. 9439, pp. 313–327. Springer, Cham (2015). Scholar
  13. 13.
    Bramas, Q., Tixeuil, S.: The random bit complexity of mobile robots scattering. Int. J. Found. Comput. Sci. 28(2), 111–134 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Canepa, D., Defago, X., Izumi, T., Potop-Butucaru, M.: Flocking with oblivious robots. In: Bonakdarpour, B., Petit, F. (eds.) SSS 2016. LNCS, vol. 10083, pp. 94–108. Springer, Cham (2016). Scholar
  15. 15.
    Canepa, D., Potop-Butucaru, M.G.: Stabilizing flocking via leader election in robot networks. In: Masuzawa, T., Tixeuil, S. (eds.) SSS 2007. LNCS, vol. 4838, pp. 52–66. Springer, Heidelberg (2007). Scholar
  16. 16.
    Clément, J., Défago, X., Potop-Butucaru, M.G., Izumi, T., Messika, S.: The cost of probabilistic agreement in oblivious robot networks. Inf. Process. Lett. 110(11), 431–438 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Cohen, R., Peleg, D.: Robot convergence via center-of-gravity algorithms. In: Královic̆, R., Sýkora, O. (eds.) SIROCCO 2004. LNCS, vol. 3104, pp. 79–88. Springer, Heidelberg (2004). Scholar
  18. 18.
    Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34(6), 1516–1528 (2005)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors and movements. SIAM J. Comput. 38(1), 276–302 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Courtieu, P., Rieg, L., Tixeuil, S., Urbain, X.: Impossibility of gathering, a certification. Inf. Process. Lett. 115(3), 447–452 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: Autonomous mobile robots with lights. Theoret. Comput. Sci. 609, 171–184 (2016)MathSciNetCrossRefGoogle Scholar
  22. 22.
    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). Scholar
  23. 23.
    Défago, X., Potop-Butucaru, M.G., Clément, J., Messika, S., Raipin Parvédy, P.: Fault and Byzantine tolerant self-stabilizing mobile robots gathering - feasibility study. CoRR abs/1602.05546 (2016)Google Scholar
  24. 24.
    Dieudonné, Y., Levé, F., Petit, F., Villain, V.: Deterministic geoleader election in disoriented anonymous systems. Theoret. Comput. Sci. 506, 43–54 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Dieudonne, Y., Petit, F.: Circle formation of weak robots and Lyndon words. Inf. Process. Lett. 101(4), 156–162 (2007)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Dieudonné, Y., Petit, F.: Robots and demons (the code of the origins). In: Crescenzi, P., Prencipe, G., Pucci, G. (eds.) FUN 2007. LNCS, vol. 4475, pp. 108–119. Springer, Heidelberg (2007). Scholar
  27. 27.
    Dieudonné, Y., Petit, F.: Scatter of robots. Parallel Process. Lett. 19(1), 175–184 (2009)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Dieudonné, Y., Petit, F.: Self-stabilizing gathering with strong multiplicity detection. Theoret. Comput. Sci. 428, 47–57 (2012)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)CrossRefGoogle Scholar
  30. 30.
    Dolev, D., Lynch, N.A., Pinter, S.S., Stark, E.W., Weihl, W.E.: Reaching approximate agreement in the presence of faults. J. ACM (JACM) 33(3), 499–516 (1986)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theoret. Comput. Sci. 337(1–3), 147–168 (2005)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Gervasi, V., Prencipe, G.: Flocking by a set of autonomous mobile robots. Technical report TR-01-24, Universitat di Pisa (2001)Google Scholar
  33. 33.
    Gervasi, V., Prencipe, G.: Coordination without communication: the case of the flocking problem. Discret. Appl. Math. (2003)Google Scholar
  34. 34.
    Heriban, A., Défago, X., Tixeuil, S.: Optimally gathering two robots. In: Bellavista, P., Garg, V.K. (eds.) Proceedings of the 19th International Conference on Distributed Computing and Networking. ICDCN 2018, 4–7 January 2018, Varanasi, India, pp. 3:1–3:10. ACM, New York (2018)Google Scholar
  35. 35.
    Izumi, T., Bouzid, Z., Tixeuil, S., Wada, K.: The BG-simulation for Byzantine mobile robots. CoRR abs/1106.0113 (2011)Google Scholar
  36. 36.
    Izumi, T., Bouzid, Z., Tixeuil, S., Wada, K.: Brief announcement: the BG-simulation for Byzantine mobile robots. In: Peleg, D. (ed.) DISC 2011. LNCS, vol. 6950, pp. 330–331. Springer, Heidelberg (2011). Scholar
  37. 37.
    Izumi, T., Kaino, D., Potop-Butucaru, M.G., Tixeuil, S.: On time complexity for connectivity-preserving scattering of mobile robots. Theoret. Comput. Sci. 738, 42–52 (2018)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Izumi, T., et al.: The gathering problem for two oblivious robots with unreliable compasses. SIAM J. Comput. 41(1), 26–46 (2012)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Qadi, A., Huang, J., Farritor, S., Goddard, S.: Localization and follow-the-leader control of a heterogeneous group of mobile robots. IEEE/ASME Trans. Mechatron. 11, 205–215 (2006)CrossRefGoogle Scholar
  40. 40.
    Lindhe, M.: A flocking and obstacle avoidance algorithm for mobile robots. Ph.D. thesis, KTH Stockholm (2004)Google Scholar
  41. 41.
    Ooshita, F., Tixeuil, S.: On the self-stabilization of mobile oblivious robots in uniform rings. Theoret. Comput. Sci. 568, 84–96 (2015)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Pattanayak, D., Mondal, K., Ramesh, H., Mandal, P.S.: Fault-tolerant gathering of mobile robots with weak multiplicity detection. In: Proceedings of the 18th International Conference on Distributed Computing and Networking, 5–7 January 2017, Hyderabad, India, p. 7. ACM (2017)Google Scholar
  43. 43.
    Prencipe, G.: Corda: distributed coordination of a set of autonomous mobile robots. In: Proceedings of ERSADS, May 2001, pp. 185–190 (2001)Google Scholar
  44. 44.
    Renaud, P., Cervera, E., Martinet, P.: Towards a reliable vision-based mobile robot formation control. In: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, 28 September–2 October 2004, pp. 3176–3181. IEEE (2004)Google Scholar
  45. 45.
    Souissi, S.: Fault-resilient cooperation of autonomous mobile robots with unreliable compass sensors. Ph.D. thesis, Graduate School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), September 2007Google Scholar
  46. 46.
    Souissi, S., Défago, X., Yamashita, M.: Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. ACM Trans. Auton. Adapt. Syst. 4(1), 9:1–9:27 (2009)CrossRefGoogle Scholar
  47. 47.
    Souissi, S., Izumi, T., Wada, K.: Oracle-based flocking of mobile robots in crash-recovery model. Theoret. Comput. Sci. 412(33), 4350–4360 (2011)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Suzuki, I., Yamashita, M.: A theory of distributed anonymous mobile robots formation and agreement problems. Technical report, Department of Electrical Engineering and Computer Science, Wisconsin University of Milwaukee, June 1994Google Scholar
  49. 49.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefGoogle Scholar
  50. 50.
    Viglietta, G.: Rendezvous of two robots with visible bits. In: Flocchini, P., Gao, J., Kranakis, E., Meyer auf der Heide, F. (eds.) ALGOSENSORS 2013. LNCS, vol. 8243, pp. 291–306. Springer, Heidelberg (2014). Scholar
  51. 51.
    Yang, Y., Souissi, S., Défago, X., Takizawa, M.: Fault-tolerant flocking for a group of autonomous mobile robots. J. Syst. Softw. 84(1), 29–36 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xavier Défago
    • 1
  • Maria Potop-Butucaru
    • 2
    Email author
  • Sébastien Tixeuil
    • 2
  1. 1.School of ComputingTokyo Institute of TechnologyTokyoJapan
  2. 2.Sorbonne Université, CNRS, Laboratoire d’Informatique de Paris 6, LIP6ParisFrance

Personalised recommendations