Skip to main content
SpringerLink
Log in

STATE

Distributed algorithm for uniform circle formation by multiple mobile robots

  • Original Research Paper
  • Published:
Intelligent Service Robotics Aims and scope Submit manuscript

Abstract

Multi-robot pattern formation has a wide range of applications, such as inspection of hazardous regions, parallel and simultaneous transportation of load, area exploration, etc. This problem has been investigated both from the scientific and engineering perspectives. There is a whole body of experimental work on robot formations, and at the same, there is no dearth of theoretical research addressing the same problem. Several assumptions considered in these theoretical studies are overly simplified with an understanding that they will somehow be reasonably approximated. Although these theoretical research works are sound and complete, they do not show how an actual implementation compares with the idealized scenario. A new practical model is suggested in this paper for geometric pattern formation. This model uses approximate solutions to some of the assumptions considered in theoretical research works. A novel algorithm, STATE, is proposed and is shown to perform better than Défago and Konagaya’s algorithm for uniform circle formation. Both the algorithms are implemented on a real multi-robot test bed. A new framework for inter-robot communication is developed. It supports seamless asynchronous and non-blocking robot-to-computer, and robot-to-robot communication.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Fredslund J, Matarić M (2002) A general algorithm for robot formations using local sensing and minimal communication. IEEE Trans Robot Autom 18(5):837–846. doi:10.1109/TRA.2002.803458

    Article  Google Scholar 

  2. Fax J, Murray R (2002) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49(9):1465–1476. doi:10.1109/TAC.2004.834433

    Article  MathSciNet  Google Scholar 

  3. Krishnanand K, Ghose D (2005) Formations of minimalist mobile robots using local-templates and spatially distributed interactions. Robot Auton Syst 53:194–213. doi:10.1016/j.robot.2005.09.006

    Article  Google Scholar 

  4. Hao Y, Agrawal SK (2005) Planning and control of UGV formations in a dynamic environment: a practical framework with experiments. Robot Auton Syst 51:101–110. doi:10.1016/j.robot.2005.01.001

    Article  Google Scholar 

  5. Marshall JA, Fung T, Broucke ME et al (2006) Experiments in multirobot coordination. Robot Auton Syst 54(3):265–275. doi:10.1016/j.robot.2005.10.004

    Article  Google Scholar 

  6. Antonelli G, Arrichiello F, Chakraborti S, Chiaverini S (2007) Experiences of formation control of multi-robot systems with the Null-Space-based Behavioral control. In: Proceedings of IEEE international conference on robotics and automation. doi:10.1109/ROBOT.2007.363126

  7. Antonelli G, Arrichiello F, Chiaverini S (2009) Experiments of formation control with multi-robot systems using the null-space-based behavioral control. IEEE Trans Control Syst Technol 17(5):1173–1182. doi:10.1109/TCST.2008.2004447

    Article  Google Scholar 

  8. Antonelli G, Arrichiello F, Chiaverini S (2010) Flocking for multi-robot systems via the null-space-based behavioral control. Swarm Intell 4:37–56. doi:10.1007/s11721-009-0036-6

    Article  Google Scholar 

  9. Mead R, Long R, Weinberg JB (2009) Fault-tolerant formations of mobile robots. In: Proceedings of IEEE/RSJ international conference on intelligent robots and systems. doi:10.1109/IROS.2009.5353996

  10. Monteiro S, Bicho E (2010) Attractor dynamics approach to formation control: theory and application. Auton Robot 29(3–4):331–355. doi:10.1007/s10514-010-9198-8

    Article  Google Scholar 

  11. Suzuki I, Yamashita M (1999) Distributed anonymous mobile robots: formation of geometric patterns. SIAM J Comput 28(4):1347–1363. doi:10.1137/S009753979628292X

    Article  MathSciNet  MATH  Google Scholar 

  12. Prencipe G (2001) CORDA: distributed coordination of a set of autonomous mobile robots. In: Proceedings of 4th European Research Seminar on advances in distributed systems (ERSADS 2001), pp 185–190

  13. Debest XA (1995) Remark about self-stabilizing systems. Commun ACM 38(2):115–117

    Google Scholar 

  14. Sugihara K, Suzuki I (1996) Distributed algorithms for formation of geometric patterns with many mobile robots. J Robot Syst 3(13):127–139. doi:10.1002/(SICI)1097-4563(199603)13:3$<$127:AID-ROB1$>$3.0.CO;2-U

    Article  MATH  Google Scholar 

  15. Ando H, Oasa Y, Suzuki I, Yamashita M (1999) Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans Robot Autom 15(5):818–828. doi:10.1109/70.795787

    Article  Google Scholar 

  16. Flocchini P, Prencipe G, Santoro N, Widmayer P (2005) Gathering of asynchronous robots with limited visibility. Theor Comput Sci 337(1–3):147–168. doi:10.1016/j.tcs.2005.01.001

    Article  MathSciNet  MATH  Google Scholar 

  17. Flocchini P, Prencipe G, Santoro N, Widmayer P (1999) Hard tasks for weak robots: the role of common knowledge in pattern formation by autonomous mobile robots. In: Proceedings of 10th international symposium on algorithms and computation (ISAAC 1999). doi:10.1007/3-540-46632-0_10

  18. Cao YU, Fukunaga AS, Kahng A (1997) Cooperative mobile robotics: antecedents and directions. Auton Robot 4(1):7–27. doi:10.1023/A:1008855018923

    Article  Google Scholar 

  19. Krick L, Broucke ME, Francis BA (2009) Stabilisation of infinitesimally rigid formations of multi-robot networks. Int J Control 82(3):423–439. doi:10.1080/00207170802108441

    Article  MathSciNet  MATH  Google Scholar 

  20. Leonard NE, Paley DA, Davis RE, Fratantoni DM, Lekien F, Zhang F (2010) Coordinated control of an underwater glider fleet in an adaptive ocean sampling field experiment in monterey bay. J Field Robot 27(6):718–740. doi:10.1002/rob.20366

    Article  Google Scholar 

  21. Chatzigiannakis I, Markou M, Nikoletseas S (2004) Distributed circle formation for anonymous oblivious robots. In: Ribeiro CC, Martins SL (eds) Experimental and efficient algorithms, Chapter 12, Vol. 3059. Springer, Berlin pp 159–174. doi:10.1007/978-3-540-24838-5_12

  22. Défago X, Konagaya A (2002) Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: Proceedings of the second ACM international workshop on principles of mobile computing. doi:10.1145/584490.584509

  23. Défago X, Souissi S (2008) Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity. Theor Comput Sci 396(1–3):97–112. doi:10.1016/j.tcs.2008.01.050

    Article  MathSciNet  MATH  Google Scholar 

  24. Elor Y, Bruckstein AM (2011) Uniform multi-agent deployment on a ring. Theor Comput Sci 412(8–10):783–795. doi:10.1016/j.tcs.2010.11.023

    Article  MathSciNet  MATH  Google Scholar 

  25. Flocchini P, Prencipe G, Santoro N (2008) Self-deployment of mobile sensors on a ring. Theor Comput Sci 402(1):67–80. doi:10.1016/j.tcs.2008.03.006

    Article  MathSciNet  MATH  Google Scholar 

  26. Souissi S, Défago X, Katayama T (2004) Convergence of a self-stabilizing circle formation algorithm for cooperative mobile robotics. In: Proceedings of scientific French-speaking workshops (JSF’04), Tokyo, Japan

  27. Gautam A, Mohan S, Misra JP (2012) A practical framework for uniform circle formation by multiple mobile robots. In: Proceedings of IEEE 7th international conference on industrial and information systems (ICIIS). doi:10.1109/ICIInfS.2012.6304765

  28. Gautam A, Mohan S (2013) A distributed algorithm for circle formation by multiple mobile robots. In: Proceedings of 2013 international conference on control, automation, robotics and embedded systems (CARE)

  29. Gautam A, Saxena A, Mall P, Mohan S (2014) Positioning multiple mobile robots for geometric pattern formation: An empirical analysis. In: Proceedings of seventh international conference on contemporary computing (IC3)

  30. Dieudonné Y, Labbani-Igbida O, Petit F (2008) Circle formation of weak mobile robots. ACM Trans Auton Adapt Syst (TAAS). doi:10.1145/1452001.1452006

  31. Dieudonné Y, Dolev S, Petit F, Segal M (2009) Brief announcement: deaf, dumb, and chatting robots. In: Proceedings of the 28th ACM symposium on principles of distributed computing. doi:10.1145/1582716.1582781

  32. Howard A (2006) Multi-robot simultaneous localization and mapping using particle filters. Int J Robot Res 25(12):1243–1256. doi:10.1177/0278364906072250

    Article  Google Scholar 

  33. Meltzer J, Gupta R, Yang M-H, Soatto S (2004) Simultaneous localization and mapping using multiple view feature descriptors. In: Proceedings of 2004 IEEE/RSJ international conference on intelligent robots and systems. doi:10.1109/IROS.2004.1389616

  34. Prencipe G (2002) Distributed coordination of a set of autonomous mobile robots. Ph.D. Thesis, Università di Pisa

  35. Mondada F, Bonani M, Raemy X, Pugh J, et al (2009) The e-puck, a robot designed for education in engineering. Infoscience, EPFL’s scientific publications. https://infoscience.epfl.ch/record/135236/files/epuck-robotica2009.pdf Accessed 13 Jun 2016

  36. Garg VK (2004) Resource allocation. In: Concurrent and distributed computing in java, Wiley, IEEE Press, pp 138–141

  37. Bruce J, Balch T, Veloso M (2000) Fast and inexpensive color image segmentation for interactive robots. In: Proceedings of the 2000 IEEE/RSJ international conference on intelligent robot and systems (IROS 2000)

  38. Chang F, Chen C-J, Lu C-J (2004) A linear-time component-labeling algorithm using contour tracing technique. Comput Vis Image Underst 93(2):206–220. doi:10.1016/j.cviu.2003.09.002

    Article  Google Scholar 

  39. Gutiérrez A, Campo A, Dorigo M, Donate J, Monasterio-Huelin F, Magdalena L (2009) Open e-puck range & bearing miniaturized board for local communication in swarm robotics. In: Proceedings of IEEE international conference on robotics and automation. doi:10.1109/ROBOT.2009.5152456

  40. Cianci CM, Raemy X, Pugh J, Martinoli A (2006) Communication in a swarm of miniature robots: the e-puck as an educational tool for swarm robotics. Infoscience, EPFL’s scientific publications. https://infoscience.epfl.ch/record/100015/files/44330103.pdf Accessed 13 Jun 2016

  41. Radchuk D. (2013) Boost.Asio C++ network programming cookbook. PACKT Publishing (open source), Birmingham, UK

  42. Russell S, Norvig P (2014) Intelligent agents. In: Artificial intelligence: a modern approach. 3rd edn. Pearson Education Limited, EdinburgGate, pp 31–32

  43. Kuhn HW (1955) The hungarian method for the assignment problem. Naval Res Logist Q 2(1–2):83–97. doi:10.1002/nav.3800020109

    Article  MathSciNet  MATH  Google Scholar 

  44. Dieudonné Y, Petit F (2007) Circle formation of weak robots and Lyndon words. Inf Proc Lett 101(4):156–162. doi:10.1016/j.ipl.2006.09.008

    Article  MathSciNet  MATH  Google Scholar 

  45. Calculator, Wilcoxon (2013) Scistatcalc: Wilcoxon signed rank test calculator. Scistatcalc.blogspot.in. http://scistatcalc.blogspot.in/2013/10/wilcoxon-signed-rank-test-calculator.html Accessed 13 Jun 2016

Download references

Author information

Authors and Affiliations

  1. Birla Institute of Technology and Science, Department of Computer Science, BITS, Vidyavihar, Pilani, 333031, Rajasthan, India

    Avinash Gautam & Sudeept Mohan

Authors
  1. Avinash Gautam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sudeept Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Avinash Gautam.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gautam, A., Mohan, S. STATE. Intel Serv Robotics 9, 347–366 (2016). https://doi.org/10.1007/s11370-016-0205-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11370-016-0205-6

Keywords

Search

Navigation