Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Automatic Generation of Persistent Formations for Multi-agent Networks Under Range Constraints

  • Published:
Mobile Networks and Applications Aims and scope Submit manuscript

Abstract

In this paper we present a collection of graph-based methods for determining if a team of mobile robots, subjected to sensor and communication range constraints, can persistently achieve a specified formation. What we mean by this is that the formation, once achieved, will be preserved by the direct maintenance of the smallest subset of all possible pairwise inter-agent distances. In this context, formations are defined by sets of points separated by distances corresponding to desired inter-agent distances. Further, we provide graph operations to describe agent interactions that implement a given formation, as well as an algorithm that, given a persistent formation, automatically generates a sequence of such operations. Experimental results are presented that illustrate the operation of the proposed methods on real robot platforms.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Balch T, Arkin RC (1998) Behavior-based formation control for multirobot teams. IEEE Trans Robot Automat 14(6):926–939, Dec

    Article  Google Scholar 

  2. Cortés J, Martínez S, Bullo F (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans Robot Automat 51(8):1289–1298, Aug

    Google Scholar 

  3. Desai J, Ostrowski J, Kumar V (2001) Modeling and control of formations of nonholonomic mobile robots. IEEE Trans Robot Automat 17(6):905–908, Dec

    Article  Google Scholar 

  4. Do KD, Pan J (2007) Nonlinear formation control of unicycle-type mobile robots. Robot Auton Syst 55(3):191–204, March

    Article  Google Scholar 

  5. Egerstedt M, Hu X (2001) Formation constrained multi-agent control. IEEE Trans Robot Automat 17(6):947–951, Dec

    Article  Google Scholar 

  6. Kalantar S, Zimmer UR (2007) Distributed shape control of homogeneous swarms of autonomous underwater vehicles. Auton Robots 22(1):37–53, January

    Article  Google Scholar 

  7. Kaminka GA, Glick R (2006) Towards robust multi-robot formations. In: Conference on international robotics and automation, Orlando, 15–19 May 2006, pp 582–588

  8. Lawton J, Beard R, Young B (2003) A decentralized approach to formation maneuvers. IEEE Trans Robot Automat 19(6):933–941, Dec

    Article  Google Scholar 

  9. Leonard NE, Fiorelli E (2001) Virtual leaders, artificial potentials and coordinated control of groups. In: Proceedings of the IEEE conference on decision and control 2001, Orlando, December 2001, pp 2968–2973

  10. Lin J, Morse A, Anderson B (2003) The multi-agent rendezvous problem. In: Proceedings of the 42nd IEEE conference on decision and control, Maui, December 2003, pp 1508–1513

  11. Sugihara K, Suzuki I (1990) Distributed motion coordination of multiple robots. In: Proceedings of IEEE int. symp. on intelligent control, Philadelphia, 5–7 September 1990, pp 138–143

  12. Vig L, Adams JA (2006) Multi-robot coalition formation. IEEE Trans Robot 22(4):637–649, August

    Article  Google Scholar 

  13. Yuan L, Weidong C, Yugeng X (2006) Energy-efficient aggregation control for mobile sensor networks. In: International conference on intelligent computing, vol 344. Intelligent control and automation, Kunming, August 2006, pp 188–193

  14. Zhijun T, Ozguner U (2006) On non-escape search for a moving target by multiple mobile sensor agents. In: American control conference, American automatic control council, IEEE, Minneapolis, June 2006, p 6

    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 Automat 15:818–828, Oct

    Article  Google Scholar 

  16. Eren T, Whiteley W, Anderson BDO, Morse AS, Belhumeur PN (2005) Information structures to secure control of rigid formations with leader–follower architecture. In: Proceedings of the American control conference, Portland, June 2005, pp 2966–2971

  17. Fax JA, Murray RM (2002) Graph laplacian and stabilization of vehicle formations. In: Proceedings of the 15th IFAC conf, Barcelona, 21–26 July 2002, pp 283–288

  18. Fax J, Murray R (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Automat Contr 49:1465–1476, Sept

    Article  MathSciNet  Google Scholar 

  19. Jadbabaie JLA, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Automat Contr 48(6):988–1001, June

    Article  MathSciNet  Google Scholar 

  20. Ji M, Egerstedt M (2007) Distributed coordination control of multi-agent systems while preserving connectedness. IEEE Trans Robot 23:693–703

    Article  Google Scholar 

  21. Lin Z, Broucke M, Francis B (2004) Local control strategies for groups of mobile autonomous agents. IEEE Trans Automat Contr 49(4):622–629

    Article  MathSciNet  Google Scholar 

  22. Kim Y, Mesbahi M (2006) On maximizing the second smallest eigenvalue of a state-dependent graph laplacian. IEEE Trans Automat Contr 51:116–120, Jan

    Article  MathSciNet  Google Scholar 

  23. Ren W, Beard R (2004) Consensus of information under dynamically changing interaction topologies. In: Proceedings of the American control conference 2004, vol 6, Boston, 30 June–2 July 2004, pp 4939–4944

  24. Saber RO, Murray RM (2002) Distributed structural stabilization and tracking for formations of dynamic multi-agents. In: Proceedings of the 41st IEEE conference on decision and control 2002, vol 1, Las Vegas, December 2002, pp 209–215

  25. Saber RO, Murray RM (2003) Flocking with obstacl avoidance: cooperation with limited communication in mobile networks. In: Proceedings of the 42nd IEEE conference on decision and control 2003, vol 2, Maui, December 2003, pp 2022–2028

  26. Saber RO, Murray RM (2003) Agreement problems in networks with directed graphs and switching toplogy. In: Proceedings of the 42nd IEEE conference on decision and control 2003, vol 4, Maui, December 2003, pp 4126–4132

  27. Hendrickx JM, Anderson BDO, Delvenne J-C, Blondel VD (2000) Directed graphs for the analysis of rigidity and persistence in autonomous agent systems. Int J Robust Nonlinear Control 17:960–981

    Article  MathSciNet  Google Scholar 

  28. Hendrickx JM, Fidan B, Yu C, Anderson BDO, Blondel VD (2006) Elementary operations for the reorganization of minimally persistent formations. In: Proceedings of the mathematical theory of networks and systems (MTNS) conference, no. 17, Kyoto, July 2006, pp 859–873

  29. Gluck H (1975) Almost all simply connected closed surfaces are rigid. In: Geometric topology. Lecture notes in Math, vol 438. Springer, Berlin, pp 225–239

    Google Scholar 

  30. Roth B (1981) Rigid and flexible frameworks. Am Math Mon 88(1):6–21

    Article  MATH  Google Scholar 

  31. Tay T, Whiteley W (1985) Generating isostatic frameworks. Topol Struct 11:21–69

    MATH  MathSciNet  Google Scholar 

  32. Laman G (1970) On graphs and rigidity of plane skeletal structures. J Eng Math 4(4):331–340, October

    Article  MATH  MathSciNet  Google Scholar 

  33. Jacobs DJ, Hendrickson B (1997) An algorithm for two-dimensional rigidity percolation: the pebble game. J Comput Phys 137(2):346–365, June

    Article  MATH  MathSciNet  Google Scholar 

  34. Smith BS, Egerstedt M, Howard A (2008) Automatic deployment and formation control of decentralized multi-agent networks. In: Proceedings of the IEEE international conference on robotics and automation, Pasadena, 19–23 May 2008

  35. Baillieul J, Suri A (2003) Information patterns and hedging brockett’s theorem in controlling vehicle formations. In: Proceedings of the 42nd IEEE international conference on decision and control, Maui, December 2003, pp 556–563

  36. Eren T, Whiteley W, Anderson BD, Morse AS, Belhumeur PN (2005) Information structures to secure control of rigid formations with leader–follower architecture. In: Proceedings of the 2005 American control conference, vol 4, Portland, June 2005, pp 2966–2971

Download references

Acknowledgements

This work was partially supported under a contract with the National Aeronautics and Space Administration. We also thank Julien Hendrickx for helpful discussions about graph rigidity and persistence.

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Brian S. Smith, Magnus Egerstedt & Ayanna Howard

Authors
  1. Brian S. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Magnus Egerstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ayanna Howard
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brian S. Smith.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, B.S., Egerstedt, M. & Howard, A. Automatic Generation of Persistent Formations for Multi-agent Networks Under Range Constraints. Mobile Netw Appl 14, 322–335 (2009). https://doi.org/10.1007/s11036-009-0153-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11036-009-0153-x

Keywords

Search

Navigation