Skip to main content

On the Formation Control of Multiagent Systems Under Nearly Cyclic Pursuit

  • Conference paper
  • First Online:
Intelligent Autonomous Systems 13

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 302))

Abstract

We consider the problem of formation control of multiple agents under the nearly cyclic pursuit strategy. A control law is designed under this strategy for n agents to rendezvous at a point and also form a specific formation, dictated by an extra agent, called beacon. We derive constraint on the gain in k–circulant matrix to make the system stable. Formation tracking for n agents is achieved by applying an exogenous input to the beacon. We prove that the agents in nearly cyclic interaction are controllable under the beacon. Simulations and analytical results demonstrate the effectiveness of the proposed method.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 349.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 449.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Oggier. F, Bruckstein. A. : On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane. Operator Theory: Advances and Applications. 218, 513–539, (2011)

    Google Scholar 

  2. Eduardo. G, Martinez. H, et all. : Convergence and collision avoidance in formation control. A survey of the artificial potential functions approach. InTech, (Chapter in Multi-Agent Systems-Modeling, Control, Programming, Simulations and Applications), (2011)

    Google Scholar 

  3. Leonard. N, Fiorelli. E. : Virtual leaders, artificial potentials and coordinated control of groups. In Proceedings of the IEEE International Conference on Decision and Control, pp. 2968–2973, (2001)

    Google Scholar 

  4. Dimarogonas. D, Kyriakopoulos. K. : Distributed cooperative control and collision avoidance for multiple kinematic agents. In Proceedings of the IEEE International Conference on Decision and Control, IEEE, San Diego, USA, pp. 721–726, (2006)

    Google Scholar 

  5. Tanner. H. G, Kumar. A. : Towards Decentralization of Multi-robot Navigation Functions. In Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp. 4132–4137, (2005)

    Google Scholar 

  6. Ogren. P, Egerstedt. M, and X. Hu. : A control Lyapunov function approach to multi-agent coordination. IEEE Transactions on Robotics and Automation, vol. 18, pp, 847–851, October (2002)

    Google Scholar 

  7. Blach. T, Arkin. R. : Behavior-based formation control for multi-robots Systems. IEEE Transactions on Robotics and Automation, vol. 14, no. 12, (1998)

    Google Scholar 

  8. Egerstedt. M, Johansson K.H., Lygeros. J, and Sastry. S. : Behavior Based Robotics Using Regularized Hybrid Automata. In Proceedings of the IEEE International Conference on Decision and Control, Phoenix, AZ, Dec, (1999)

    Google Scholar 

  9. Lin, Z, Broucke. M, and Francis, B. : Local control strategies for groups of mobile autonomous agents. IEEE Transactions on Automatic Control, 49(4), 622–629, (2004)

    Google Scholar 

  10. Marshall. J. A, Broucke. M, and Francis B. A. : Formations of vehicles in cyclic pursuit. IEEE Transactions on Automatic Control, vol. 49, pp. 1963–1974, (2004)

    Google Scholar 

  11. Marshall. J. A, Tsai. D. : Periodic formations of multivehicle systems. In IET Control Theory and Applications, vol. 5, no. 2, pp. 389–396, March (2011)

    Google Scholar 

  12. Smith. S, Broucke M, and Francis. B. : A Hierarchical Cyclic Pursuit Scheme for Vehicle Networks. Automatica, 41(6):1045–1053, (2005)

    Google Scholar 

  13. Pavone. M, Frazzoli. E, : Decentralized Policies for Geometric Pattern Formation and Path Coverage. Journal of Dynamic Systems, Measurement, and Control, vol. 129, pp. 633–643, September (2007)

    Google Scholar 

  14. Boman. E. : The Moore Penrose pseudoinverse of an arbitrary, square, k-circulant matrix. Linear and Multilinear Algebra, 50:175–179, (2002)

    Google Scholar 

  15. Lafferriere. G, Williams A, Caughman. J, Veerman. P. : Decentralized control of vehicle formations. Systems Control Lett. 54 (9) 899–910, (2005)

    Google Scholar 

  16. Desai. J, Ostrowski. J, and Kumar. V. : Modeling and Control of Formations of Nonholonomic Mobile Robots. IEEE Transactions on Robotics and Automation, Vol. 17(6), pp. 905–908, (2001)

    Google Scholar 

  17. Moore. K, Lucarelli. D. : Forced and constrained consensus among cooperating agents. IEEE International Conference on Networking, Sensing and Control, Tucson, AZ, (2005)

    Google Scholar 

  18. Ren. W. : Multi-vehicle consensus with a time-varying reference state. Systems and Control Letters 56. pp. 474–483, (2007)

    Google Scholar 

  19. Mesbahi. M, Egerstedt. M. : Graph Theoretic Methods in Multiagent Networks. Princeton University Press, (2010)

    Google Scholar 

  20. Casti. J. : Linear Dynamical Systems. Academic Press, INC, (1987)

    Google Scholar 

  21. Kailath. T. : Linear Systems. Prentice-Hall, New Jersey, (1980)

    Google Scholar 

  22. Ren. W, Beard. R. : Information consensus in multivehicle cooperative control. IEEE Control Systems Magazine, (2007)

    Google Scholar 

Download references

Acknowledgments

This research was supported in part by the University Research Grant, UBD/PNC2/2/RG/1(259).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Trung Dung Ngo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Iqbal, M., Ngo, T.D. (2016). On the Formation Control of Multiagent Systems Under Nearly Cyclic Pursuit. In: Menegatti, E., Michael, N., Berns, K., Yamaguchi, H. (eds) Intelligent Autonomous Systems 13. Advances in Intelligent Systems and Computing, vol 302. Springer, Cham. https://doi.org/10.1007/978-3-319-08338-4_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08338-4_41

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08337-7

  • Online ISBN: 978-3-319-08338-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics