Advertisement

UAV Formation Control: Theory and Application

  • Brian D. O. Anderson
  • Bariş Fidan
  • Changbin Yu
  • Dirk Walle
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 371)

Abstract

Unmanned airborne vehicles (UAVs) are finding use in military operations and starting to find use in civilian operations. UAVs often fly in formation, meaning that the distances between individual pairs of UAVs stay fixed, and the formation of UAVs in a sense moves as a rigid entity. In order to maintain the shape of a formation, it is enough to maintain the distance between a certain number of the agent pairs; this will result in the distance between all pairs being constant. We describe how to characterize the choice of agent pairs to secure this shape-preserving property for a planar formation, and we describe decentralized control laws which will stably restore the shape of a formation when the distances between nominated agent pairs become unequal to their prescribed values. A mixture of graph theory, nonlinear systems theory and linear algebra is relevant. We also consider a particular practical problem of flying a group of three UAVs in an equilateral triangle, with the centre of mass following a nominated trajectory reflecting constraints on turning radius, and with a requirement that the speeds of the UAVs are constant, and nearly (but not necessarily exactly) equal.

Keywords

Formation control surveillance UAV rigid formation persistent formation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hubbard, S., Babak, B., Sigurdsson, S., Magnusson, K.: A model of the formation of fish schools and migrations of fish. Ecological Modelling 174, 359–374 (2004)CrossRefGoogle Scholar
  2. 2.
    Janson, S., Middendorf, M., Beekman, M.: Honey bee swarms: How do scouts guide a swarm of uninformed bees? Animal Behaviour 70(1), 349–358 (2005)CrossRefGoogle Scholar
  3. 3.
    Shao, J., Xie, G., Wang, L.: Leader-following formation control of multiple mobile vehicles. IET Control Theory and Applications 1, 545–552 (2007)CrossRefGoogle Scholar
  4. 4.
    Tay, T., Whiteley, W.: Generating isostatic frameworks. Structural Topology 11, 21–69 (1985)MATHMathSciNetGoogle Scholar
  5. 5.
    Jackson, B., Jordan, T.: Connected rigidity matroids and unique realizations of graphs. Journal of Combinatorial Theory B(94), 1–29 (2004)Google Scholar
  6. 6.
    Olfati-Saber, R., Murray, R.M.: Distributed cooperative control of multiple vehicle formations using structural potential functions. In: Proc. of the 15th IFAC World Congress, Barcelona, Spain, pp. 1–7 (2002)Google Scholar
  7. 7.
    Eren, T., Whiteley, W., Morse, A.S., Belhumeur, P.N., Anderson, B.D.: Sensor and network topologies of formations with direction, bearing and angle information between agents. In: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, pp. 3064–3069 (December 2003)Google Scholar
  8. 8.
    Lin, Z., Francis, B., Maggiore, M.: Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans, on Automatic Control 50, 121–127 (2005)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Yu, C., Hendrickx, J., Fidan, B., Anderson, B., Blondel, V.: Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence. Automatica, 387–402 (March 2007)Google Scholar
  10. 10.
    Laman, G.: On graphs and rigidity of plane skeletal structures. J. Engrg. Math. 4, 331–340 (1970)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Anderson, B., Yu, C., Fidan, B., Hendrickx, J.: Control and information architectures for formations. In: Proc. IEEE International Conference on Control Applications, Munich, Dermany, vol. 56, pp. 1127–1138 (October 2006)CrossRefGoogle Scholar
  12. 12.
    Hendrickx, J., Anderson, B., Delvenne, J.-C, Blondel, V.: Directed graphs for the analysis of rigidity and persistence in autonomous agent systems. International Journal of Robust Nonlinear Control 17, 960–981 (2007)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Yu, C., Anderson, B., Dasgupta, S., Fidan, B.: Control of minimally persistent formations in the plane (submitted for publication, December 2006)Google Scholar
  14. 14.
    Anderson, B., Yu, C., Dasgupta, S., Morse, A.: Control of a three coleaders formation in the plane. Systems & Control Letters 56, 573–578 (2007)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Cao, M., Morse, A., Yu, C., Anderson, B., Dasgupta, S.: Controlling a triangular formation of mobile autonomous agents. In: IEEE Conference on Decision and Contol (to appear 2007)Google Scholar
  16. 16.
    Olfati-Saber, R., Murray, R.M.: Distributed cooperative control of multiple vehicle formations using structural potential functions. In: Proc. of the 15th IFAC World Congress, Barcelona, Spain, pp. 1–7 (2002)Google Scholar
  17. 17.
    Olfati-Saber, R., Murray, R.M.: Graph rigidity and distributed formation stabilization of multivehicle systems. In: Proc of the 41st IEEE Conf. on Decision and Control, Las Vegas, NV, pp. 2965–2971 (2002)Google Scholar
  18. 18.
    Krick, L.: Application of graph rigidity information control of multi-robot networks. Master’s thesis, Department of Electrical and Computer Engineering, University of Toronto (2007)Google Scholar
  19. 19.
    Paley, D., Leonard, N.E., Sepulchre, R.: Collective motion: bistability and trajectory tracking. In: Proc. of the 43rd IEEE Conference on Decision and Control, vol. 2, pp. 1932–1937 (2004)Google Scholar
  20. 20.
    Justh, E.W., Krishnaprasad, P.S.: Equilibria and steering laws for planar formations. Systems and Control Letters 52(1), 25–38 (2004)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Smith, S.L., Broucke, M.E., Francis, B.A.: Stabilizing a multi-agent system to an equilibrium polygon formation. In: Proc. 17th International Symposium on Mathematical Theory of Networks and Systems, pp. 2415–2424 (2006)Google Scholar
  22. 22.
    Anderson, B., Dasgupta, S., Yu, C.: Control of directed formations with leader-first follower structure. In: IEEE Conference on Decision and Contol (to appear, 2007)Google Scholar
  23. 23.
    Drake, S., Brown, K., Fazackerley, J., Finn, A.: Autonomous control of multiple uavs for the passive location of radars. Tech. report, Defence Science and Technology Organisation, pp. 403–409 (2005)Google Scholar
  24. 24.
    Ledger, D.: Electronic warfare capabilities of mini UAVs. In: Proc. the Electronic Warfare Conference, Kuala Lumpur (2002)Google Scholar
  25. 25.
    Sandeep, S., Fidan, B., Yu, C.: Decentralized cohesive motion control of multi-agent formations. In: Proc. 14th Mediterranean Conference on Control and Automation (June 2006)Google Scholar
  26. 26.
    Fidan, B., Anderson, B., Yu, C., Hendrickx, J.: Modeling and Control of Complex Systems, ch. Persistent Autonomous Formations and Cohesive Motion Control, pp. 247–275. Taylor & Francis, London (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Brian D. O. Anderson
    • 1
  • Bariş Fidan
    • 1
  • Changbin Yu
    • 1
  • Dirk Walle
    • 2
  1. 1.Rsearch School of Information Sciences and EngineeringThe Australian National University and National ICT AustraliaCanberraAustralia
  2. 2.Delft Center for Systems and ControlDelft University of TechnologyDelftThe Netherlands

Personalised recommendations