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.
This work is supported by National ICT Australia, which is funded by the Australian Government’s Department of Communications, Information Technology and the Arts and the Australian Research Council through the Backing Australia’s Ability Initiative.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
Shao, J., Xie, G., Wang, L.: Leader-following formation control of multiple mobile vehicles. IET Control Theory and Applications 1, 545–552 (2007)
Tay, T., Whiteley, W.: Generating isostatic frameworks. Structural Topology 11, 21–69 (1985)
Jackson, B., Jordan, T.: Connected rigidity matroids and unique realizations of graphs. Journal of Combinatorial Theory B(94), 1–29 (2004)
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)
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)
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)
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)
Laman, G.: On graphs and rigidity of plane skeletal structures. J. Engrg. Math. 4, 331–340 (1970)
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)
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)
Yu, C., Anderson, B., Dasgupta, S., Fidan, B.: Control of minimally persistent formations in the plane (submitted for publication, December 2006)
Anderson, B., Yu, C., Dasgupta, S., Morse, A.: Control of a three coleaders formation in the plane. Systems & Control Letters 56, 573–578 (2007)
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)
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)
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)
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)
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)
Justh, E.W., Krishnaprasad, P.S.: Equilibria and steering laws for planar formations. Systems and Control Letters 52(1), 25–38 (2004)
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)
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)
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)
Ledger, D.: Electronic warfare capabilities of mini UAVs. In: Proc. the Electronic Warfare Conference, Kuala Lumpur (2002)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anderson, B.D.O., Fidan, B., Yu, C., Walle, D. (2008). UAV Formation Control: Theory and Application. In: Blondel, V.D., Boyd, S.P., Kimura, H. (eds) Recent Advances in Learning and Control. Lecture Notes in Control and Information Sciences, vol 371. Springer, London. https://doi.org/10.1007/978-1-84800-155-8_2
Download citation
DOI: https://doi.org/10.1007/978-1-84800-155-8_2
Publisher Name: Springer, London
Print ISBN: 978-1-84800-154-1
Online ISBN: 978-1-84800-155-8
eBook Packages: EngineeringEngineering (R0)