research-article

The geometry of flocking

Author:

Bernard ChazelleAuthors Info & Claims

SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometry

Pages 19 - 28

https://doi.org/10.1145/1810959.1810963

Published: 13 June 2010 Publication History

Abstract

The convergence time for flocking in the Vicsek-Cucker-Smale model is known to be bounded by a tower-of-twos of height linear in the number of birds. We improve the height to logarithmic, which matches the known lower bound. In the process, we introduce an intriguing geometric object, the "flight net", and develop the idea of a "virtual agent." These two concepts give us insight into early flocking behavior, which is still the most mysterious aspect of these dynamical systems.

References

[1]

Chazelle, B. Natural algorithms, Proc. 20th ACM-SIAM SODA 2009, 422--431.

Digital Library

[2]

Chazelle, B. The convergence of bird flocking, arXiv:0905.4241v1, 2009.

[3]

Chazelle, B. Analytical tools for natural algorithms, Proc. 1st Symposium on Innovations in Computer Science (2010), Beijing, 32--41.

[4]

Chazelle, B. A geometric approach to collective motion, SoCG 2010.

Digital Library

[5]

Cucker, F., Smale, S. Emergent behavior in flocks, IEEE Trans. Automatic Control 52 (2007), 852--862.

[6]

Hendrickx, J.M., Blondel, V.D. Convergence of different linear and non-linear Vicsek models, Proc. 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto (Japan), July 2006, 1229--1240.

[7]

Ji, M., Egerstedt, M. Distributed coordination control of multi-agent systems while preserving connectedness, IEEE Transactions on Robotics 23 (2007), 693--703.

Digital Library

[8]

Landau, H.J., Odlyzko, A.M. Bounds for eigenvalues of certain stochastic matrices, Linear algebra and Its Applications 38 (1981), 5--15.

[9]

Li, S., Wang, H. Multi-agent coordination using nearest neighbor rules: revisiting the Vicsek model, 2004, arXiv:cs/0407021v2

[10]

Lorenz, J. A stabilization theorem for dynamics of continuous opinions, Physica A: Statistical Mechanics and its Applications 355 (2005), 217--223.

[11]

Moreau, L. Stability of multiagent systems with time-dependent communication links, IEEE Transactions on Automatic Control 50 (2005), 169--182.

[12]

Moshtagh, N., Jadbabaie, A., Daniilidis, K. Distributed geodesic control laws for flocking of nonholonomic agents, Proc. 44th IEEE Conference on Decision and Control and European Control Conference 2005 (ECC-CDC'05), Seville, Spain.

[13]

Olfati-Saber, R. Flocking for multi-agent dynamic systems: algorithms and theory, IEEE Transactions on Automatic Control 51 (2006), 401--420.

[14]

Reynolds, C.W. Flocks, herds, and schools: A distributed behavioral model, Computer Graphics 21 (1987), 25--34.

Digital Library

[15]

Shi, H., Wang, L., Chu, T. Coordination of multiple dynamic agents with asymmetric interactions, Proc. 2005 IEEE International Symposium on Intelligent Control, Cyprus (2005), 1423--1428.

[16]

Tahbaz-Salehi, A., Jadbabaie, A. On recurrence of graph connectivity in Vicsek's model of motion coordination for mobile autonomous agents, Proc. 2007 American Control Conference, New York, NY (2007), 699--704.

[17]

Tanner, H.G., Jadbabaie, A., Pappas, G.J. Stable flocking of mobile agents, Part I: fixed topology, Proc. IEEE Conference on Decision and Control, Maui, Hawaii (2003), 2010--2015.

[18]

Tanner, H.G., Jadbabaie, A., Pappas, G.J. Stable flocking of mobile agents, Part II: dynamic topology, Proc. IEEE Conference on Decision and Control, Maui, Hawaii (2003), 2016--2021.

[19]

Tanner, H.G., Jadbabaie, A., Pappas, G.J. Flocking in fixed and switching networks, IEEE Trans. Automatic Control 52 (2007), 863--868.

[20]

Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I., Shochet, O. Novel type of phase transition in a system of self-driven particles, Physical Review Letters 75 (1995), 1226--1229.

Cited By

Ben-Shahar ODolev SDolgin ASegal M(2018)Direction election in flocking swarmsAd Hoc Networks10.1016/j.adhoc.2012.05.00112(250-258)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1016/j.adhoc.2012.05.001
Chazelle BKirkpatrick DMitchell J(2010)A geometric approach to collective motionProceedings of the twenty-sixth annual symposium on Computational geometry10.1145/1810959.1810983(117-126)Online publication date: 13-Jun-2010
https://dl.acm.org/doi/10.1145/1810959.1810983

Index Terms

The geometry of flocking
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometry

June 2010

452 pages

ISBN:9781450300162

DOI:10.1145/1810959

Program Chairs:
David Kirkpatrick
University of British Columbia, Canada
,
Joseph Mitchell
SUNY Stony Brook, USA

Copyright © 2010 ACM.

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Published: 13 June 2010

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SoCG '10

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SoCG '10: Symposium on Computational Geometry

June 13 - 16, 2010

Utah, Snowbird, USA

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Cited By

Ben-Shahar ODolev SDolgin ASegal M(2018)Direction election in flocking swarmsAd Hoc Networks10.1016/j.adhoc.2012.05.00112(250-258)Online publication date: 27-Dec-2018
https://dl.acm.org/doi/10.1016/j.adhoc.2012.05.001
Chazelle BKirkpatrick DMitchell J(2010)A geometric approach to collective motionProceedings of the twenty-sixth annual symposium on Computational geometry10.1145/1810959.1810983(117-126)Online publication date: 13-Jun-2010
https://dl.acm.org/doi/10.1145/1810959.1810983

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