Flocks and formations

Journal of Statistical Physics

Volumn 121, Issue 5-6, 2005, Pages 901-936

  Veerman, J J P ^a   Lafferriere, G ^a   Caughman, J S ^a   Williams, A ^a  

^a PORTLAND STATE UNIVERSITY   (United States)

Author keywords

Communication graphs; Directed graph laplacians; Linear feedback and control; Stability of formations; Systems of ordinary differential equations

Indexed keywords

EID: 29044444581     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-6999-9     Document Type: Article

References (29)

1. V. I. Arnold, Ordinary Differential Equations, (MIT Press, 1973).
2. R. Brualdi and H. Ryser, Combinatorial Matrix Theory, Encyclopedia of Mathematics and Its Applications (Cambridge University Press, 1991).
3. J. Caughman and J. J. P. Veerman, Kernels of Directed Graph Laplacians (Portland State University, 2005, submitted for Publication).
4. Note added in Proof: A different formulation of these results has very recently appeared in: R. Agaev, P. Cheobotarev, On the spectrum of NonSymmetric Laplacian Matrices, Lin. Alg. & Appl. 399: 157-168 (2005).
5. J. A. Fax, Optimal and Cooperative Control of Vehicle Formations, Ph. D. Thesis, (California Institute of Technology, 2001).
6. J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Automatic Control 49(9): 1465-1476 (2003).
7. B. Francis, personal communication.
8. C. Godsil and G. Royle, Algebraic Graph Theory (Springer, 2001).
9. D. Gliedes de Figueiredo, Análise de Fourier e Equações Diferenciais Pardais, IMPA-CNPQ (Rio de Janeiro, 1977).
10. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, Linear Algebra (Academic Press, 1974).
11. A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automatic Control 48(6):998-1001 (2003).
12. G. Lafferriere, J. Caughman and A. Williams, Graph theoretic methods in the stability of vehicle formations, Proc. 2004 Am. Control Conf. 3724-3729 (2004).
13. G. Lafferriere, A. Williams, J. Caughman and J. J. P. Veerman, Decentralized control of vehicle formations, System & Control Lett. 54: 899-910 (2005).
14. J. Lawton, R. Beard and B. Young, A decentralized approach to formation maneuvers, IEEE Trans. Robotics and Automation 19(6):933-941 (2003).
15. J. Milnor, Dynamics: Introductory Lecture Notes (Stony Brook Preprint, 2001).
16. L. Moreau, Leaderless coordination via bidirectional and unidirectional time- dependent communication, Proc. IEEE Conf. Decision and Control 3070-3075 (2003).
17. A. Okubo, Dynamical aspects of animal grouping: swarms, schools, flocks, and herds, Adv. Biophys. 22:1-94 (1986).
18. R. Olfati-Saber and R. Murray, Agreement problems in networks with directed graphs and switching topology Proc IEEE Conference on Decision and Control 4126-4132 (2003).
19. R. Olfati-Saber and R. Murray, Consensus protocols for networks of dynamic agents in Proc. IEEE Conference on Decision and Control 4126-4132 (2003).
20. J. K. Parrish, personal communication.
21. J. K. Parrish, S. V. Viscido and D. Grünbaum, Self-organized fish schools: an examination of emergent properties, Biol. Bull. 202:296-305 (2002).
22. W. Ren and R. Beard, Consensus of information under dynamically changing interaction topologies, Proc. Am. Control Conf. 4939-4944 (2004).
23. W. Ren and R. Beard, A decentralized scheme for spacecraft formation flying via the virtual structure approach, AIAA J. of Guidance, Control and Dynamics 27(1):73-82 (2004).
24. W. Ren and R. Beard, Consensus seeking of multi-agent systems under dynamically changing interaction topologies, IEEE Trans. Autom. Control, To Appear.
25. C. Reynolds, Flocks, herds, and schools: distributed behavioral model in computer graphics, SIGGRAPH Conf. Proc. 21(4):25-34 (1987). In addition his website http://www.red3d.com/cwr/boids contains a lot of information and links.
26. A.G Sparks, Special issue on control of satellite formations, Intl J. of Robust and Nonlinear Control 12(2-3) (2002).
27. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel Type of Phase transition in a System of Self-Driven Particles, Phys. Rev. Lett. 75(6): 1226-1229 (1995).
28. A. Williams, S. Glavǎski and T. Samad, Formations of formations: hierarchy and stability, Proc. Am. Control Conf. 2992-2997 (2004).
29. A. Williams, G. Lafferriere and J. J. P. Veerman, Stable Motions of Vehicle Formations, (Portland State University, 2005).