Flocks and Formations
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The columns of J are the eigenvectors of L corresponding to eigenvalue 0; consequently, they determine the consensus trajectories of the process (1) and the flocking trajectories [10].
“The columns of J are the eigenvectors of L corresponding to the eigenvalue 0; consequently, they determine the consensus trajectories of the process (1) and the flocking trajectories [10].”
From Comments on "Consensus and cooperation in networked multi-agent systems" (2010) · cites this paper as [10]
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Cites
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339 · see citing works
Godsil, C., & Royle, G. (2001) · Graduate Texts in Mathematics · doi:10.1007/978-1-4613-0163-9 · Cited by 8,154 · see citing works
Flocks, herds and schools: A distributed behavioral model
Reynolds, C. W. (1987) · ACM SIGGRAPH Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH) · doi:10.1145/37401.37406 · Cited by 7,795 · see citing works
Novel Type of Phase Transition in a System of Self-Driven Particles
Vicsek, T., Czirók, A., Ben‐Jacob, E., Cohen, I., & Shochet, O. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.1226 · Cited by 7,395 · see citing works
Ordinary Differential Equations
Stewart, J. M. (2017) · Cambridge University Press eBooks · doi:10.1017/9781108120241.010 · Cited by 7,299 · see citing works
Flocks, herds and schools: A distributed behavioral model
Reynolds, C. W. (1987) · ACM SIGGRAPH Computer Graphics · doi:10.1145/37402.37406 · Cited by 5,148 · see citing works
Information Flow and Cooperative Control of Vehicle Formations
Fax, J. A., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834433 · Cited by 4,616 · see citing works
Differential Equations, Dynamical Systems, and Linear Algebra
Hirsch, M. W., & Smale, S. (1974) · Pure and applied mathematics · doi:10.1016/s0079-8169(08)x6044-1 · Cited by 3,119 · see citing works
A decentralized approach to formation maneuvers
Lawton, J., Beard, R. W., & Young, B. J. (2003) · IEEE Transactions on Robotics and Automation · doi:10.1109/tra.2003.819598 · Cited by 1,066 · see citing works
Brualdi, R. A., & Ryser, H. J. (1991) · Cambridge University Press eBooks · doi:10.1017/cbo9781107325708 · Cited by 1,046 · see citing works
Brualdi, R. A. (2006) · Discrete mathematics and its applications · doi:10.1201/9781420010572.pt2 · Cited by 1,019 · see citing works
Consensus protocols for networks of dynamic agents
Saber, R. O., & Murray, R. M. (2004) · Proceedings of the 2003 American Control Conference, 2003. · doi:10.1109/acc.2003.1239709 · Cited by 901 · see citing works
Dynamical aspects of animal grouping: Swarms, schools, flocks, and herds
OKUBO, A. (1986) · Advances in Biophysics · doi:10.1016/0065-227x(86)90003-1 · Cited by 880 · see citing works
Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach
Ren, W., & Beard, R. W. (2004) · Journal of Guidance Control and Dynamics · doi:10.2514/1.9287 · Cited by 737 · see citing works
Self-Organized Fish Schools: An Examination of Emergent Properties
Parrish, J. K., Viscido, S. V., & Grünbaum, D. (2002) · Biological Bulletin · doi:10.2307/1543482 · Cited by 706 · see citing works
Ordinary Differential Equations.
Brauer, F., Arnold, V. I., & Cook, R. (1993) · American Mathematical Monthly · doi:10.2307/2324802 · Cited by 647 · see citing works
Decentralized control of vehicle formations
Lafferriere, G., Williams, A., Caughman, J. S., & Veerman, J. J. P. (2005) · Systems & Control Letters · doi:10.1016/j.sysconle.2005.02.004 · Cited by 619 · see citing works
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Saber, R. O., & Murray, R. M. (2004) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2003.1271796 · Cited by 211 · see citing works
On the spectra of nonsymmetric Laplacian matrices
Agaev, R., & Chebotarev, P. (2005) · Linear Algebra and its Applications · doi:10.1016/j.laa.2004.09.003 · Cited by 177 · see citing works
Consensus of information under dynamically changing interaction topologies
Ren, W., & Beard, R. W. (2004) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2004.1384632 · Cited by 152 · see citing works
Optimal and Cooperative Control of Vehicle Formations
Fax, J. A. (2002) · doi:10.7907/m4n7-ak02 · Cited by 137 · see citing works
IEEE conference on decision and control
Grimble, M. J. (1987) · IEE Proceedings D Control Theory and Applications · doi:10.1049/ip-d.1987.0034 · Cited by 126 · see citing works
Kernels of Directed Graph Laplacians
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Moreau, L. (2004) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2003.1273094 · Cited by 79 · see citing works
Graph theoretic methods in the stability of vehicle formations
Lafferriere, G., Caughman, J. S., & Williams, A. (2004) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2004.1384492 · Cited by 71 · see citing works
Self-citationFormations of formations: hierarchy and stability
Williams, A., Glavaški, S., & Samad, T. (2004) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2004.1384367 · Cited by 54 · see citing works
Self-citationStable motions of vehicle formations
Williams, A., Lafferriere, G., & Veerman, J. J. P. (2006) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2005.1582133 · Cited by 27 · see citing works
Self-citationSparks, A. G. (2002) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.677 · Cited by 2 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- [14]14. J. Milnor, Dynamics: Introductory Lecture Notes, Stony Brook Preprint, 2001.
- [22]22. W. Ren, R. Beard, Consensus Seeking of Multi-Agent Systems under Dynamically Changing Interac- tion Topologies, IEEE TRans. Autom. Control, To Appear.
- [24]24. A.G. Sparks, Special Issue on Control of Satellite Formations, Intl J. of Robust and Nonlinear Control, 12(2-3), 2002.
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- Authors
- Veerman, J. J. P., Lafferriere, G., Caughman, J. S., & Williams, A.
- Affiliations
- Portland State University (US)
- Corresponding author
- Veerman, J. J. P.
- Venue
- Journal of Statistical Physics
- Published
- 2005-12
- Volume
- 121
- Issue
- 5-6
- Pages
- 901-936
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W2073108694
- Cited by
- 61
- References
- 28
- Citations by year
- 2021: 2 · 2020: 1 · 2019: 2 · 2017: 2 · 2016: 3 · 2015: 1 · 2014: 3 · 2013: 5 · 2012: 4
- FWCI
- 5.30
- Type
- journal article
- Language
- en
- Open access
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Journal of Statistical Physics (publishedVersion)
- PDXScholar (Portland State University) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Keywords
- flocking, formation flying, multi-agent systems, communication topology, linear feedback, graph connectivity
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