The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
Coordination of groups of mobile autonomous agents using nearest neighbor rules
Open accessAbstract
In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
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Cites
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 25,904
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Godsil, C., & Royle, G. (2001) · Graduate Texts in Mathematics · doi:10.1007/978-1-4613-0163-9 · Cited by 8,154
Flocks, herds and schools: A distributed behavioral model
Reynolds, C. W. (1987) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/37401.37406 · Cited by 7,954
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
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
Non-negative Matrices and Markov Chains
Seneta, E. B. (1981) · Springer series in statistics · doi:10.1007/0-387-32792-4 · Cited by 2,858
Bollobás, B. (2001) · doi:10.1017/cbo9780511814068 · Cited by 2,639
Flocks, herds, and schools: A quantitative theory of flocking
Toner, J., & Tu, Y. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.58.4828 · Cited by 1,654
Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together
Toner, J., & Tu, Y. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4326 · Cited by 1,277
Virtual leaders, artificial potentials and coordinated control of groups
Leonard, N. E., & Fiorelli, E. (2003) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2001.980728 · Cited by 1,270
Modeling and control of formations of nonholonomic mobile robots
Desai, J. P., Ostrowski, J. P., & Kumar, V. (2001) · IEEE Transactions on Robotics and Automation · doi:10.1109/70.976023 · Cited by 1,172
THE LAPLACIAN SPECTRUM OF GRAPHS y
Mohar, B. (1991) · Cited by 1,099
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
The Laplacian spectrum of graphs
Newman, M. (2001) · Library and Archives Canada (Government of Canada) · Cited by 674
Products of indecomposable, aperiodic, stochastic matrices
Wolfowitz, J. (1963) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1963-0154756-3 · Cited by 490
Bounded semigroups of matrices
Berger, M. A., & Wang, Y. (1992) · Linear Algebra and its Applications · doi:10.1016/0024-3795(92)90267-e · Cited by 389
A control Lyapunov function approach to multiagent coordination
Ögren, P., Egerstedt, M., & Hu, X. (2002) · IEEE Transactions on Robotics and Automation · doi:10.1109/tra.2002.804500 · Cited by 387
From Individuals to Aggregations: the Interplay between Behavior and Physics
Flierl, G. R., Grünbaum, D., Levin, S. A., & Olson, D. B. (1999) · Journal of Theoretical Biology · doi:10.1006/jtbi.1998.0842 · Cited by 378
Equations Descriptive of Fish Schools and Other Animal Aggregations
Breder, C. M. (1954) · Ecology · doi:10.2307/1930099 · Cited by 364
Sets of matrices all infinite products of which converge
Daubechies, I. C., & Lagarias, J. C. (1992) · Linear Algebra and its Applications · doi:10.1016/0024-3795(92)90012-y · Cited by 354
Tendency-distance models of social cohesion in animal groups
Warburton, K., & Lazarus, J. H. (1991) · Journal of Theoretical Biology · doi:10.1016/s0022-5193(05)80441-2 · Cited by 272
Collective Motion of Self-Propelled Particles: Kinetic Phase Transition in One Dimension
Czirók, A., Barabási, A.-Ĺ., & Vicsek, T. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.209 · Cited by 271
GRAPH LAPLACIANS AND STABILIZATION OF VEHICLE FORMATIONS
Fax, J. A., & Murray, R. M. (2002) · IFAC Proceedings Volumes · doi:10.3182/20020721-6-es-1901.00090 · Cited by 238
Products of Indecomposable, Aperiodic, Stochastic Matrices
Wolfowitz, J. (1963) · Proceedings of the American Mathematical Society · doi:10.2307/2034984 · Cited by 222
Modelling Social Animal Aggregations
Grünbaum, D., & Ōkubo, A. (1994) · Lecture notes in biomathematics · doi:10.1007/978-3-642-50124-1_18 · Cited by 183
Virtual leaders, artificial potentials and coordinated control of groups
Leonard, N. E., & Fiorelli, E. (2002) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/.2001.980728 · Cited by 132
Noise-induced breakdown of coherent collective motion in swarms
Mikhailov, A. S., & Zanette, D. H. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.60.4571 · Cited by 128
Distributed structural stabilization and tracking for formations of dynamic multi-agents
Olfati‐Saber, R., & Murray, R. M. (2003) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/cdc.2002.1184493 · Cited by 119
A control Lyapunov function approach to multi-agent coordination
Ögren, P., Egerstedt, M., & Hu, X. (2002) · Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes · doi:10.1109/.2001.981040 · Cited by 96
Corrigendum/addendum to: Sets of matrices all infinite products of which converge
Daubechies, I. C., & Lagarias, J. C. (2001) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00314-1 · Cited by 75
Schenk, C. P., Schütz, P., Bode, M., & Purwins, H. ‐. (1998) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.57.6480 · Cited by 69
Convergence of infinite products of matrices and inner-outer iteration schemes
Elsner, L., Bru, R., & Neumann, M. (1994) · Publikationen an der Universität Bielefeld (Universität Bielefeld) · Cited by 44
Stability analysis of one-dimensional asynchronous swarms
Liu, Y., Passino, K. M., & Polycarpou, M. M. (2001) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2001.945799 · Cited by 39
Stability and paracontractivity of discrete linear inclusions
Vladimirov, A., Elsner, L., & Beyn, W. (2000) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00094-x · Cited by 26
Infinite products and paracontracting matrices
Beyn, W., & Elsner, L. (1997) · Electronic Journal of Linear Algebra · doi:10.13001/1081-3810.1006 · Cited by 25
A Bound for the Disturbance — to — Tracking — Error Gain of a Supervised Set-Point Control System
Morse, A. S. (1998) · Springer eBooks · doi:10.1007/978-1-4471-1276-1_3 · Cited by 22
Self-citationRhodius, A. (1997) · Linear Algebra and its Applications · doi:10.1016/0024-3795(95)00706-7 · Cited by 12
Flagged first, then by citations
Research works printed but not linked: 4
- Grunbaum, 1994, Modeling social animal aggregations, 296
- Morse, Dwell-time switching, 176
- Morse, 2001, Virtual shells for avoiding collisions
- Tanner, 2002, Distributed coordination strategies for groups of mobile autonomous agents
Cited by
Sorted by citations
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Consensus and Cooperation in Networked Multi-Agent Systems
Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007) · Proceedings of the IEEE · doi:10.1109/jproc.2006.887293 · Cited by 10,522
Consensus seeking in multiagent systems under dynamically changing interaction topologies
Ren, W., & Beard, R. W. (2005) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2005.846556 · Cited by 6,563
Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory
Olfati‐Saber, R. (2006) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2005.864190 · Cited by 5,034
Distributed Subgradient Methods for Multi-Agent Optimization
Nedic, A., & Ozdaglar, A. (2009) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2008.2009515 · Cited by 3,719
Metadata
- Authors
- Jadbabaie, A., Lin, J., & Morse, A. S.
- Affiliations
- Yale University (US)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2003-06
- Volume
- 48
- Issue
- 6
- Pages
- 988-1001
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2165744313
- Cited by
- 8,339
- References
- 37
- Citations by year
- 2026: 114 · 2025: 184 · 2024: 244 · 2023: 281 · 2022: 265 · 2021: 288 · 2020: 336 · 2019: 364 · 2018: 429 · 2017: 501 · 2016: 500 · 2015: 554 · 2014: 640 · 2013: 556 · 2012: 571
- FWCI
- 209.52
- Type
- journal article
- Language
- en
- Open access
- green
- repository.upenn.edu
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- Scholarly Commons (University of Pennsylvania) (submittedVersion)
- ScholarlyCommons (University of Pennsylvania) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Distributed Control Multi-Agent Systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Opinion Dynamics and Social Influence
- Physical Sciences › Engineering › Control and Systems Engineering › Traffic control and management
- Keywords
- Vicsek model, collective coordination, nearest neighbor rule, multi-agent systems, convergence analysis, switched linear systems, common quadratic Lyapunov function, distributed coordination, flocking
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