## Stability analysis of swarms (2003)

Venue: | IEEE Transactions on Automatic Control |

Citations: | 114 - 5 self |

### BibTeX

@ARTICLE{Gazi03stabilityanalysis,

author = {Veysel Gazi and Kevin M. Passino},

title = {Stability analysis of swarms},

journal = {IEEE Transactions on Automatic Control},

year = {2003},

volume = {48},

pages = {692--697}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract — In this brief article we specify an “individual-based ” continuous time model for swarm aggregation in n-dimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model. I.

### Citations

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Citation Context ...omous air vehicles have emerged and this has increased the interest of engineers in swarms. For example, in [12] the authors describe formation control strategies for autonomous air vehicles, whereas =-=[13]-=-, [14], [15], [16], [17] describe different approaches for formation control of multi-agent (multi-robot) teams. In [13] a behavior based formation control of multiple land robots integrated with the ... |

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Citation Context ...ls and so on. See also [5] and references therein for other related work. In parallel to the mathematical biologists there are a number of physicists who have done important work on swarming behavior =-=[6]-=-, [7], [8], [9], [10], [11]. The general approach the physicists take is to model each individual as a particle and study the collective behavior due to their interaction. Many of them assume that par... |

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Citation Context ...emerged and this has increased the interest of engineers in swarms. For example, in [12] the authors describe formation control strategies for autonomous air vehicles, whereas [13], [14], [15], [16], =-=[17]-=- describe different approaches for formation control of multi-agent (multi-robot) teams. In [13] a behavior based formation control of multiple land robots integrated with the other navigational goals... |

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Citation Context ...tween individual robots and robot groups. The force laws are inverse-power or spring force laws incorporating both attraction and repulsion. Another work on distributed formation control of robots is =-=[20]-=-, where the authors consider asynchronous distributed control and geometric pattern formation of multiple anonymous (or identical) robots. Important work on swarm stability is given by Beni and cowork... |

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Citation Context ...term to achieve asymptotic stability of the formation. The article in [18] describes a systematic framework for studying feasibility of formations for both undirected and directed type formations. In =-=[19]-=- Reif and Wang consider distributed control approach of groups of robots, called social potential fields method, which is based on artificial force laws between individual robots and robot groups. The... |

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Citation Context ...air vehicles have emerged and this has increased the interest of engineers in swarms. For example, in [12] the authors describe formation control strategies for autonomous air vehicles, whereas [13], =-=[14]-=-, [15], [16], [17] describe different approaches for formation control of multi-agent (multi-robot) teams. In [13] a behavior based formation control of multiple land robots integrated with the other ... |

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Citation Context ...hicles have emerged and this has increased the interest of engineers in swarms. For example, in [12] the authors describe formation control strategies for autonomous air vehicles, whereas [13], [14], =-=[15]-=-, [16], [17] describe different approaches for formation control of multi-agent (multi-robot) teams. In [13] a behavior based formation control of multiple land robots integrated with the other naviga... |

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Citation Context ...we obtain a bound on the swarm size, which depends only on the parameters of the swarm model. Biologists have been working on understanding and modeling of swarming behavior for a long time [1], [2], =-=[3]-=-, [4]. The general understanding now is that the swarming behavior is a result of an interplay between a long range attraction and a short range repulsion between the individuals. In [1] Breder sugges... |

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Citation Context ... have emerged and this has increased the interest of engineers in swarms. For example, in [12] the authors describe formation control strategies for autonomous air vehicles, whereas [13], [14], [15], =-=[16]-=-, [17] describe different approaches for formation control of multi-agent (multi-robot) teams. In [13] a behavior based formation control of multiple land robots integrated with the other navigational... |

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Citation Context ...kinetic energy and the artificial potential energy as a Lyapunov function to prove closed loop stability and employ a dissipative term to achieve asymptotic stability of the formation. The article in =-=[18]-=- describes a systematic framework for studying feasibility of formations for both undirected and directed type formations. In [19] Reif and Wang consider distributed control approach of groups of robo... |

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Citation Context ... and references therein for other related work. In parallel to the mathematical biologists there are a number of physicists who have done important work on swarming behavior [6], [7], [8], [9], [10], =-=[11]-=-. The general approach the physicists take is to model each individual as a particle and study the collective behavior due to their interaction. Many of them assume that particles are moving with cons... |

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Citation Context ...ry similar to the problem of platooning of vehicles in automated highway systems, an area that has been studied extensively (see, for example, [27], [28], [29] and references therein). Recent work in =-=[30]-=- is focusing on extending the work in [23], [24] to the multidimensional case by imposing special constraints on the topology of the “leader” movements and using specific communication topology. The r... |

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Citation Context ...ver, we obtain a bound on the swarm size, which depends only on the parameters of the swarm model. Biologists have been working on understanding and modeling of swarming behavior for a long time [1], =-=[2]-=-, [3], [4]. The general understanding now is that the swarming behavior is a result of an interplay between a long range attraction and a short range repulsion between the individuals. In [1] Breder s... |

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Citation Context ...Moreover, we obtain a bound on the swarm size, which depends only on the parameters of the swarm model. Biologists have been working on understanding and modeling of swarming behavior for a long time =-=[1]-=-, [2], [3], [4]. The general understanding now is that the swarming behavior is a result of an interplay between a long range attraction and a short range repulsion between the individuals. In [1] Bre... |

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Citation Context ...tain a bound on the swarm size, which depends only on the parameters of the swarm model. Biologists have been working on understanding and modeling of swarming behavior for a long time [1], [2], [3], =-=[4]-=-. The general understanding now is that the swarming behavior is a result of an interplay between a long range attraction and a short range repulsion between the individuals. In [1] Breder suggested a... |

25 |
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Citation Context ...cent years, engineering applications such as formation control of multirobot teams and autonomous air vehicles have emerged and this has increased the interest of engineers in swarms. For example, in =-=[12]-=- the authors describe formation control strategies for autonomous air vehicles, whereas [13], [14], [15], [16], [17] describe different approaches for formation control of multi-agent (multi-robot) te... |

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Citation Context ... one dimension, the problem of swarming is very similar to the problem of platooning of vehicles in automated highway systems, an area that has been studied extensively (see, for example, [27], [28], =-=[29]-=- and references therein). Recent work in [30] is focusing on extending the work in [23], [24] to the multidimensional case by imposing special constraints on the topology of the “leader” movements and... |

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Citation Context ...so [5] and references therein for other related work. In parallel to the mathematical biologists there are a number of physicists who have done important work on swarming behavior [6], [7], [8], [9], =-=[10]-=-, [11]. The general approach the physicists take is to model each individual as a particle and study the collective behavior due to their interaction. Many of them assume that particles are moving wit... |

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Citation Context ...hat in one dimension, the problem of swarming is very similar to the problem of platooning of vehicles in automated highway systems, an area that has been studied extensively (see, for example, [27], =-=[28]-=-, [29] and references therein). Recent work in [30] is focusing on extending the work in [23], [24] to the multidimensional case by imposing special constraints on the topology of the “leader” movemen... |

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Citation Context ...tions for the asynchronous convergence of the swarm to a synchronously achievable configuration. Swarm stability under total asynchronism (i.e., asynchronism with time delays) was first considered in =-=[23]-=-, [24]. In [23] a one dimensional discrete time totally asynchronous swam model is proposed and stability (swarm cohesion) is proved. The authors prove asymptotic convergence under total asynchronism ... |

18 |
A class of attraction/repulsion functions for stable swarm aggregations
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Citation Context ...multidimensional case by imposing special constraints on the topology of the “leader” movements and using specific communication topology. The results in this article were first published in [31]. In =-=[32]-=- we describe a class of attraction/repulsion functions that can be used for swarm aggregations. In [33], on the other hand, we analyzed the stability of swarms moving in a profile of nutrients or toxi... |

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Citation Context ...ee also [5] and references therein for other related work. In parallel to the mathematical biologists there are a number of physicists who have done important work on swarming behavior [6], [7], [8], =-=[9]-=-, [10], [11]. The general approach the physicists take is to model each individual as a particle and study the collective behavior due to their interaction. Many of them assume that particles are movi... |

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Citation Context ...d so on. See also [5] and references therein for other related work. In parallel to the mathematical biologists there are a number of physicists who have done important work on swarming behavior [6], =-=[7]-=-, [8], [9], [10], [11]. The general approach the physicists take is to model each individual as a particle and study the collective behavior due to their interaction. Many of them assume that particle... |

13 | Stability of a one-dimensional discretetime asynchronous swarm
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Citation Context ... the other hand, the authors consider a mobile swarm model and prove that cohesion will be preserved during motion under certain conditions, expressed as bounds on the maximum possible time delay. In =-=[25]-=- we obtained similar results to those in [23] for a swarm with a different mathematical model for the intermember interactions and motions using some earlier results developed for parallel and distrib... |

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Citation Context ... the authors consider asynchronous distributed control and geometric pattern formation of multiple anonymous (or identical) robots. Important work on swarm stability is given by Beni and coworkers in =-=[21]-=- and [22]. In [21] they consider a synchronous distributed control method for discrete one and two dimensional swarm structures and prove stability in the presence of disturbances using Lyapunov metho... |

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Citation Context ...on. See also [5] and references therein for other related work. In parallel to the mathematical biologists there are a number of physicists who have done important work on swarming behavior [6], [7], =-=[8]-=-, [9], [10], [11]. The general approach the physicists take is to model each individual as a particle and study the collective behavior due to their interaction. Many of them assume that particles are... |

7 |
On the Flow Capacity of Automated Highways
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Citation Context ...Note that in one dimension, the problem of swarming is very similar to the problem of platooning of vehicles in automated highway systems, an area that has been studied extensively (see, for example, =-=[27]-=-, [28], [29] and references therein). Recent work in [30] is focusing on extending the work in [23], [24] to the multidimensional case by imposing special constraints on the topology of the “leader” m... |

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Citation Context ...ors consider asynchronous distributed control and geometric pattern formation of multiple anonymous (or identical) robots. Important work on swarm stability is given by Beni and coworkers in [21] and =-=[22]-=-. In [21] they consider a synchronous distributed control method for discrete one and two dimensional swarm structures and prove stability in the presence of disturbances using Lyapunov methods. On th... |

6 |
Stability Analysis of Social Foraging Swarms: Combined Effects of Attractant/Repellent
- Gazi, Passino
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Citation Context ...ng specific communication topology. The results in this article were first published in [31]. In [32] we describe a class of attraction/repulsion functions that can be used for swarm aggregations. In =-=[33]-=-, on the other hand, we analyzed the stability of swarms moving in a profile of nutrients or toxic substances and showed collective convergence of all the individuals to more favorable regions of the ... |

4 | Modeling social animal aggregations. Frontiers in Theoretical Biology - Grunbaum, Okubo - 2002 |

1 | Novel type of phase transition in a system of self-driven particles,” Phys. Rev - Press - 1997 |

1 | Formation of complex bacterial colonies via self-generated vortices,” Phys - no - 1995 |

1 | 2003 697 [32] , “A class of attraction/repulsion functions for stable swarm aggregations - Conf, Anchorage - 2002 |

1 | 01 D T P x + M x T P x 1 T x PDP 01 T T D P x + x P x (4) Manuscript received April 26, 2001; revised February 7, 2002. Recommended by Associate Editor R. Datko. This work was supported by NSFC Project 60074026, by Guangdong Province Natural Science Found - PDP |