## Flocking for multi-agent dynamic systems: Algorithms and theory (2006)

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Venue: | IEEE Transactions on Automatic Control |

Citations: | 150 - 1 self |

### BibTeX

@ARTICLE{Olfati-saber06flockingfor,

author = {Reza Olfati-saber},

title = {Flocking for multi-agent dynamic systems: Algorithms and theory},

journal = {IEEE Transactions on Automatic Control},

year = {2006},

volume = {51},

pages = {401--420}

}

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### Abstract

Submitted to the IEEE Transactions on Automatic Control Technical Report CIT-CDS 2004-005 In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called α-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or α-agents, and virtual agents associated with α-agents called β- and γ-agents. We show that the tracking/migration problem for flocks can be solved using an algorithm with a peer-to-peer architecture. Each node (or macro-agent) of this peer-to-peer network is the aggregation of all three species of agents. The implication of this fact is that “flocks

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Citation Context ...s are made in Section 10. 2 Preliminaries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory =-=[2, 7, 15]-=-, algebraic graph theory [12], spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set... |

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Citation Context ...le. A successful example of such an approach is the use of gyroscopic forces for obstacle avoidance in [3, 4]. For a comprehensive treatment of obstacle avoidance in robotics, please refer to Latombe =-=[20]-=-. 8 Simulation Results In this section, we present several simulation results of 2-D and 3-D flocking. For every case, a computer animation is available upon request. The following parameters remain f... |

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Citation Context ...k performed by dynamic agents over (visually invisible) self-organized networks in nature. The self-organizing feature of flocks/schools [34] can provide a deeper insight in design of sensor networks =-=[5, 28, 13, 8, 1]-=-. Particle-based flocking is also one of the elements of 3-D animation technology that has revolutionized the entertainment industry. This success is partly owe to the pioneering work of Reynolds [40]... |

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Citation Context ...networks and suggests analytical exploration of complex networks with dynamic topologies; Olfati-Saber & Murray [32] used potential functions induced by rigid graphs for formation control; and Khatib =-=[18]-=- and Rimon & Koditschek [44] used artificial potentials for obstacle avoidance. A number of recent papers on flocking/swarming, [17, 50, 11], make a set of assumptions that lead to algorithms with som... |

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Citation Context ...k performed by dynamic agents over (visually invisible) self-organized networks in nature. The self-organizing feature of flocks/schools [34] can provide a deeper insight in design of sensor networks =-=[5, 28, 13, 8, 1]-=-. Particle-based flocking is also one of the elements of 3-D animation technology that has revolutionized the entertainment industry. This success is partly owe to the pioneering work of Reynolds [40]... |

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Citation Context ... including animal behavior, physics & biophysics, social sciences, and computer science have been fascinated by the emergence of flocking/swarming/schooling in groups of agents via local interactions =-=[47, 38, 37, 36, 29, 40, 53, 51, 48, 26, 14, 52, 34]-=-. Examples of these agents include birds, fish, penguins, ants, bees, and crowds. The engineering applications of flocking include massive mobile sensing in an environment; parallel and simultaneous t... |

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Citation Context ...ical exploration of complex networks with dynamic topologies; Olfati-Saber & Murray [32] used potential functions induced by rigid graphs for formation control; and Khatib [18] and Rimon & Koditschek =-=[44]-=- used artificial potentials for obstacle avoidance. A number of recent papers on flocking/swarming, [17, 50, 11], make a set of assumptions that lead to algorithms with some (or all) of the following ... |

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Citation Context ... including animal behavior, physics & biophysics, social sciences, and computer science have been fascinated by the emergence of flocking/swarming/schooling in groups of agents via local interactions =-=[47, 38, 37, 36, 29, 40, 53, 51, 48, 26, 14, 52, 34]-=-. Examples of these agents include birds, fish, penguins, ants, bees, and crowds. The engineering applications of flocking include massive mobile sensing in an environment; parallel and simultaneous t... |

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Citation Context ...g. These phenomena do not constitute flocking in the sense described in Section 9. Some past research with strong connections to this paper include the work by the following researchers: Fax & Murray =-=[9]-=- used graph Laplacians for multi-vehicle formation stabilization; Mesbahi [23, 24] emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be... |

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Citation Context ... fixed topology is studied. In [17], Justh & Krishnaprasad proposed an algorithm for swarming that requires all-to-all interconnections and is only analyzed for the case of two agents. Gazi & Passino =-=[11]-=- employed social potentials to study cohesion in swarms using a centralized mechanism. Tanner et al. in [50] proposed a centralized algorithm for a particle system that leads to irregular collapse for... |

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Citation Context ... including animal behavior, physics & biophysics, social sciences, and computer science have been fascinated by the emergence of flocking/swarming/schooling in groups of agents via local interactions =-=[47, 38, 37, 36, 29, 40, 53, 51, 48, 26, 14, 52, 34]-=-. Examples of these agents include birds, fish, penguins, ants, bees, and crowds. The engineering applications of flocking include massive mobile sensing in an environment; parallel and simultaneous t... |

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Citation Context ...all-to-all interconnections and is only analyzed for the case of two agents. Gazi & Passino [11] employed social potentials to study cohesion in swarms using a centralized mechanism. Tanner et al. in =-=[50]-=- proposed a centralized algorithm for a particle system that leads to irregular collapse for generic initial states. They also proposed a distributed algorithm that leads to irregular fragmentation 1 ... |

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Citation Context ...lts in [16] were further extended to networks with directed topologies by Moreau [27] and Ren & Beard [39]. The convergence analysis of a nonlinear consensus/alignment protocol was first presented in =-=[45]-=-. Helbing et al. [14] studied the escape panic phenomenon in which a crowd that is trapped in a large building (or arena) attempts to evacuate that location in case of an emergency. In Liu et al. [22]... |

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Citation Context ...naries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory [2, 7, 15], algebraic graph theory =-=[12]-=-, spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set of vertices V = {1, 2 . . . ... |

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Modern Graph Theory, volume 184 of Graduate Texts in Mathematics
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Citation Context ...s are made in Section 10. 2 Preliminaries The theoretical framework presented in this paper for both creation and stability analysis of flocking behavior relies on some basic concepts in graph theory =-=[2, 7, 15]-=-, algebraic graph theory [12], spatially induced graphs [31], and consensus problems [45, 33] that are discussed in the following. 2.1 Graphs and Nets A graph G is a pair (V, E) that consists of a set... |

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Citation Context ...[45]. Helbing et al. [14] studied the escape panic phenomenon in which a crowd that is trapped in a large building (or arena) attempts to evacuate that location in case of an emergency. In Liu et al. =-=[22]-=-, stability analysis of one-dimensional swarms with a fixed topology is studied. In [17], Justh & Krishnaprasad proposed an algorithm for swarming that requires all-to-all interconnections and is only... |

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31 |
Collision avoidance for multiple agent systems
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Citation Context ... only two classes of scalable flocking algorithms that do not possess properties a) through e) and successfully lead to creation of flocking in presence of obstacles. Namely, the work by Chang et al. =-=[4]-=- that uses gyroscopic forces for collision avoidance and the work by Olfati-Saber [31] (summarized in [46]) which uses multi-species collective potential functions for both imposing inter-agent constr... |

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Citation Context ...rapped in a large building (or arena) attempts to evacuate that location in case of an emergency. In Liu et al. [22], stability analysis of one-dimensional swarms with a fixed topology is studied. In =-=[17]-=-, Justh & Krishnaprasad proposed an algorithm for swarming that requires all-to-all interconnections and is only analyzed for the case of two agents. Gazi & Passino [11] employed social potentials to ... |

28 |
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Citation Context ...on 9. Some past research with strong connections to this paper include the work by the following researchers: Fax & Murray [9] used graph Laplacians for multi-vehicle formation stabilization; Mesbahi =-=[23, 24]-=- emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be examples of statedependent graphs); Cortes & Bullo [5] and Cortes et al. [6] intr... |

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Citation Context ...lementation or analysis of the above rules is that they have broad interpretations. The issue of how to interpret Reynolds rules was resolved after publication of more recent papers by Reynolds [41], =-=[42]-=-. Among the first groups of physicists who studied flocking from a theoretical perspective were Viscek et al. [53], Toner & Tu [51], and Shimoyama et al. [48]. The work of Vicsek et al. was mainly foc... |

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Citation Context ...een a great interest among control scientists in analysis of alignment phenomenon and consensus problems. This includes the alignment results in networks with switching topologies by Jadbabaie et al. =-=[16]-=- and Olfati-Saber & Murray [33]. The results in [16] were further extended to networks with directed topologies by Moreau [27] and Ren & Beard [39]. The convergence analysis of a nonlinear consensus/a... |

26 |
Flocking with obstacle avoidance: Cooperation with limited communication in mobile networks
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Citation Context ...sfully lead to creation of flocking in presence of obstacles. Namely, the work by Chang et al. [4] that uses gyroscopic forces for collision avoidance and the work by Olfati-Saber [31] (summarized in =-=[46]-=-) which uses multi-species collective potential functions for both imposing inter-agent constraints and obstacle avoidance. So far, there are no analytical results that relate the algorithm in [4] to ... |

24 |
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23 | Communication complexity of multi-robot systems
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22 |
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Citation Context ...forms of swarming behaviors using a network with all-to-all interconnections (i.e. a centralized algorithm). Other continuum models of alignment/swarming were proposed by Mogilner and Eldstein-Keshet =-=[25, 26]-=- with consideration of the sensing issues. Recently, there has been a great interest among control scientists in analysis of alignment phenomenon and consensus problems. This includes the alignment re... |

20 |
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schools: A quantitative theory of flocking
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Fish in schools
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9 |
State-dependent graphs
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Citation Context ...on 9. Some past research with strong connections to this paper include the work by the following researchers: Fax & Murray [9] used graph Laplacians for multi-vehicle formation stabilization; Mesbahi =-=[23, 24]-=- emphasized the role of state-dependent graphs in information networks (interestingly, “dynamic flocks” turn out to be examples of statedependent graphs); Cortes & Bullo [5] and Cortes et al. [6] intr... |

5 |
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Citation Context ... Cortes & Bullo [5] and Cortes et al. [6] introduced distributed algorithms for placement of mobile sensors that appears to be closely related to flocking in a constrained space; Rabichini & Frazzoli =-=[43]-=- proposed an energy-efficient method for determining the split time in a multi-vehicle rejoin/split maneuver; Leonard & Fiorelli [21] used artificial potentials for formation keeping; Ogren et al. [28... |

3 |
Flocking with Obstacle Avoidance
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(Show Context)
Citation Context ...hrough e) and successfully lead to creation of flocking in presence of obstacles. Namely, the work by Chang et al. [4] that uses gyroscopic forces for collision avoidance and the work by Olfati-Saber =-=[31]-=- (summarized in [46]) which uses multi-species collective potential functions for both imposing inter-agent constraints and obstacle avoidance. So far, there are no analytical results that relate the ... |

3 |
Rigid definitions of schooling behavior are inadequate
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Citation Context ...oup does not stop near qd and moves along the specified desired group velocity pd. After passing both obstacles, the agents form a giant flock as shown in Fig. 17 (f). 9 What Constitutes Flocking? In =-=[35]-=-, Partridge provides a brief survey of various definitions of “schooling in fish” by animal behavior scientists that spans half a century from 1927 to 1981. The length of this period is a clear indica... |

3 |
The chorus-line hypothesis of maneuver in avian flocks
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Blind Fish Can School
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