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New Perspectives in the Study of Swarming Systems

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Title: New Perspectives in the Study of Swarming Systems


1
New Perspectives in the Study of Swarming Systems
  • Cristián Huepe
  • Unaffiliated NSF Grantee - Chicago, IL. USA
  • Collaborators
  • M. Aldana and H. Larralde UNAM, Mexico
  • V. M. Kenkre and V. Dossetti UNM, USA
  • A. E. Turgut Mid. East Tech U., Turkey
  • F. Cucker City U of Hong Kong, China

This work was supported by the National Science
Foundation under Grant No. DMS-0507745. _________
__________________________________________________
_____
2
  • Outline
  • Overview of Swarming Systems
  • Computer Science Biology
  • Appl. Math Physics Engineering
  • New Perspectives
  • Additional quantities
  • Lessons from minimal systems
  • Network approach
  • Developing connections to real systems
  • New swarming robots

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
3
  • Outline
  • Overview of Swarming Systems
  • Computer Science Biology
  • Appl. Math Physics Engineering
  • New Perspectives
  • Additional quantities
  • Lessons from minimal systems
  • Network approach
  • Developing connections to real systems
  • New swarming robots

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
4
  • Overview of Swarming Systems Research

Computer Science Craig Reynolds (US RD
Sony Computer Entertainment) Xiaoyuan Tu
(Graphics Lab, U of Toronto - AiLive Inc )
Michael Girard (Comp. Graph. Research, Ohio State
U) Helmut Lorek, Matthew White (U of
Oldenburg) Jessica Hodgins (GVU, Georgia
Inst. of Tech.) Hiroki Sayama (SUNY
Binghamton)
Biology Iain Couzin (Oxford/Princeton)
Stephen Simpson (U of Sidney) Julia Parrish,
Daniel Grünbaum (U of Washington) Steven
Viscido (U of South Carolina) Leah
Edelstein-Keshet (U of British Columbia)
Charlotte Hemelrijk (U of Groningen)
New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
5
Computer Science Q Which 1980 arcade game
first demonstrated the animation technique now
known as "flocking?" A Rip-Off It featured
smart enemies that sought out target objects and
could change goals while avoiding collisions with
each other. -- Trivia slide, SIGGRAPH 2001
Electronic Pre-show (Tim Skelly)
  • Craig W. Reynolds seminal work
  • Flocks, Herds, and Schools A Distributed
    Behavioral Model
    Computer Graphics, 21(4), pp. 25-34,
    1987
  • Defined Boids and simple interaction rules
  • Challenges
  • Create realistic-looking computer animated swarms
    for movies
  • Generate agents with collective strategies for
    computer games
  • Develop agents for Game of Life-style virtual
    universes
  • Develop efficient algorithms
  • H. Lorek M. White Parallel bird
    flocking simulation Parallel
    Processing for Graphics and Scientific
    Visualization, 1993

? Separation
? Alignment
? Cohesion
New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
6
  • Overview of Swarming Systems Research

Computer Science Craig Reynolds (US RD
Sony Computer Entertainment) Xiaoyuan Tu
(Graphics Lab, U of Toronto - AiLive Inc )
Michael Girard (Comp. Graph. Research, Ohio State
U) Helmut Lorek, Matthew White (U of
Oldenburg) Jessica Hodgins (GVU, Georgia
Inst. of Tech.) Hiroki Sayama (SUNY
Binghamton)
Biology Iain Couzin (Oxford/Princeton)
Stephen Simpson (U of Sidney) Julia Parrish,
Daniel Grünbaum (U of Washington) Steven
Viscido (U of South Carolina) Leah
Edelstein-Keshet (U of British Columbia)
Charlotte Hemelrijk (U of Groningen)
New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
7
Biology "...and the thousands of fishes moved
as a huge beast, piercing the water. They
appeared united, inexorably bound to a common
fate. How comes this unity?"
--
Anonymous, 17th century
  • Motivation
  • Similar swarming behavior observed in very
    different animal species
  • Fish schools bird flocks can involve from a few
    individuals to several thousands
  • Locust plagues can contain 109 individuals
    traveling thousands of kilometers
  • New experiments
  • International StarFlAG project involving 5 EU
    countries
  • Controlled lab experiments with fish tanks and
    insect arenas
  • Challenges
  • Understand the causes of swarming behavior
  • Reverse-engineer the biological interactions
  • Control swarms
  • Study the higher-order computational capabilities
    of swarms
  • I. Couzin Collective minds

    Essay in Nature, Vol 445, February 2007

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
8
  • Overview of Swarming Systems Research

Engineering Richard Murray (CALTECH)
Naomi Leonard (Princeton) Reza Olfati-Saber
(Dartmouth College) Ali Jadbabaie (U of
Pennsylvania) Stephen Morse (Yale U) Kevin
Lynch and Randy Freeman (Northwestern U),
Francesco Bullo (UCSB) Vijay Kumar (U of
Pennsylvania)
Applied Math Physics Tamás Vicsek
(Eötvös Loránd U), Chad Topaz, Andrea
Bertozzi, Maria DOrsogna (UCLA) Herbert
Levine (UCSD) Edward Ott (U of Maryland)
Bruno Eckhardt (U Marburg) Maximino Aldana
(UNAM) Udo Erdmann (Helmholtz Association),
Hugues Chaté (CEA-Saclay)
New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
9
Engineering
  • Motivation
  • Groups of robots will be more effective than
    single robots for
  • Deploying sensor networks
  • Carrying-out tasks in parallel
  • Micro-robotic applications
  • New technologies
  • Mini-robots by iRobot (SwarmBot), LIS (s-bot),
    EPFL (e-puck)
  • Underwater sensor robot networks (N. Leonard, S.
    Ramp)
  • Military technology
  • Challenges
  • Develop control algorithms for groups of
    autonomous robots that are
  • Decentralized
  • Scalable

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
10
  • Overview of Swarming Systems Research

Engineering Richard Murray (CALTECH)
Naomi Leonard (Princeton) Reza
Olfati-Saber (Dartmouth College) Ali
Jadbabaie (U of Pennsylvania) Stephen Morse
(Yale U) Kevin Lynch and Randy Freeman
(Northwestern U), Francesco Bullo (UCSB)
Vijay Kumar (U of Pennsylvania)
Applied Math Physics Tamás Vicsek
(Eötvös Loránd U), Chad Topaz, Andrea
Bertozzi, Maria DOrsogna (UCLA) Herbert
Levine (UCSD) Edward Ott (U of Maryland)
Bruno Eckhardt (U Marburg) Maximino Aldana
(UNAM) Udo Erdmann (Helmholtz Association),
Hugues Chaté (CEA-Saclay)
New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
11
Applied Math Physics
  • Motivation
  • Understand essential components of swarming
    dynamics
  • Models
  • Agent-based algorithms
  • Discrete time
  • Continuous time (ODEs)
  • Field-based algorithms (PDEs)
  • Challenges
  • Link to statistical mechanics, granular systems,
    and other agent dynamics
  • Universality at phase transitions? Conserved
    quantities? Energy cascades?
  • Can field equations be deduced from microscopic
    interactions?
  • What is the meaning of integro-differential PDE
    models?
  • Symmetry breaking only captures initial
    homogeneous field perturbations (like Jeans
    instability, but no longer-time dynamics)

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
12
Applied Math Physics
  • The Vicsek model
  • Numerical simulations
  • Periodic box
  • N100 to N100 000
  • Control parameters
  • Mean density
  • Noise level
  • Interactions per displacement

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
13
The Vicsek Model
  • Order parameter
  • Alignment
  • Magnetization
  • Main result
  • Second-order phase transition at critical noise
    value

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
14
  • Outline
  • Overview of Swarming Systems
  • Computer Science Biology
  • Appl. Math Physics Engineering
  • New Perspectives
  • Additional quantities
  • Lessons from minimal systems
  • Network approach
  • Developing connections to real systems
  • New swarming robots

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
15
  • Outline
  • Overview of Swarming Systems
  • Computer Science Biology
  • Appl. Math Physics Engineering
  • New Perspectives
  • Additional quantities
  • Lessons from minimal systems
  • Network approach
  • Developing connections to real systems
  • New swarming robots

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
16
  • New Perspectives
  • Additional quantities
  • Degree of alignment (magnetization)
  • Local density
  • Distance to nearest neighbor

17
? Additional quantities Comparison of minimal
models
  • Vicsek Model
  • Standard Vicsek Algorithm (SVA)
  • Original Vicsek Algorithm (OVA)
  • Grégoire Chaté model (GCM)

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
18
? Additional quantities Comparison of minimal
models
  • SVA OVA
  • GCA

19
  • Observations
  • OVA larger finite-size effect than SVA
  • OVA others Unrealistically high local
    densities
  • Evidence of universal critical behavior at the
    phase transition?
  • Analysis of cluster-size distribution
  • SVA GCA
  • Cumulative distribution of cluster sizes for
    N8192, s0.5, mean density 1/8

20
  • Order of the phase transitions? Grégoire
    Chaté PRL 92 (2004) 025702
  • All models appear to present 1st order transition
    at low densities
  • GCA displays clear 1st order transition at high
    densities
  • SVA OVA apparent 2nd order transition becomes
    1st order for very large systems

21
  • New Perspectives
  • Lessons from minimal systems
  • The Cucker-Smale (CS) model
  • With
  • Convergence to non-zero initial condition
    dependant agent-speed
  • CS with informed agents
  • Defining
  • The system becomes simply

22
  • Analytical convergence results
  • Defining
  • We can prove

23
  • Numerical results
  • Convergence
  • Final group velocity
  • Comparison CS informed / Detailed
    swarming model

24
  • New Perspectives
  • Network approach
  • Motivation We replace
  • Moving agents by fixed nodes.
  • Effective long-range interactions by a few
    long-range connections.
  • Each node linked with probability 1-p to one of
    its K neighbors and p to any other node.
  • Small-world effect
  • 1 of long range connections
  • Phase with long-range order appears

p 0.1
25
Analytic Solution
  • Mean-field approximation
  • Vicsek time-step and order parameter
  • Order parameter
  • The calculation requires
  • Expressing PDFs in terms
  • of moments
  • A random-walk analogy
  • Central limit theorem
  • Expansion about the
  • phase transition point

26
The randomized position case
  • Agents are repositioned randomly at every
    time-step
  • Comparison of numerical and analytic solutions
  • N 20000, K 5 (top) K 20 (bottom)
  • Vicsek noise Chate noise

27
The combined noise case
  • Two types of noise are combined by using
  • With xi and zeta random variables
  • Region of first order transition grows with K
  • Equivalent analytic results obtained for Boolean
    model with intrinsic and extrinsic noise.

28
  • Outline
  • Overview of Swarming Systems
  • Computer Science Biology
  • Appl. Math Physics Engineering
  • New Perspectives
  • Additional quantities
  • Lessons from minimal systems
  • Network approach
  • Developing connections to real systems
  • New swarming robots

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
29
  • Outline
  • Overview of Swarming Systems
  • Computer Science Biology
  • Appl. Math Physics Engineering
  • New Perspectives
  • Additional quantities
  • Lessons from minimal systems
  • Network approach
  • Developing connections to real systems
  • New swarming robots

New perspectives in the study of swarming systems
ESAM Northwestern U 10/03/2008
30
  • New Perspectives
  • Swarming robots
  • The KOBOT system
  • Developed at the KOVAN research lab of the
    Department of Computer Engineering (Middle East
    Technical University, Ankara, Turkey) for swarm
    robotic studies
  • Relative positions measured by eight infrared
    sensors
  • Directions measured and broadcasted using digital
    compass module
  • Physical simulator currently used to study large
    systems of KOBOTs

31
  • Saturation in KOBOT radio communication implies
    direct analogy to random network inputs for
    angular interactions
  • Stiff-vectorial network model
  • Comparison of robot dynamics and analytic results

32
  • New Perspectives
  • New data on biological swarms
  • New experimental data may challenge our
    assumptions
  • E.g. 1) Starling in flight S T A R F L A G
  • E.g. 2) Cannibalistic interactions in crickets
    and locust

33
Fin
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