Emergent Crowd Behavior Ching-Shoei Chiang 1 Christoph Hoffmann 2 Sagar Mittal 2 1 ) Computer...
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Emergent Crowd BehaviorChing-Shoei Chiang1
Christoph Hoffmann2
Sagar Mittal2
1) Computer Science, Soochow University, Taipei, R.O.C.2) Computer Science, Purdue University, West Lafayette, IN
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Problem
• Many crowds have no central control • Individual decisions, based on limited
cognition, create an emergent crowd behavior
• How can we script the collective behavior by prescribing the limited individual behavior?
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Applications?
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Robotics
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Fish Vortex
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Starlings flocking
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Modeling Crowds
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Some Prior Art
• Reynolds, 1988 and 1999– Three core rules (separation, alignment, cohesion)– Behavior hierarchy
• Couzin, 2002 and 2005– Investigate core rules– Determine leadership fraction
• Bajec et al., 2005– Fuzzy logic
• Cucker and Smale, 2007– Convergence results
• Itoh and Chua, 2007– Chaotic trajectories
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Core Rules (Reynolds ‘88)
• First to articulate these rules
• Centroid used for attraction
• Limited perception
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Couzin’s Model
• Seven parameters– Zonal radii (rr , ro , ra)
– Field of perception (a)– Speed of motion (s)– Speed of turning (q)– Error (s)
• Focus on direction
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Emergent Behavior
• Does the flock stay together?
• Higher-order group behavior?
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Characterizing Flock Behavior
• Group polarization
• Group momentum
• where vk is the velocity vector, xk the position vector, and
the centroid’s position
1
1 Nk
k k
vp
N v
1
1k k
Nk k
k k
r x x
r vm
N r
x
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Couzin’s Formation Types
• Swarm (A): m ≈ 0, p ≈ 0
• Torus (B): m > 0.7, p ≈ 0
• Dynamic parallel (C): m ≈ 0, p ≈ 0.8
• Highly parallel (D): m ≈ 0, p ≈ 1
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Swarm Behavior
• Random milling around• Start behavior for random initial
position/orientation• Stable for Dro near zero with Dra large
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Sample Run – Highly Parallel, N=100
take-off, t≈100
rr= 1ro= 8ra= 23t ≈ 200
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Sample Run – Toroidal, N=100
organizational phase (at t≈50)
centroid track at t≈530
rr= 1ro= 5ra= 17t ≈500
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Loss of Cohesion – N=100
rr= 1ro= 4ra= 9t = 37
individuals leavesubgroups form
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Our Questions
• How does the choice of the zonal parameters and the initial configuration affect:– Cohesion of the flock ?– Formation type ?
• Is this behavior scale-independent ?• Do the answers in 3D differ from 2D ?
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N=100, s=0, q=40o, a=270o
Region of breakup approximately Dra+Dro < 8
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N=50, 100, 200, 400s=0, 0.05 rad, 0.10 rad
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2D Vs. 3D
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The 2D graph could almost be the 3D graph, but doubled in size… but why?
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The 2D graph could almost be the 3D graph, but doubled in size… but why?
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Much more noise for low ra and high ro
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Configuration Dependence
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3D:5x5x4 grid
3D:plane hexagon,30 trials
2D:plane hexagon,48 trials
2D:R=5, random
Initial Configuration in 2D and 3D
Cohesion
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Some Observations
• 2D and 3D scenarios differ in how they evolve• Cohesion and swarm type is not scale-invariant– In triangle: subgroup development– In saw-tooth notch: individuals take off
• Cohesion and swarm type has dependence on initial configurations―the collective memory.
• No dynamic parallel behavior
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Acknowledgements
• NSC Taiwan grant NSC 97-2212-E-031-002• NSF grant DSC 03-25227• DOE award DE-FG52-06NA26290.