Emergent Crowd Behavior Ching-Shoei Chiang 1 Christoph Hoffmann 2 Sagar Mittal 2 1 ) Computer Science, Soochow University, Taipei, R.O.C. 2 ) Computer Science, Purdue University, West Lafayette, IN
Apr 01, 2015
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
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?
Applications?
Robotics
Fish Vortex
Starlings flocking
Modeling Crowds
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
Core Rules (Reynolds ‘88)
• First to articulate these rules
• Centroid used for attraction
• Limited perception
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
Emergent Behavior
• Does the flock stay together?
• Higher-order group behavior?
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
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
Swarm Behavior
• Random milling around• Start behavior for random initial
position/orientation• Stable for Dro near zero with Dra large
Sample Run – Highly Parallel, N=100
take-off, t≈100
rr= 1ro= 8ra= 23t ≈ 200
Sample Run – Toroidal, N=100
organizational phase (at t≈50)
centroid track at t≈530
rr= 1ro= 5ra= 17t ≈500
Loss of Cohesion – N=100
rr= 1ro= 4ra= 9t = 37
individuals leavesubgroups form
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 ?
N=100, s=0, q=40o, a=270o
Region of breakup approximately Dra+Dro < 8
N=50, 100, 200, 400s=0, 0.05 rad, 0.10 rad
2D Vs. 3D
The 2D graph could almost be the 3D graph, but doubled in size… but why?
The 2D graph could almost be the 3D graph, but doubled in size… but why?
Much more noise for low ra and high ro
Configuration Dependence
3D:5x5x4 grid
3D:plane hexagon,30 trials
2D:plane hexagon,48 trials
2D:R=5, random
Initial Configuration in 2D and 3D
Cohesion
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
Acknowledgements
• NSC Taiwan grant NSC 97-2212-E-031-002• NSF grant DSC 03-25227• DOE award DE-FG52-06NA26290.