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Emergent Crowd Behavior

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. Problem. Many crowds have no central control

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Emergent Crowd Behavior

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  1. Emergent Crowd Behavior Ching-Shoei Chiang1Christoph Hoffmann2Sagar Mittal2 1) Computer Science, Soochow University, Taipei, R.O.C.2) Computer Science, Purdue University, West Lafayette, IN

  2. 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?

  3. Applications?

  4. Robotics

  5. Fish Vortex

  6. Starlings flocking

  7. Modeling Crowds

  8. 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

  9. Core Rules (Reynolds ‘88) • First to articulate these rules • Centroid used for attraction • Limited perception

  10. 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

  11. Emergent Behavior • Does the flock stay together? • Higher-order group behavior?

  12. Characterizing Flock Behavior • Group polarization • Group momentum • where vk is the velocity vector, xk the position vector, and the centroid’s position

  13. 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

  14. Swarm Behavior • Random milling around • Start behavior for random initial position/orientation • Stable for Dro near zero with Dra large

  15. Sample Run – Highly Parallel, N=100 take-off, t≈100 rr= 1ro= 8ra= 23t ≈ 200

  16. Sample Run – Toroidal, N=100 organizational phase (at t≈50) rr= 1ro= 5ra= 17t ≈500 centroid track at t≈530

  17. Loss of Cohesion – N=100 rr= 1ro= 4 ra= 9t = 37 individuals leavesubgroups form

  18. 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 ?

  19. N=100, s=0, q=40o, a=270o Region of breakup approximately Dra+Dro < 8

  20. N=50, 100, 200, 400s=0, 0.05 rad, 0.10 rad

  21. 2D Vs. 3D

  22. The 2D graph could almost be the 3D graph, but doubled in size… but why?

  23. The 2D graph could almost be the 3D graph, but doubled in size… but why?

  24. Much more noise for low ra and high ro

  25. Configuration Dependence

  26. Initial Configuration in 2D and 3D 3D:5x5x4 grid 3D:plane hexagon,30 trials 2D:plane hexagon,48 trials 2D:R=5, random Cohesion

  27. 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

  28. Acknowledgements • NSC Taiwan grant NSC 97-2212-E-031-002 • NSF grant DSC 03-25227 • DOE award DE-FG52-06NA26290.

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