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 Individual decisions, based on limited cognition, create an emergent crowd behavior How can we script the collective behavior by prescribing the limited individual behavior?
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 (r r, r o, r a ) – Field of perception ( ) – Speed of motion (s) – Speed of turning ( ) – Error ( ) Focus on direction
Emergent Behavior Does the flock stay together? Higher-order group behavior?
Characterizing Flock Behavior Group polarization Group momentum where v k is the velocity vector, x k the position vector, and the centroid’s position
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 r o near zero with r a large
Sample Run – Highly Parallel, N=100 take-off, t≈100 r r = 1 r o = 8 r a = 23 t ≈ 200
Sample Run – Toroidal, N=100 organizational phase (at t≈50) centroid track at t≈530 r r = 1 r o = 5 r a = 17 t ≈500
Loss of Cohesion – N=100 r r = 1 r o = 4 r a = 9 t = 37 individuals leave subgroups 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, =0, =40 o, =270 o Region of breakup approximately r a + r o < 8
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.