1. Flocking and Group Behavior
Brian Salomon

2. Papers
Reynolds, C.W. Flocks, Herds, and Schools: A Distributed Behavioral Model. Computer Graphics, 21(2):25-34,1987.
Tu, X., and Terzopoulos, D. Artificial Fishes: Physics, Locomotion, Perception, Behavior. In Computer Graphics: Proceedings of SIGGRAPH 94, , 1994.

3. Reynolds
Birds

4. Motivation Flocks are interesting because Purpose
Overall fluid movement from discrete actors
Emergent Behavior
Purpose
Higher level animation
Automatic constraint satisfaction

5. Boids Bird-oid Oriented particles Rendered as a geometric shape
Independent computation: “distributed”

6. Movement Coordinate System travels with boid y
Intermittent translation and rotation about X and Y, not a real flight model, no notion of lift, gravity
Speed may not exceed certain limit through viscous damping, acceleration may not exceed fraction of max speed.
Banking, keeps negative Y pointing in direction of acceleration (including gravity) y z x

7. Flocking Reason for flocking Flocking in nature is scalable
Predator protection
Finding food
Mating opportunities
Flocking in nature is scalable
Schools of fish 17 miles long with millions of fish
Implies O(1) complexity

8. Simulated Flocking Three behaviors
Collision Avoidance (other boids and obstacles)
Velocity Matching
Flock Centering (move towards centroid of neighbors)
Algorithm is O(N2). More on this later.
Diagrams from Craig Reynolds’ boids page

9. Behaviors
Each behavior produces a normalized vector and an importance [0,1]
Strict priority order as opposed to averaging
Once magnitude is used up subsequent behaviors have no say

10. Simulated Flocking, cont’d
Flocks may split when obstacle encountered, but may not rejoin
Not realistic (more like fish in murky water)
Actual birds use long range vision:
Rate of propagation of maneuvers can be as high as 3 times startle reaction time

11. Perception
Complete knowledge led to unrealistic behavior. Flocking requires locality.
Boid surrounded by a zone (sphere) of sensitivity. Specified by two parameters, radius and exponent (1/rn falloff up to rmax).
Found n=1 was unnatural but n=2 worked well. Vague notion of gravity vs spring, seems like hackery

12. Scripting, “Going Z for the Winter”
Want more control
Add a point of attraction or direction of movement
Can be position dependent
Can only apply to certain boids
Can change over time

13. Environmental Obstacles
Don’t want simple repulsion because it is OK to be near obstacles, just don’t want to fly at them.
Algorithm:
Look along Z for obstacles
If found find nearest silhouette point and add 1 body length, use this radial vector for collision avoidance
Works for obstacles that are spheres, cylinders, planes, boxes

14. Complexity Described algorithm is O(N2) but:
Treating each boid as a separate computer changes complexity to O(N)
Could use spatial decomposition to achieve O(1)

15. Results Some Applets: http://www.red3d.com/cwr/boids/

16. Tu and Terzopoulos
Fish

17. Motivation Schooling and other behaviors Memory
Eating
Wandering
Mating
Memory
More accurate Perception
Physically based motion

18. Fish Model 23 Nodes, 91 Springs, 12 Contractible Springs
diagram from the paper

19. Physical Simulation
xi(t)=[xi(t), yi(t), zi(t)] v(t)=dx/dt a(t)=d2x/dt2
Si,j ~ spring between nodes i and j
li,j ~ resting length
ci,j ~ spring constant
fsi,j ~ force from spring Si,j on node i, fsj,i= -fsi,j
ri,j=xj(t)-xi(t)
ei,j=|ri,j|-li,j
fsi,j=ci,jei,j(t)ri,j/|ri,j|

20. Physical Simulation, cont’d
mi(d2xi/dt2) + i(dxi/dt) – wi=fwi
fwi ~ external forces
wi ~ sum of spring forces
Sparse Matrix, integrated using Implicit Euler.

21. External Forces for Swimming
When fish swings tail left to right water is displaced. Moving water applies force to tail proportional to volume of water displaced.
Instantaneous force is proportional to
-∫s(n·v)nds
s ~ surface
v ~ relative velocity of surface to water
n ~ surface normal
Approximate by triangulating surface with vertices at nodes. Use f=min(0, -A(n·v)n) and give 1/3 force to each node of triangle. A = triangle area.

22. Muscles
Contract resting length (li,j from previous slide) up to lmini,j
To swim contract one side while relaxing other in periodic manner
To turn contract one side sharply and then slowly relax
There are three muscle sections with four muscles each. Swimming uses front two groups, turning uses back two.

23. Motor Controllers
According to Paper only 3 motor controllers (Swim, Turn-Left, Turn-Right).
move muscles by specifying amplitude and frequency for two muscle sections to generate muscle movements described on previous slide
For Swim empirically found maximum speed parameters and specify rest in terms of max
For turn found params for 30 °,45 °,60 °,90° turn. Interp for turns in between these values. Multiple turns for greater than 90° .
But, next section talks about using pectoral fins for braking, rising, etc. No mention of how this fits into the controllers. Presumably these are used by the swim controller.

24. Perception Vision Temperature Cyclopean solid angle of 300
Lookup properties of visible objects.
Access to shading information
Average whole picture for “light” perception
Effective radius determined by murkiness
Temperature

25. Mental State Three functions determine the mental state of a fish
Hunger:
H(t) = min[1-ne(t)R(∆tH)/,1]
ne(t) ~ amount of food eaten
R(x) = 1 – p0x po ~ rate of digestion
∆tH ~ time since last meal
 ~ appetite

26. Mental State, cont’d Libido L(t) = min[s(∆tL)(1-H(t)), 1] Fear
s(x) = p1x p1 ~ libido constant
H is hunger from previous slide
∆tH ~ time since last mating
Fear
F(t) = min[Do/di(t), 1]
Do = 100
di(t) = distance to visible predator i

27. Intentions diagram from paper
Focuser selects target of intention if necessary

28. Behavior Intentions generate behaviors
Behaviors use muscle controllers
Behaviors:
avoiding-static-obstacle
avoiding-fish
eating-food
mating
leaving
wandering
escaping
schooling
Some have sub-behaviors (chase-target sub-behavior of eating-food)

29. Schooling

30. Results

31. Questions/Comments?