Flocking and Group Behavior

1. Flocking and Group Behavior Luv Kohli COMP259 March 24, 2003

2. Outline • First, birdies! • Craig Reynolds paper on flocking • Then, fishies! • Tu & Terzopoulos paper on artificial fishes

3. What is a flock? • One definition: a group of birds or mammals assembled or herded together

4. Why model flocking? • It looks cool • Difficult to animate using traditional keyframing or other techniques • Hard to script the path • Hard to handle motion constraints • Hard to edit motion

5. Boids! • “boids” comes from “bird-oids” • Similar to particle systems, but have orientation • Have a geometric shape used for rendering • Behavior-based motion

6. Boid motion (1) • Boids have a local coordinate system

7. Boid motion (2) • Flight is accomplished using a dynamic, incremental, and rigid geometrical transformation • Flight path not specified in advance • Forward motion specified as incremental translations in local +Z direction

8. Boid motion (3) • Rotation about X, Y, and Z axes for pitch, yaw, and roll • No notion of lift or gravity (except for banking) • Limits set for maximum speed and maximum acceleration

9. Flocking motion • Boids must coordinate with flockmates • Two main desires: • Stay close to the flock • Avoid collisions with the flock • Flocking seems to have evolved due to protection from predators, higher chances of finding food, mating, etc.

10. Flocking – 3 Behaviors (1) • Collision avoidance: avoid collisions with nearby flockmates

11. Flocking – 3 Behaviors (2) • Velocity matching: attempt to match velocity with nearby flockmates

12. Flocking – 3 Behaviors (3) • Flock centering: attempt to stay close to nearby flockmates

13. Arbitrating behaviors • Behavioral urges produce acceleration requests: normalized 3D vector with importance in [0,1] • Priority acceleration allocation is used instead of averaging acceleration requests • Acceleration requests are prioritized and the most important ones are used up to a maximum acceleration

14. Simulated perception • Unrealistic for each boid to have complete knowledge • Flocking depends upon a localized view of the world • Each boid has a spherical neighborhood of sensitivity, based upon a radius and an exponent: 1/rn • Can be exaggerated in forward direction

15. Scripted flocking • More control is needed for animation (e.g., flocks should be near point A at time t0 and near point B at time t1) • Flock has a migratory urge towards a global target • Global target can be moving and can vary depending on boids or other factors

16. Avoiding obstacles (1) • Force field approach • Obstacles have a field of repulsion • Boids increasingly repulsed as they approach obstacle • Drawbacks: • Approaching a force in exactly the opposite direction • Flying alongside a wall

17. Avoiding obstacles (2) • Steer-to-avoid approach • Boid only considers obstacles directly in front of it • Finds silhouette edge of obstacle closest to point of eventual impact • A vector is computed that will aim the boid at a point one body length beyond the silhouette edge

18. Avoiding obstacles (3)

19. Algorithmic considerations • Naïve algorithm is O(N2) • This can be significantly reduced: • Localizing each boid’s perception • Parallelization • Spatial partitioning can be used to achieve O(1)

20. On to fish! • Want to model schooling and other behaviors: • Eating • Avoiding predators • Mating • Modeled with limited memory, perception of the world, behavior, and physics

21. Overview

22. Physics-based fish model (1) • Dynamic fish model consisting of 23 nodal point masses and 91 springs • Spring arrangement maintains structural stability while allowing flexibility • 12 springs run the length of the body to serve as simple muscles

23. Physics-based fish model (2)

24. Mechanics (1) • Each node has: • mass mi • Position xi(t) = [xi(t) yi(t) zi(t)] • Velocity vi(t) = dxi/dt • Acceleration ai(t) = d2xi/dt2

25. Mechanics (2) • Spring Sij connects node i to node j • Spring constant cij • Rest length lij • Deformation eij = ||rij|| - lij • rij = xj(t) – xi(t) • Exerts force fsij = cijeij(t)rij/||rij|| on node i, and –fsij on node j

26. Mechanics (3) • Equations of motion specified by: mi(d2xi/dt2) + ρi(dxi/dt) – wi = fwi ρi= damping factor wi(t) = sum of spring forces fwi = external (hydrodynamic) forces • Integrated using numerically stable implicit Euler method

27. How to swim fish-style (1) • Artificial fish moves by contracting muscles • Forward motion achieved by swinging tail, which displaces water • Displaced water produces a reaction force normal to the fish’s body and proportional to the displaced volume

28. How to swim fish-style (2) • Instantaneous force proportional to ∫s(n·v)nds • s = surface • v = relative velocity between surface and fluid • n = unit outward normal function over surface • Approximated withf=min(0, -A(n·v)n), whereA is triangle area. (1/3)f isgiven to each triangle node

29. How to swim fish-style (3) • Tail swinging achieved by contracting swimming muscles on one side and relaxing on the other side periodically • Turning achieved by contracting one side sharply, relaxing the other side, then slowly relaxing the contracted side • Swimming uses back two muscle groups, turning uses front two muscle groups

30. Motor controllers • Artificial fish has three motor controllers • Swim-MC(speed) • Converts speed into contraction amplitude and frequency • Left-turn-MC(angle) • Right-turn-MC(angle) • Converts angle into parameters for muscles

31. Sensory perception (1) • Vision sensor: vision is cyclopean • Covers 300 degree spherical angle extending to some effective radius based on water translucency • Vision sensor has access to geometry, material properties, and illumination information • Image is averaged to determine overall light

32. Sensory perception (2) • Temperature sensor • Samples ambient water temperature at center of fish’s body

33. Mental state (1) • Fish’s mental state specified by: • Hunger • H(t) = min[1-ne(t)R(∆tH)/,1] • ne(t) = amount of food consumed • R(x) = 1 – p0x, po = digestion rate • ∆tH = time since last meal •  = appetite • p0 = 0.005 results in ravenous fish

34. Mental state (2) • Fish’s mental state specified by: • Libido • L(t) = min[s(∆tL)(1-H(t)), 1] • s(x) = p1x, p1 = libido constant • H is hunger • ∆tL = time since last mating • p1 = 0.01 results in sexual mania

35. Mental state (3) • Fish’s mental state specified by: • Fear • F(t) = min(sum(min[Do/di(t), 1]),1) • Do = 100 (constant) • di(t) = distance to visible predator i

36. Intention generator

37. Satisfying intentions • Once an intention is selected, control is passed to a behavior routine • Eight behaviors: • Avoiding-static-obstacle • Avoiding-fish • Eating-food • Mating • Leaving • Wandering • Escaping • Schooling • Behaviors can also have subroutines that are called

38. Schooling

39. Different fish types • Predators, prey, pacifists • Each type has different intentions which lead to different behavioral patterns • Pacifists exhibit mating behavior based upon criteria for being interested in potential mates

40. Pacifists • A male fish selects a mate as follows: • A female of the same species is preferred to one of other species • Closer females are more attractive than ones further away • A female fish selects a mate similarly but shows preference to male fish size (stronger, more protective) rather than proximity

41. References • Reynolds, C. W., 1987. "Flocks, Herds, and Schools: A Distributed Behavioral Model." Computer Graphics, 21(4): 25-34. • Tu, X. and Terzopoulos, D. "Artificial fishes: Physics, locomotion, perception, behavior." Proc. ACM SIGGRAPH '94 Conference.