Flocking and Group Behavior

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Flocking and Group Behavior

• Luv Kohli
• COMP259
• March 24, 2003

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Outline

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

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What is a flock?

• One definition a group of birds or mammals
  assembled or herded together

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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

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Boids!

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

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Boid motion (1)

• Boids have a local coordinate system

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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

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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

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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.

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Flocking 3 Behaviors (1)

• Collision avoidance avoid collisions with nearby
  flockmates

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Flocking 3 Behaviors (2)

• Velocity matching attempt to match velocity with
  nearby flockmates

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Flocking 3 Behaviors (3)

• Flock centering attempt to stay close to nearby
  flockmates

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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

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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

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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

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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

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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

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Avoiding obstacles (3)
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Algorithmic considerations

• Naïve algorithm is O(N2)
• This can be significantly reduced
• Localizing each boids perception
• Parallelization
• Spatial partitioning can be used to achieve O(1)

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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

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Overview
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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

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Physics-based fish model (2)
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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

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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

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Mechanics (3)

• Equations of motion specified by
• mi(d2xi/dt2) ?i(dxi/dt) wi fwi
• ?i damping factor
• wi(t) sum of spring forces
• fwi external (hydrodynamic) forces
• Integrated using numerically stable implicit
  Euler method

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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 fishs body and proportional to the
  displaced volume

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How to swim fish-style (2)

• Instantaneous force proportional to
  ?s(nv)nds
• s surface
• v relative velocity between surface
  and fluid
• n unit outward normal function over
  surface
• Approximated withfmin(0, -A(nv)n), whereA is
  triangle area. (1/3)f isgiven to each triangle
  node

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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

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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

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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

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Sensory perception (2)

• Temperature sensor
• Samples ambient water temperature at center of
  fishs body

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Mental state (1)

• Fishs mental state specified by
• Hunger
• H(t) min1-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

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Mental state (2)

• Fishs mental state specified by
• Libido
• L(t) mins(?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

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Mental state (3)

• Fishs mental state specified by
• Fear
• F(t) min(sum(minDo/di(t), 1),1)
• Do 100 (constant)
• di(t) distance to visible predator i

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Intention generator
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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

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Schooling
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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

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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

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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.