Group Behaviors and Artificial Life

1
Group Behaviors and Artificial Life

• Claire OShea
• COMP 259 Spring 2005

2
Overview

• Motivation
• Flocks, Herds, and Schools
• Artificial Fishes
• Cognitive Modeling
• Constrained Animation of Flocks
• Summary

3
Motivation

• Many animations require natural-looking behavior
  from a large number of characters
• Flock of birds
• School of fish
• Crowd of people

4
Motivation

• How do we generate this motion?
• Keyframe every character
• This is very labor-intensive, usually ends up
  looking unrealistic
• OR...
• Let each character generate its own motion!
• Much easier, and produces natural, unscripted
  motion

5
Motivation

• Questions about this method
• How do we write rules to define natural behavior?
• Can self-directed characters do anything
  intelligent?
• How can we give the animator some control over
  the scene?
• Well find out in the papers

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Flocks, Herds, and Schools A Distributed
Behavioral Model

• Craig W. Reynolds, 1987

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Flocks, Herds, and Schools

• A flock is simply the result of the interaction
  between the behaviors of individual birds.
• Model a flock of boids (bird-oids) as a
  particle system
• Each particle has an orientation
• Behavior of one particle depends on other
  particles

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Flocks, Herds, and Schools

• Modeling boid flight
• The boid itself can move only in one direction
  (forward along its local positive z-axis)
• The boid steers by rotating about its local x and
  y axes
• The boids local coordinate system can move and
  rotate freely within world coordinates

9
Flocks, Herds, and Schools

• Modeling boid flight
• Banking turns
• The y-axis is always aligned with the direction
  of acceleration
• During straight flight, this is gravity
• During a turn, radial forces cause the bird to
  bank (rotate around its z-axis)

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Flocks, Herds, and Schools

• Modeling boid flight
• Gravity is used only to help define banking
  angle it is not actually applied as a force
• Upper bounds are set on speed and acceleration
• Other forces (buoyancy, drag) are not modeled

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Flocks, Herds, and Schools

• Modeling flocking behavior
• Three basic rules, each of which generates an
  acceleration request
• Collision Avoidance
• Avoid running into other boids or static
  obstacles
• Velocity Matching
• Match velocity with nearby flockmates
• Flock Centering
• Stay close to nearby flockmates

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Flocks, Herds, and Schools

• Combining acceleration requests
• Weighted average
• Fails in certain critical situations (ex.
  imminent collisions)
• Prioritized allocation
• Acceleration requests are accepted in priority
  order, until the maximum acceleration is reached
• Works well (at least for this simple system)

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Flocks, Herds, and Schools

• Simulated Perception
• All the behavior rules depend only on nearby
  objects
• An individual boid is only aware of other boids
  which lie in a spherical region around it
• Sensitivity falls off as the inverse square of
  the distance

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• Demo A flock of boids

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Artificial Fishes Physics, Locomotion,
Perception, Behavior

• Xiaoyuan Tu and Demetri Terzopoulos, 1994

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Artificial Fishes

• Simulate a fish using a holistic model
• Physical form
• Movement
• Perception
• Behavior

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Artificial Fishes

• Fish Physics
• Spring-mass model
• 23 point masses, 91 springs
• External springs are muscles
• Fish moves by changing the rest length of these
  springs!

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Artificial Fishes

• Fish Movement Swimming
• Fish swings its tail back and forth by
  alternately contracting and relaxing the muscles
  on each side
• Displacement of water produces a reaction force
  normal to the fishs body (Fiw)
• r1, s2, r2, s2 amplitude and frequency of
  muscle contractions
• Control amount of force, and thus swimming speed
• Optimal values found experimentally

A reaction force (Fiw) is applied at point ni and
acts along the inward normal. It propels
the fish both sideways and forward.
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Artificial Fishes

• Fish Movement Turning
• Fish quickly contracts the muscles on one side
  while relaxing them on the other
• r0, s0, r1, s1 contraction amplitude and
  frequency of the turning muscles
• Experimentally determined for turns of 30, 45,
  60, and 90 degrees
• Arbitrary turns are generated by interpolating
  these parameters

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Artificial Fishes

• More Fish Movement
• Pitch and yaw are controlled by the pectoral fins
• Force applied on the fins
• Raising or lowering the leading edge of the fin
  makes the fish swim up or down
• Setting the two fins at different angles causes
  fish to roll
• Setting fins perpendicular to body decreases
  forward speed

fishs velocity
angle of fin to body
surface area
fins normal vector
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Artificial Fishes

• Fish Perception
• Simplified simulation of vision
• Fish can see things that are within its viewing
  volume (a 300 degree solid angle around its head)
  and not occluded
• Radius of viewing volume determined by
  translucency of the water

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Artificial Fishes

• Fish Behavior
• Fish behavior is influenced by several factors
• Individual habits (preset by animator)
• Mental state (functions evaluated at each
  timestep)
• Perceived environment
• Intention generator picks an intention based on
  these factors.

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Artificial Fishes

• Fish Behavior
• Mental state
• Hunger
• Libido
• Fear

digestion rate
time since last meal
appetite
amount eaten
libido function
time since last mating
distance to predator i
fear of predator i
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Artificial Fishes

• Intention Generator
• Decides on a behavior based on mental state and
  priority ordering
• Check for imminent collisions
• Check for nearby predators (calculate F(t))
• Evaluate hunger and libido (H(t) and L(t))
• Evaluate happiness with the ambient conditions

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Artificial Fishes
A complete fish model
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Artificial Fishes

• Different types of fish can be created just by
  changing the intention generator!
• Predator Prey

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• Demo Foraging Fish

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Cognitive Modeling Knowledge, Reasoning and
Planning for Intelligent Characters

• John Funge, Xiaoyuan Tu, and Demetri Terzopoulos,
  1999

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Cognitive Modeling

• Builds on the idea of a holistic character model,
  but adds another layer cognitive modeling
• Character can learn about its environment
• Character can plan ahead to achieve goals

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Cognitive Modeling

• Some AI background situation calculus
• Situation a description of the state of the
  world at a given time
• Fluent a property of the world that can change
  over time
• Primitive action function that translates from
  one situation to another situation
• Precondition axiom a statement about the state
  of the world before the primitive action
• Effect axiom a statement about the state of the
  world after the primitive action

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Cognitive Modeling

• Situation calculus examples
• (These examples are in CML, a language developed
  for this paper)
• Fluent
• Broken(x, s)
• Precondition axiom
• action drop(x) possible when Holding(x)
• Effect axiom
• occurrence drop(x) results in Broken(x)

Whether x is broken in situation s
A primitive action
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Cognitive Modeling

• Domain knowledge specification
• Character should not have perfect knowledge of
  the world this is unrealistic and uninteresting.
• A better model character makes plans based on
  limited information, knows when it needs more
  information
• Need a way to express uncertainty about aspects
  of the world!

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Cognitive Modeling

• Interval-valued Epistemic Fluents
• The usual way to represent uncertainty in AI is
  with epistemic ?-fluents, but these are difficult
  to implement.
• An alternative is to use interval arithmetic!
• For each sensory fluent f, introduce an
  interval-valued epistemic fluent If.
• The width of the IVE fluent expresses uncertainty
  about the value of f.

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Cognitive Modeling

• Interval-valued Epistemic Fluents Example
• speed(x, s) the speed of object x in situation
  s
• Ispeed(s) what the character thinks the speed
  of x is in situation s
• Suppose we know the speed at s0
• speed(x, s0) 20
• Ispeed(s0) lt20, 20gt
• As time goes on, we are less
• certain about the value!
• speed(x, s1) 25
• Ispeed(s1) lt10, 30gt

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Cognitive Modeling

• Character direction
• A character can plan by finding a sequence of
  primitive actions that accomplish a goal
• Equivalent to searching a tree
• Complexity exponential in the length of the
  plan!
• Animator can prune the search space by
  specifying complex actions (sequences of
  primitive actions)
• Results in nondeterministic behavior the same
  goal can be accomplished in many different ways!

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Cognitive Modeling

• Creating an animation with smart characters
• Still need all the lower-level modules (physics,
  perception, behavior, etc)
• Add a reasoning engine to choose a low-level
  behavior!

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Cognitive Modeling

• Example Prehistoric world
• A T-Rex wants to chase raptors out of its
  territory
• It knows that they will run away when it
  approaches, so it herds them out

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Cognitive Modeling

• Example Undersea world
• A merman tries to escape from a shark
• The merman hides behind obstacles, so that the
  shark cant see him

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Constrained Animation of Flocks

• Matt Anderson, Eric McDaniel, and Stephen
  Chenney, 2003

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Constrained Animation of Flocks

• The papers we have looked at so far focus on
  creating animations with minimal input from the
  animator
• But in real applications, the animator usually
  wants to specify what happens in the scene!

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Constrained Animation of Flocks

• Two-step model for constrained animation
• Produce a trajectory that satisfies the
  constraints
• Evaluate plausibility and refine the trajectory

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Constrained Animation of Flocks

• Constraints
• Point constraints a character must be at a point
  at a certain time
• Center-of-mass constraints the center of mass of
  some group must be at a point at a certain time
• Shape constraints a group must lie inside a
  polygonal shape
• Except for point constraints, these are not
  guaranteed to be satisfied only approximated.

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Constrained Animation of Flocks

• Behavior model
• Based on Reynolds model
• Each character gets a randomly sampled wander
  impulse at each timestep.
• The wander contribution added to the character is
  a combination of this wander impulse and the
  normalized wander contribution from the previous
  timestep.

wci-1 previous wander contribution (normalized)
wii current wander impulse wci total wander
contribution for this timestep
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Constrained Animation of Flocks

• Finding initial trajectories
• Find configurations that satisfy all the
  constraints, then interpolate trajectories in the
  windows between them
• Possible methods (some or all of these may be
  used)
• Forward simulation
• Path transformation
• Backward simulation

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Constrained Animation of Flocks

• Finding initial trajectories
• Forward simulation
• Used when initial conditions are given for a
  window
• Position characters to meet initial conditions,
  then run an unconstrained simulation using the
  behavior model

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Constrained Animation of Flocks

• Finding Initial Trajectories
• Path Transformation
• Used when the window is part of a sequence of
  point or COM constraints
• Fit a B-spline curve through the sequence of
  points
• Run a forward simulation, and at each timestep,
  move the character onto the curve

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Constrained Animation of Flocks

• Finding Initial Trajectories
• Backward Simulation
• Used when end constraints are given for the
  window
• Position characters to meet end constraints, then
  run the simulation backwards (just reverse the
  birds perception)
• Blend the resulting trajectory (xbackward) with
  the forward simulation (xforward) using a
  weighting function

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Constrained Animation of Flocks

• Evaluating plausibility of an animation
• Determine whether the wander impulses are
  plausibly distributed (gw)
• Determine how well the animation satisfies the
  COM and shape constraints (gc, gs)
• Bias the animation toward producing a single
  flock (gf)
• The overall plausibility function

49
Constrained Animation of Flocks

• Evaluating the wander impulses
• From the given trajectories, we can deduce the
  wander impulse of each character at each timestep
• gw evaluates whether the wander impulses look
  like they were sampled from the right
  distribution
• In this model, the wander impulses had uniformly
  random direction and normally distributed length,
  so we evaluate how well the lengths wii fit a
  normal distribution

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Constrained Animation of Flocks

• Evaluating constraint enforcement
• Center of mass constraints
• COM(A, t) is the center of mass of the group at
  time t
• Cx is the center of mass defined in the
  constraint
• Shape constraints
• cs is a user-defined constant
• dist(S, A, t) calculates the sum-of-squares
  distance of each character from the shape

51
Constrained Animation of Flocks

• Generating a better animation
• If the current animation fails the plausibility
  test, the system generates a new one using one of
  the following strategies
• Completely re-generate some or all of the
  trajectories
• Add random bumps to a trajectory
• Change the characters velocity along a
  trajectory
• Only point constraints are enforced during this
  phase

52
Constrained Animation of Flocks

• Repeat the sampling process for a given number of
  iterations, or until a plausible animation is
  found.

This animation was generated in 1000 iterations
(about two hours)
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• Demo Constrained Flocking

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Summary

• Flocks, Herds, and Schools
• Simulates boid physics, perception, and
  behavior
• Fairly unrealistic physics no attempt to
  actually model flight
• Fast and simple to implement, scales well to
  large numbers of characters
• No real control possible from animator

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Summary

• Artificial Fishes
• Simulates fish physics, perception, behavior, and
  intentions
• Realistic physics is used for movement (though
  not always for rendering)
• Intention generator enables fish to engage in
  complex behaviors
• No animator control possible, except in choosing
  initial values

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Summary

• Cognitive Modeling
• Adds another layer of character simulation
  (cognitive model)
• IVE fluents create a realistic model of
  characters domain knowledge
• Tree searching lets character plan ahead to
  accomplish a goal
• Animator can help control scene by scripting a
  series of actions

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Summary

• Constrained Animation of Flocks
• Introduces random variation into the trajectories
  using a wander impulse
• Allows animator to specify constraints on
  movement
• Not real-time requires an iterative refining
  process
• Produces plausible enough trajectories, not
  always completely realistic ones

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Summary

• AI methods can generate complex animation of
  multiple characters without low-level control
  from the animator
• Behavior rules can be combined with a
  physically-based model to create realistic scenes
• Problems
• Difficult to implement user-specified constraints
• Complexity issue hard to generate scenes with
  many characters in real time