Group Behaviors and Artificial Life

1. Group Behaviors and Artificial Life Claire O’Shea 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? We’ll find out in the papers…

6. “Flocks, Herds, and Schools: A Distributed Behavioral Model” Craig W. Reynolds, 1987

7. “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

8. “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 boid’s 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)

10. “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

11. “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

12. “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)

13. “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

14. Demo: A flock of boids

15. “Artificial Fishes: Physics, Locomotion, Perception, Behavior” Xiaoyuan Tu and Demetri Terzopoulos, 1994

16. “Artificial Fishes” • Simulate a fish using a “holistic model” • Physical form • Movement • Perception • Behavior

17. “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!

18. “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 fish’s 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.

19. “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

20. “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 fish’s velocity angle of fin to body surface area fin’s normal vector

21. “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

22. “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.

23. “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

24. “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

25. “Artificial Fishes” A complete fish model:

26. “Artificial Fishes” • Different types of fish can be created just by changing the intention generator! Predator: Prey:

27. Demo: Foraging Fish

28. “Cognitive Modeling: Knowledge, Reasoning and Planning for Intelligent Characters” John Funge, Xiaoyuan Tu, and Demetri Terzopoulos, 1999

29. “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

30. “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

31. “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

32. “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!

33. “Cognitive Modeling” • Interval-valued Epistemic Fluents • The usual way to represent uncertainty in AI is with epistemic κ-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.

34. “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) = <20, 20> As time goes on, we are less certain about the value! speed(x, s1) = 25 Ispeed(s1) = <10, 30>

35. “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!

36. “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!

37. “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

38. “Cognitive Modeling” • Example: Undersea world • A merman tries to escape from a shark • The merman hides behind obstacles, so that the shark can’t see him

39. “Constrained Animation of Flocks” Matt Anderson, Eric McDaniel, and Stephen Chenney, 2003

40. “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!

41. “Constrained Animation of Flocks” • Two-step model for constrained animation • Produce a trajectory that satisfies the constraints • Evaluate plausibility and refine the trajectory

42. “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.

43. “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. ŵci-1: previous wander contribution (normalized) wii: current wander impulse wci: total wander contribution for this timestep

44. “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

45. “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

46. “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

47. “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:

48. “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:

50. “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