Flocking and Group Behavior Brian Salomon

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, 43--50, 1994.

Reynolds Birds

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

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

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

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

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

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

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

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

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

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

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)

Results Some Applets: http://www.red3d.com/cwr/boids/ http://members.ozemail.com.au/~dcrombie/project/applet.html

Tu and Terzopoulos Fish

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

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

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|

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.

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.

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.

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.

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

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

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

Intentions diagram from paper Focuser selects target of intention if necessary

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)

Schooling

Results http://mrl.nyu.edu/~dt/animat-vision/

Questions/Comments?