Behavioral Animation Simulation of Flocking Birds

Transcription

1 Behavioral Animation Simulation of Flocking Birds Autonomous characters determine their actions Simulating the paths of individuals in: flocks of birds, schools of fish, herds of animals crowd scenes 1. Physics of Flight 2. Boids: Geometric Flight, Simulated Perception 3. Flocking Behaviour 4. Avoiding Obstacles

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3 Physics of Flight (simple) Flight: movement through air (fluid) Air is a fluid: the force to deform it depends on how fast it is deformed, not how much. Heavier-than-air flight subject to 4 forces: drag weight thrust lift

4 Physics of Flight Drag (d): in the direction of relative fluid flow (relative wind) approximately opposite to the flight path Weight (w): due to gravity perceived weight due to other accelerations Thrust (t): powered flight force (wing flapping) Lift (l): generally upwards, perpendicular to drag At a steady horizontal flight: t t = v v ; t = d ; l = w

5 Physics of Flight: Drag drag force limits speed d = C d ( 1 2 ρv2 )S d [ kgm ]... drag force s 2 C d [1]... drag coefficient (shape, surface friction ρ [ kg ]... fluid density 3 v [ m]... speed s S [m 2 ]... cross-section area aerodynamic shape and material minimize drag

6 Physics of Flight: Lift lift keeps the flyer airborne; counters gravity l = C l ( 1 2 ρv2 )A l [ kgm ]... lift force s 2 C l [1]... lift coefficient (wing construction... ) ρ [ kg ]... fluid density 3 v [ m]... speed s A [m 2 ]... wing area

7 Physics of Flight: Thrust powered flight force a t = t m t [ kgm ]... thrust force s 2 a t [ m ]... acceleration due to thrust s 2 m [kg]... mass

8 Physics of Flight: Weight due to gravity w = mg w [ kgm ]... weight force s 2 g [ m ]... gee (gravity) s 2 m [kg]... mass flyers minimize weight

9 Physics of Flight: Weight descend: t = d-c (when not accelerating) no need for power (gliders) climb: t = d+c needs more power

10 Physics of Flight: Perceived Weight increase of weight in turns, or accelerated entries to climbs more lift needed in a turn; can climb less in a turn

11 Geometric Flight Geometric flight: the animated motion of a flyer along a path; the result of incremental translations forward and steering; increment rate >= frame rate Flight control: thrust (wing flapping): speed pitch: altitude, up/down roll (bank): direction, left/right no explicit yaw Fly to goal: if the situation permits, steer in the direction of a scripted goal (DEMO)

12 Boids: Flocking Behaviour Craig Reynolds (1986): a computer model of coordinated animal motion; boid: bird-oid, a bird-like flying object Start with a boid capable of geometric flight; add simulated perception, follow three "environmental urges": separation: steer to avoid local crowding alignment: match the headings of local flockmates (steer in the same direction) (velocity matching: attempt to match the velocity of local flockmates) cohesion: move towards the avg. position of flockmates images:

13 Flocking Algorithm Separation: us = c s nbr d s d 2 Alignment: Cohesion: u v = c v nbr u c = c c nbr s h nbr s d u... urge vector c s, c v, c c... parameters (constants) nbr... neighbour s... sensitivity function images:

14 Flocking Algorithm Sensitivity function: models limited perception s = a p a = d h + 1 p = f( d ); 0 p 1, e.g. p = max(0, 1 d r ) s... sensitivity function a... factor dependent on angle p... distance factor r... perception radius

15 Obstacle Avoidance Directing the paths of objects moving in an environment to avoid collisions with (static) objects; steer clear of obstacles, away from an imminent impact Techniques: simulated forces steer away from the surface steer away from the centre steer along the surface steer towards a silhouette edge

16 Obstacle Avoidance Steer away from the surface:

17 Obstacle Avoidance Steer away away from the centre: spherical force field

18 Obstacle Avoidance Steer along the surface (curb feeler):

19 Obstacle Avoidance Steer towards a silhouette edge: spiral search

20 Finding Parameters Tuning of parameters and rules produces various behaviours starting point = physical reality trial/error evolutionary techniques (DEMO)