Boids: Modeling and Understanding

emergent behavior

Sudeep Pillaisudeepp@umich.edu

Background

• Natural and often seen, yet so intriguingo Discrete birds, but an overall fluidic motion

o Magnificent synchronized behaviors

• Each bird dependent on each othero Based on local perception, they control themselves

o No awareness of global perspective

o Seems like a distributed control

o Is it intentional??

• Formationso Classic “Flying V” formation

– Reduce overall drag force as compared to flying alone

– Upwash produces free lift allowing lower angle of attack

– Lead bird – Two flanking birds dissipate downwash

Intentional flocking

• Reduced Energy expenditureo Greater number cause further reduction in induced drag

– Birds towards the middle gain considerable advantage

– Flanking birds gain free lift through upwash

– Reduced induced drag for birds being flanked

– Research – 70% more flight time, reduced heart rates

– Lead bird – Two flanking birds dissipate downwash

• Communication & Cooperationo Mutual cooperation – Flock Rotations

Evolved over time

Efficient flying formation thereby increasing flight time

Distribution of responsibility within flock during rotations

The “Flying V” formation

• Protection from predatorso Statistically improved survival of gene pool from attacks

o Each creature has knowledge of its local perception

o Cry signals for predator warning increases reaction time

• Improved foragingo Larger effective search patterns

• Advantages for social and mating activities

More reasons to flocking

• Formation of efficient flying ordero Reduced Energy expenditure

o Effective communication among flock

o Improved knowledge and avoidance of predator

o Improved foraging

o Increased social and mating activities

• Emergence - Complex global behavior (flocking)

arising from simple local interaction

Emergent behavior

• Do we model emergence in behavior or the

result of emergence (i.e. flocking) ?o Relatively trivial (using current technology) to create a model

that simulates flocking (boids)

o Less trivial to model emergence and tracing the path towards

flocking

• Accomplishing • the former leads us to understanding the latter

• the latter is difficult, and very specific

Modeling emergent behavior

• Basicso Separation, Alignment, Cohesion

• Slight modifications (In decreasing order of precedence)

o Collision Avoidance – avoid collision with nearby flockmates

o Velocity Matching – match velocity with nearby flockmates

o Flock Centering – stay close to nearby flockmates

• Additional modificationso Tendency towards goal, Limiting flock speed, Bounding

workspace, Perching, Obstacle avoidance, Boid neighborhood

Modeling boids

The Algorithm

flock_init_positions()

Structure b (boids)FOR EACH BOID b

b.position =25* [2*rand-1; 2*rand-1;2* rand-1];b.velocity = [0;0;0];

END

Main instance

Flock_init_positions ()LOOP

flock_draw_boids()flock_move()

END LOOP

Rule 1 : SeperationPROCEDURE rule1(boid bJ)

Vector c = 0;FOR EACH BOID b

IF b != bJ THENIF |b.position - bJ.position| < 100 THEN

c = c - (b.position - bJ.position)END IF

END IFENDRETURN c v1

END PROCEDURE

Rule 2: Velocity Matching PROCEDURE rule2(boid bJ)

Vector pvJ

FOR EACH BOID bIF b != bJ THEN

pvJ = pvJ + b.velocityEND IF

ENDpvJ = pvJ / N-1RETURN (pvJ - bJ.velocity) / 8 v2

END PROCEDURE

Rule 3: Flock centering PROCEDURE rule3(boid bJ)

Vector pcJ

FOR EACH BOID bIF b != bJ && |b.position - bj.position| < 8

THENpcJ = pcJ + b.position

END IFENDpcJ = pcJ / N-1RETURN (pcJ - bJ.position) / 100 v3

END PROCEDURE

Moving boids – flock_move()PROCEDURE

move_all_boids_to_new_positions()Vector v1, v2, v3Boid bFOR EACH BOID b

v1 = rule1(b)v2 = rule2(b)v3 = rule3(b)…..…..…..b.velocity = b.velocity + v1 + v2 + v3 + ….b.position = b.position + b.velocity

ENDEND PROCEDURE

The Algorithm (2) – Further additions

Predator interaction Same procedure as tendency towards goal, except a negative effect.

Return –v (from tend_to_goal) v6

FLOCK LEARNING Fitness functions being iteratively manipulated based on behavior needs

FOR EACH BOID bv1 = c1*rule1(b)v2 = c2*rule2(b)v3 = c3*rule3(b)…..

b.velocity = b.velocity + v1 + v2 + v3 + ….b.position = b.position + b.velocity

END

Tendency towards goal – flock_tendency()

PROCEDURE tend_to_goal(Boid b)Vector goalRETURN (goal - b.position) / 100 v4

END PROCEDURE

Limiting Speed – flock_limitvel()PROCEDURE limit_velocity(Boid b)

Integer vlimVector vIF norm(b.velocity) > vlim THEN

b.velocity = (b.velocity/|b.velocity|*vlim)END IF

END PROCEDURE

Workspace bound – flock bound()PROCEDURE bound_position(Boid b)

Integer Xmin, Xmax, Ymin……Vector vIF b.position.x < Xmin THEN

v.x = 10ELSE IF b.position.x > Xmax THEN

v.x = -10END IF…......Return v v5

END PROCEDURE

Moving boids – flock_move()PROCEDURE

move_all_boids_to_new_positions()Vector v1, v2, v3Boid bFOR EACH BOID b

v1 = rule1(b)v2 = rule2(b)v3 = rule3(b)…..…..…..b.velocity = b.velocity + v1 + v2 + v3 + ….b.position = b.position + b.velocity

ENDEND PROCEDURE

• Anti-flockingo Dispersion of flock due to predator

o Negating flock centering almost solves the problem

• Other behaviorso Negating separation – Boids run into each other

o Negating velocity matching – Boids have semi-chaotic

oscillations

• Different permutations of different behaviors with different fitness

functions not necessarily modeling flocks realistically

Other possibilities

• Trial and error and manual tweaking of

parameters using GAso Flocks can be tuned to exhibit interesting behavior

o Practical application may be limited

• Particle Swarm Optimization (PSO)o Shares evolutionary computation techniques such as GA

o Unlike GA, it has no evolution operators (crossover, mutation)

o Strategy

Initialized with random group

Closest bird to food leads the flock

Solution to the optimization is a single bird, not a group

Each bird‟s fitness is re-evaluated and optimized

Optimization

Simulation

• Modeling from the perspective of the birdo Model effects of other birds that are in its view (local)

o Model effects of aerodynamics (CFD)

o Does it support the “Flying V formation”?

• Implementing highway traffic based on

distributed behavior controlo Simple to implement

o Highly reliable

o Energy efficient

Future work

• Several models and techniques have been

developedo Some based on the behavior of flocks

o Some based on optimizing a specific task

• Similar to how we think of evolution, have

flocks „emerged‟ completely?o Flocking in groups can be beneficial, as is evident. Are we in a

transitional phase? Or will they „emerge‟ further to optimize

flocking behavior?

o Can we predict of any possible optimizations they may

possibly undertake?

My thoughts