By  Craig  W.  Reynolds  Presented  by  Daniele  Zollo  

29/9/2011  

Flocks,  Herds,  and  Schools:  A  Distributed  Behavioral  Model  

INTRODUCTION  

  The  goal  is  to  simulate  a  flock  in  computer  anima9on.  

  A  flock  is  a  group  of  objects  that  exhibit  the  general   class   of   polarized   (aligned),   non-­‐colliding,  aggregate  mo9on.    

  A  flock  is  composed  of  boids.  

  Boid   is   a   simulated  bird-­‐like  object.    

PARTICLE  SYSTEMS  

  Simulate   mo9on   of   flocks   of   boids   using  individual  behaviors.  

  Elaborate  on  a  Par9cle  System.    Par9cle   Systems   are   collec9ons   of   large  number   of   par9cles   each   with   their   own  behaviors.  

 More   realis9c   than   scrip9ng   the   paths   of  the  individual  birds.  

  Boids   must   interact   strongly   in   order   to  flock   correctly:   his   behavior   is   dependent  not   only   on   internal   state   but   also   on  external  state.  

BEHAVIORAL  ANIMATION  

  Computer  animator's  job  becomes  somewhat  like  that  of  a  theatrical  director.  

  Character's  performance  is  the  indirect  result  of  the  director's  instruc9ons  to  the  actor.  

  Not   knowing   how   a   simula9on   is   going   to  proceed   from   the   specified   behaviors   and  ini9al   condi9ons   can   produce   many  unexpected  and  pleasant  surprises.  

  But   there   is   need   of   rules   that   ensure   the  correct   behaviors   that   lead   to   simulated  flocking.  

GEOMETRIC  FLIGHT  

  A  fundamental  part  of  the  boid  model  is  the  geometric  ability  to  fly.  

  Each  boid  performs  a  mo9on  along  a  path:  a   dynamic,   incremental,   rigid   geometrical  transforma9on   of   an   object,  moving   along  and  tangent  to  a  3D  curve.  

  The   boid   is   free   to   ar9culate   or   change  shape  within  this  flying  coordinate  system.  

GEOMETRIC  FLIGHT  

  Geometric   flight   models   conserva9on   of  momentum.  An  object  in  flight  tends  to  stay  in  flight.  

  There   is   a   simple   model   of   viscous   speed  damping,   so   even   if   the   boid   con9nually  accelerates   in   one   direc9on,   it   will   not  exceed  a  certain  maximum  speed.  

  A  minimum  speed  can  also  be  specified  but  defaults  to  zero.  

  A  maximum  accelera9on  is  used  to  provide  smooth  changes  of  speed  and  heading.  

BANKING    Geometric   flight   relates   transla9on,   pitch,   and  yaw,   but   does   not   constrain   roil,   the   rota9on  about  the  local  Z  axis.  

  This  degree  of  freedom  is  used  for  banking-­‐rolling  the  object  to  align  the   local  Y  axis  with  the  (local  XY   component   of   the   total)   accelera9on   ac9ng  upon  it.  

  The   Bank   angle   is   the  angle   at   which   the  vehicle  is  inclined  about  its   longitudinal   axis  with  respect  to  its  path.  

BANKING  

  The  magnitude   of   the   turning   accelera9on  varies  directly  with  the  object's  velocity  and  with   the  curvature  of   its  path   (so   inversely  with  the  radius  of  its  turn).  

 With   correct   banking   (what   pilots   call   a  coordinated   turn)   the   object's   local   space  remains   aligned   with   the   "perceptual"   or  "accelera9onal"  coordinate  system.  

NATURAL  FLOCKS,  HERDS  AND  SCHOOLS  

  For   a   bird   to   par9cipate   in   a   flock,   it  must  have   behaviors   that   allow   it   to   coordinate  its  movements  with  those  of  its  flockmates.  

  But   these   behaviors   are   not   par9cularly  unique;   all   creatures   have   them   to   some  degree.  

  Natural   flocks   seem   to   consist   of   two  balanced,  opposing  behaviors:  •  a  desire  to  stay  close  to  the  flock  •  a   desire   to   avoid   collisions   within   the  flock.  

NATURAL  FLOCKS,  HERDS  AND  SCHOOLS  

  An  individual  bird  must  have  a  localized  and  filtered  percep9on  of  the  rest  of  the  flock.  

  A  bird  might  be  aware  of  three  categories:  •  Itself  •  its  two  or  three  nearest  neighbors  •  the  rest  of  the  flock  

  The   complexity   of   the   flocking   algorithm  described  is  basically  O(N²):  •  the   work   required   to   run   the   algorithm  grows   as   the   square   of   the   flock's  popula9on.    

SIMULATED  FLOCKS  

  In   order   of   decreasing   precedence,   the  behaviors  that  lead  to  simulated  flocking  are:  

1)  Collision  Avoidance:  avoid  collisions  with  nearby  flockmates  

2)  Velocity  Matching:             aaempt   to  match   velocity  with   nearby    

flockmates    3)  Flock  Centering:            aaempt  to  stay  close  to  nearby  flockmates    

SIMULATED  FLOCKS  

  Sta9c   collision   avoidance   and   dynamic  velocity  matching  are  complementary.  

  Sta9c   collision   avoidance   is   based   on   the  rela9ve   posi9on   of   the   flockmates   and  ignores  their  velocity.  

  Conversely,  velocity  matching   is  based  only  on  velocity  and  ignores  posi9on.  

  Sta9c  collision  avoidance  serves  to  establish  the  minimum  required  separa9on  distance;  velocity  matching  tends  to  maintain  it.  

SIMULATED  FLOCKS  

  Flock  centering  makes  a  boid  want  to  be  near  the  center  of  the  flock.  

  Flock   centering   causes   the   boid   to   fly   in   a  direc9on   that  moves   it   closer   to   the   centroid  of  the  nearby  boids.  

  If  a  boid  is  deep  inside  a  flock,  the  centroid  of  the   neighborhood   boids   is   approximately   at  the   center   of   the   neighborhood,   so   the   flock  centering  urge  is  small.  

  But   if   a   boid   is   on   the  boundary  of   the  flock,  the   flock   centering   urge   is   stronger   and   the  flight  path  will  be  deflected  somewhat  toward  the  local  flock  center.  

SIMULATED  FLOCKS  

SeparaSon:    steer  to  avoid  crowding  local  flockmates  

Alignment:    steer   towards   the   average   heading   of  local  flockmates  

Cohesion:    steer   to   move   toward   the   average  posi9on  of  local  flockmates    

     The  basic  flocking  model  consists  of  three  simple  steering  behaviors  

ARBITRATING  INDIPENDENT  BEHAVIORS  

  The   three  behaviors   that   lead   to  simulated  flocking  produce  accelera9on  requests.  

  Each   behavior   has   several   parameters   that  control   its   func9on   and   that   can   vary   the  accelera9on  requests.  

  The   easiest   way   to   combine   accelera9on  requests  is  a  them  weighted  average.  

  But   in   cri9cal   situa9ons,   such   as   poten9al  collision   with   obstacles,   conflicts   between  accelera9on  requests  can  be  dangerous.  

  The   solu9on   is   based   on   a   strict   priority  ordering  of  all  component  behaviors.  

ARBITRATING  INDIPENDENT  BEHAVIORS  

  The  accelera9on  requests  are  considered  in  priority   order   and   added   into   an  accumulator.  

  The  magnitude  of  each  request  is  measured  and  added  into  another  accumulator.  

  This  process  con9nues  un9l  the  sum  of  the  accumulated   magnitudes   gets   larger   than  the  maximum  accelera9on  value,  which  is  a  parameter  of  each  boid.  

  In  an  emergency  the  accelera9on  would  be  allocated  to  sa9sfy  the  most  pressing  needs  first.  

SIMULATED  PERCEPTION  

  The  real  bird's   informa9on  about   the  world   is  severely   limited   because   it   perceives   through  imperfect   senses   and   because   its   nearby  flockmates  hide  those  farther  away.  

  The   simula9on   must     filter   out   the   surplus  informa9on  that  are  available   to   the  sobware  that  implements  the  boid's  behavior.  

  The  behaviors  that  make  up  the  flocking  model  are  stated  in  terms  of  nearby  flockmates.  

  The   neighborhood   is   defined   as   a   spherical  zone  of  sensi9vity  centered  at  the  boid's   local  origin.  

SIMULATED  PERCEPTION  

  Flocking  requires  that  each  boid  reacts  only  to   flockmates   within   a   certain   small  neighborhood  around  itself.  

  The  neighborhood  is  characterized  by  a  distance   (measured   from   the  center   of   the   boid)   and   an  angle,  measured   from   the   boid's  direc9on  of  flight.    

  Flockmates  outside   this   local  neighborhood  are  ignored.  

AVOIDING  ENVIRONMENTAL  OBSTACLES  

  The   Force   Field   model   postulates   a   field   of  repulsion   force   emana9ng   from   the   obstacle   out  into  space;  the  boids  are   increasingly  repulsed  as  they  get  closer  to  the  obstacle.  

  If  a  boid  approaches  an  obstacle  surrounded  by  a  Force   Field   at   an   angle   such   that   it   is   exactly  opposite   to   the   direc9on   of   the   force   field,   the  boid  will  not  turn  away.  In  this  case  the  force  field  serves   only   to   slow   the   boid   by   accelera9ng   it  backwards  and  provides  no  side  thrust  at  all.  

  The   Force   Fields   tend   to   be   too   strong   close   up  and   too   weak   far   away;   avoiding   an   obstacle  should   involve   long-­‐range   planning   rather   than  panicky  correc9ons  at  the  last  minute.  

AVOIDING  ENVIRONMENTAL  OBSTACLES  

  Steer  To  Avoid   is  a  beaer  simula9on  of  a  natural  bird  guided  by  vision.  

  The  boid  considers  only  obstacles  directly  in  front  of   it   (It  finds  the   intersec9on,   if  any,  of   its   local  Z  axis  with  the  obstacle).  

  Working   in   local   perspec9ve   space,   it   finds   the  silhoueae   edge   of   the   obstacle   closest   to   the  point   of   eventual   impact.   A   radial   vector   is  computed  which  will  aim  the  boid  at  a  point  one  body  length  beyond  that  silhoueae  edge.  

CONCLUSIONS  

  This   paper   has   presented   a   model   of  polarized,   non-­‐colliding,   aggregate  mo9on,  such  as  that  of  flocks,  herds  and  schools.  

  The   model   is   based   on   simula9ng   the  behavior  of  each  boid  independently.  

  However   it   is   difficult   to   objec9vely  measure  how  valid  these  simula9ons  are.  

  But   having   approached   a   certain   level   of  realism  in  the  model,  the  parameters  of  the  simulated  flock  can  be  altered  at  will  by  the  animator   to   achieve   many   varia9ons   on  flock-­‐like  behavior.