Flocks, Herds, Swarms & Schools: Distributed Models of Behaviour

1. Flocking Behaviour

References:

Reynolds, C. "Flocks, Herds and Schools: A Distributed Behavioural Model"
Comp. Graph. Vol 21, No. 4 July 1987, (SIGGRAPH 87) p25-34.

Tu, X., Terzopoulos, D. "Artificial Fishes: Physics, Locomotion, Perception, Behaviour"
Comp. Graph. Proc. 1994, (SIGGRAPH 94) p43-50.

Characteristics of flocking behaviour

• Aggregate, polarized, non-colliding motion of a group of animals
  
  
• Behaviour propagates rapidly through a large group
  
  
• Behaviour of the flock is independent of the number of members
  
  
• Complex behaviour (difficult to animate manually)
  
  
• Reduces the chance an individual may be singled out by a predator

Some Flocking Models

A Distributed Flocking Model

Craig Reynolds presented the first distributed behavioural model of flocking behaviour in which:

Each boid follows its own set of behavioural rules (These are applied according to a bird's individual point of view, hence...) A boid can perceive only its immediate neighbours A boid is modelled visually as an oriented particle

A Boid's Behavioural Rules

In order of priority...

Craig Reynolds' website on the original boids.

Adding Interesting Behaviours

Migratory urge toward some point Steer to avoid static obstacle collisions Steer to avoid moving obstacles Eating food Mating Wandering Escaping

Real birds are believed to anticipate the movement of a wave being propagated through the flock. This anticipation of the wave of turning birds allows accelerated response to the flock's changing behaviour. The above model does not account for such long-range perception.

What is an example of an activity you perform in which you anticipate the motion of a wave of behaviour? (Hint: red; amber; green)

Applications

Super-boids, Further Extensions to the Model

• Limit max./min. force applied by boids
  
  
• Include frictional drag
  
  
• Model gravity and lift
  
  
• Separate tangential thrust and lateral steering forces
  
  
• Our boids are becoming subjects for hydro/aero-dynamics!
  

The Internal Workings of an Artificial Fish

After Tu & Terzopoulos, SIGGRAPH 1994	Tu & Terzopoulos, SIGGRAPH 1994

Schooling Behaviour Routine

	Tu & Terzopoulos, SIGGRAPH 1994

The External Workings of an Artificial Fishy

One fish two fish, red fish, blue fish...

Physical model of the fish muscular & skeletal framework.



...this one has a little star.

Algorithmic Considerations

We would like to implement the algorithm so that it was independent of the number of boids in the flock.

• We do not want an individual boid to examine the position and velocity of every other bird in the flock:
  
  

  Algorithm is of complexity O(n-squared) on a single processor. In parallel (one processor per boid) the algorithm is still O(n).

  
  
  
• Problem is the same as that encountered in collision detection.
  
  Solutions to obtain approximately constant time algorithms are many and varied, for example:
  
  
  • Spatial subdivision
    
    
  • Exploit coherence
    
    
  • Bounding spheres / boxes

2. Swarm Intelligence

References:

Millonas M. "Swarms, Phase Transitions and Collective Intelligence"
Artificial Life III, (ed) Langton, Addison-Wesley, 1994, p417-445.

Deneubourg, J-L. et al "Swarm-Made Architectures"
Towards a Practice of Autonomous Systems, Proc. of the First European
Conf. on A. Life. (eds) Varela & Bourgine, MIT Press, 1992.

Hofstadter, D.R. "Ant Fugue",
in "Godel, Escher, Bach: An Eternal Golden Braid", Penguin Books, 1980, p311-336.

Swarm

The idea of swarm intelligence arose largely from observation of the complex behaviour exhibited by the social insects (ie. bees, ants, wasps, termites).

A termite mound pinched from somebody's happy-snaps for your education.	A honey-comb pinched from somebody's happy-snaps for your education.	A wasp nest pinched from somebody's happy-snaps for your education.

Some complex behaviours exhibited by social insects include:

• trail-following
  
  
• foraging
  
  
• construction
  
  
• group defence
  
  
• gardening / farming (fungus/aphids)

A swarm is a set of mobile agents which may:

• communicate with one another directly or indirectly
  
  
• receive stimulii from the environment
  
  
• alter the environment
  
  
• perform collective / distributed problem solving

In biological swarms the agents are:

• usually non-homogeneous (different castes: drones, workers)
  
  
• dependent on the swarm as a whole for their survival

Global Behaviour from Local Rules

• Complex global behaviour of a swarm is somehow encoded in the individual organisms.
  
  
• Complex adaptive behaviour of a swarm is the result of the interactions between organisms as distinct from behaviour that is a direct result of the actions of individual organisms.

For discussion...

• Ants will choose the shortest of two paths of unequal length if the paths are presented simultaneously.
  
  
• After the ants have chosen a path they are unable to switch to a new path.
  
  
• Ants will all choose one path in preference to half of them travelling a second path, even if the paths are of equal length.

Sequential algorithms

• Regulation of an agent's building activity is dependent on the current state of the agent.
  
  
• Information is not transferred directly between agents.
  
  
• The agent does not respond automatically to local configurations unless internal state criteria are met.
  

Stigmergic algorithms

• Regulation of an agent's (nest) building activity is dependent on the current state of the (nest) environment.
  
  
• Information is not transferred directly between agents.
  
  
• The agent automatically responds to any local configuration.

Implementing the Model

• Can decompose a problem / structure into simple components and their local stopping configurations.
  
  
• One type of behaviour proceeds until a local stopping configuration is reached, triggering a new kind of behaviour.
  
  
• An action can be performed by an agent upon encountering a given environmental configuration deterministically, stochastically etc.
  
  
• Different sets of rules can be applied according to a factor such as time or the satisfaction of some other triggering condition.
  
  
• Sets of rules may be applied hierarchically depending on the success or failure of some action.
  
  
• Can implement interesting social systems using Cellular Automata.

Some simple actions...

• Grasp a particle (if not grasping one)
• Drop a particle (if grasping one)
• Move
• Turn
• Release pheromone

Examples of behaviours which may be implemented using these (or similar) actions...

• Nest construction (wasps, termites, ants)
• Shortest path following (ants)
• Food foraging and retrieval (ants)
• Heap construction (ants) (eg. ant cemetaries)

Implementing a Nest-Building Algorithm

(from Deneubourg et al., Alife I, Europe)

• A wasp may act to fill (or not fill) an empty location in a grid.
  
  
• Only three possible configurations of filled cells surrounding a wasp (in this model) stimulate the filling of the cell the wasp is currently on.
  
  
• The probability a wasp will fill a cell given some surrounding configuration is given by a probability: Ph1, Ph2, Pv.

The Sequential Algorithm

• The past activities/current state of the wasp determine its building activity.
  
  (The local environment only 'authorizes' the wasp to fill a cell.)
  
  
• At a time t, a wasp may be in a state horiz-fill or vert-fill.
  
  
• After each filling action of the wasp there is a probability Pvh that it will swap from vert to horiz-fill (or Phv that it will swap from horiz to vert-fill).
  

The Stigmergic Algorithm

• The local environmental configuration determines the wasp's building activity.
  
  
• At a time t, a wasp may execute a horiz1-fill, horiz2-fill or vert-fill each of which may occur depending on a probability Ph1, Ph2 or Pv depending on enviornmental conditions.
  

Local Configurations:				0
Sequential Algorithm:	0 If S=H 1 If S=V	0 If S=H 1 If S=V	0 If S=H 1 If S=V	0
Stigmergic Algorithm:	Pv	Ph1	Ph2	0

a. Solitary insect (N=1), seq. algorithm, Pvh=0.2, Phv=0.8 b. Solitary insect (N=1), sti. algorithm, Pv=0.8, Ph1=0.2, Ph2=0.4 c. Same as a. but with N=10 d. Same as b. but with N=10

Some real wasps' nests of different species.

Animation Applications

• Interesting effects can be obtained but the computationally-expensive methods are not frequently warranted.
  
  
• Best reserved for instances where the behaviour or effect of a swarm is of particular interest.
  
  Ie. don't bother to use a swarm model if you just want the effect of insects milling around randomly (remember Dorin's Razor)!

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