Agent Group
Università
di Modena
e Reggio
Emilia
Co-Fields: Towards a Unifying
Approach to the Engineering of
Swarm Intelligent Systems
Marco Mamei
[email protected]
ESAW '02
Franco Zambonelli
[email protected]
Co-Fields & Swarms
Letizia Leonardi
[email protected]
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Università
di Modena
e Reggio
Emilia
Motivations
 Swarm intelligence can provide useful
sources of inspiration to designing multi agent
applications.
Agent Group
 However it is very difficult to move from just a
collection of examples to a general
engineering methodology.
 Unifying abstractions for for large classes of
swarm intelligent systems is a prerequisite for
such a general methodology.
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Co-Fields & Swarms
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di Modena
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Co-Fields Model
 Co-Fields is a model for motion coordination
in a multi agent system.
Agent Group
 In the Co-Fields model, agents live in an
environment which is described by fields
(distributed data structures) that can be
spread either by the agents themselves or by
the environment.
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Co-Fields Model
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 Agents combine the fields they sense to
obtain a task dependent field (referred as the
coordination field) and then move by
following the gradient of such combined field.
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Agent Group
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B
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Co-Fields as a Unifying
Abstarction
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 A Co-Fields based system is a simple dynamical
Agent Group
system. Agents are simply seen as balls rolling upon
a surface whose shape is described by the
coordination field. Complex movements are achieved
not because of the agent will, but because dynamic
re-shaping of this surface.
 The claim of this talk is that Co-Fields can provide a
unifying abstraction to describe swarm intelligence
exemples.
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Swarm Intelligent Strategies
 Wolves Surrounding a Prey
– AI in video games, Robot coordination
Agent Group
 Birds Flocking
– Air Traffic control
 Ant Foraging
– Routing in telecommunication networks
 Ant Division of Labor
– Multitasking
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Wolves Surrounding a Prey
Natural Explanation
 Wolves simply hunt for a moose trying
Agent Group
to maintain a suitable distance from
other wolves.
 Simulations have shown that following
this simple strategy, wolves are able to
surround the prey.
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Co-Fields & Swarms
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di Modena
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Emilia
Wolves Surrounding a Prey
Co-Fields Explanation
 The moose and the wolves, propagates
these kinds of fields:
-1
0
 kme 2hm
kw
k we 2hw
1
k we 2hw
-1
 kme 2hm
0
1
Agent Group
k m
moose( x, y, t )  kme  hm  x X m   y Ym  
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wolf i ( x, y, t )  k we
Co-Fields & Swarms

 
2
 hw  x  X wi  y Ywi

 
2
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Wolves Surrounding a Prey
Co-Fields Explanation
 Then they compute the following coordination
fields and follows the gradient downhill
n
Agent Group
coord moose ( x, y, t ) 
 wolfi ( x, y, t )
i 1
n
coord wolf i ( x, y, t )  moose( x, y, t ) 
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Co-Fields & Swarms
 wolf j ( x, y, t )
j 1, j i
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Testing Co-Fields Algorithms
 Differential Equations
coord i ( X 1 , X 2 ,..., X n , t )
 v 
dt
X j
Agent Group
dx j
 Simulations (test the problem in
constrained environments)
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Wolves Surrounding a Prey
Solving the Differential Equations
 Numerically solving the differential equation:
WOLF
WOLF
WOLF
WOLF
WOLF
MOOSE
Agent Group
MOOSE
Wolves do not repeal each other:
NO surrounding
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WOLF
Wolves repeal each other:
surrounding
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Birds Flocking
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Natural Explanation
Agent Group
 The coordinated behavior of flocks can
be explained by assuming that each
bird tries to maintain a specified
distance (the one that offer best flight
conditions) from the nearest birds.
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di Modena
e Reggio
Emilia
Birds Flocking
Co-Fields Explanation
 Each bird in the flock propagates the
Agent Group
following field (repeal at short distances,
attracts on long distances):
d  ( x  X Bi ) 2  ( y  YBi ) 2
FLOCK i ( x, y, t )  d 4  2a 2  d 2
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Birds Flocking
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Co-Fields Explanation
 Then they compute the following coordination
field and follows the gradient downhill
Agent Group
CF ( x, y, t )  min ( FLOCKi ( x, y, t ) : i  1,...,n)
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Flocking
Agent Group
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Solving the Differential Equations
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Flocking
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MAS Simulation
Agent Group
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Flocking
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MAS Simulation
Agent Group
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Ants Foraging
Natural Explanation
 Ants lay down pheromone trails to guide
Agent Group
other ants towards food or back to the
anthill.
– Ants wander randomly but are attracted by
pheromones.
– Food pheromone is laid down when
returning form a food source
– Nest pheromone is laid down when leaving
the anthill
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Ants Foraging
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Co-Fields Explanation
 The environment spread and maintain two initially flat
Agent Group
fields: Food and Nest fields
 The environment reacts to ants’ movement by
wrinckling the fields’ surface.
 Ants’ movements are affected by the wrinckles
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Ants Foraging
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Co-Fields Explanation
 Analytical description of a wrinkle:
‒ K(0) is dynamically set so as to be lower that all
Agent Group
the neighboring wrinkles, to create steepness
‒ K(t) goes to 0 as t increases to accustom for
“evaporation”
wrinkle( x, y, t )  k (t  t0 )e 
 h  x  X 2   y Y 2
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
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Ant Division of Labor
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Natural Explanation
Agent Group
 Each individual ant has a response-
treshold for every task.
 It engages in task performance when
the level of the task associated stimuli
exceeds the treshold.
 It drops a task when the task associated
stimuli falls under another treshold.
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Ant Labor Division
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Co-Fields Explanation
 We can imagine that each ant is embedded in
an abstract task-space.
 Movement in this space are not actual
movement, but rather change on duties.
Task A
Task A
99%
Agent Group
99%
33%
66%
99%
Task C
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66%
66%
33%
33%
33%
33%
66%
99%
66%
Task B
99%
33%
66%
99%
Task B
Task C
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Ant Labor Division
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e Reggio
Emilia
Co-Fields Explanation
 The environment generates fields encoding
Agent Group
the stimuli encouraging ants in performing a
task.
 Ants move in this space by following the task
Task A Field
fields downhill.
Task A
Task B
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Conclusions
 We have presented a unifying
Agent Group
abstraction to deal with swarm
intelligent system; resembling: visual,
smell, pheromones, air turbolence, taskstimuli.
 It is a prerequisite for a general
engineering methodology.
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Future Works
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Theoretical Investigations
 Dynamical Systems Analysis
 Relationship with System Theory
 Other examples and better formalization
Agent Group
of the current ones
 Towards true Engineering Principles…
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Further Info
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Agent Group
 http://polaris.ing.unimo.it
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