COOPERATIVE SELF-ORGANIZATION

TO DESIGN ROBUST AND ADAPTIVE COLLECTIVES

Gauthier Picard and Marie-Pierre Gleizes

IRIT - Université Paul Sabatier

118, route de Narbonne - 31062 Toulouse Cedex FRANCE

Keywords:

Multi-agent systems, Cooperation, Self-organization.

Abstract:

This paper highlights the beneﬁts of using cooperation as the engine of adaptation and robustness for multi-

agent systems. Our work is based on the AMAS (Adaptive Multi-Agent System) approach which considers co-

operation as a self-organization mechanism to obtain adequate emergent global behaviors for systems coupled

with complex and dynamic environments. A multi-robot resource transportation task illustrates the instanti-

ation of a cooperative agent model equipped with both reactive and anticipative cooperation rules. Various

experiments underline the relevance of this approach in difﬁcult static or dynamic environments.

1 INTRODUCTION

To provide a self-organizing collective behavior, the

parts composing a system need a local criterion to

re-organize so as to provide a more adapted function

(Heylighen, 1999). Designers must specify this crite-

rion and equip parts to process and handle this crite-

rion. To the ﬁrst point, the AMAS approach answers

by using an artiﬁcial socially inspired notion, close to

symbiosis (Maturana and Varela, 1994): cooperation

(Capera et al., 2003). The second point is fulﬁlled by

using an autonomic agent approach, which provides

decision-making capabilities to parts. Cooperative

agents aim at avoiding Non Cooperative Situations

(NCS) as a generic proscriptive re-organizational rule.

The advantage of the AMAS approach is to ensure, by

providing adequate cooperative local behaviors, that

the collective will provide the adequate and adapted

global function. To design such agents, a coopera-

tive agent model is available in the ADELFE method

(Bernon et al., 2003). To highlight the relevance of

using the cooperative agent model, we propose to de-

velop a multi-robot resource transportation task, in

which several similar robots have to transport boxes

from a room to another one, by passing through nar-

row corridors, which produce spatial interferences.

This paper rather focuses on the ability of a system

to react to environmental changes and on the observa-

tion of emergent phenomena, rather than on the nomi-

nal efﬁciency of the transport task. Section 2 presents

the agents of the system –the robots– by developing

their different modules and nominal behaviors. Sec-

tion 3 explains the different cooperation rules robots

have to respect to achieve their goals in a more efﬁ-

cient way. An experiment platform has been devel-

oped to test the instantiation of the cooperative agent

model. Several results are expounded and discussed

in section 4 before concluding.

2 COOPERATIVE ROBOT

AGENTS

By using the ADELFE method, robots are described

with several modules which represent a partition

of their physical, social and cognitive capabilities

(Bernon et al., 2003).

The Perceptions Module represents inputs for

agents: position of the claim zone, position of the lay-

ing zone, a limited perception cone in which objects

(robot, box or wall) are differentiable, proximity sen-

sors (forward, backward, left and right), a compass

and the absolute spatial position. The environment

is discretized as a grid whose cells represent atomic

parts on which an object can be situated.

The Actions Module represents outputs from the

agents on their environment. Actions for the trans-

porter robots are: rest, pick, drop, forward, backward,

left and right. Robots cannot drop boxes anywhere

in the environment but only in the laying zone. They

cannot directly communicate or drop land marks on

the environment.

The Skills Module contains knowledge about the

task the agent must perform. Skills enable robots to

achieve their transportation goals. Therefore, a robot

is able to calculate which goal it must achieve in terms

of its current state: if it carries a box then it mustreach

236

Picard G. and Gleizes M. (2005).

COOPERATIVE SELF-ORGANIZATION TO DESIGN ROBUST AND ADAPTIVE COLLECTIVES.

In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics, pages 236-241

DOI: 10.5220/0001177902360241

 SciTePress

laying zone else it must reach claim zone. As a func-

tion of its current goal, the Skills Module provides an

action to process to achieve it. Moreover, robots have

intrinsic physical characteristics such as their speed,

the number of transportable boxes or the preference

to move forward rather than backward – as ants have.

Such preferences are called reﬂex values (see 2.2).

The Representations Module contains knowledge

about the environment (physical or social). The rep-

resentations a robot has on its environment are very

limited. From its perceptions, it cannot distinguish a

robot from another one, but can know if it is carrying

a box or not. It also can memorize its past absolute

position, direction, goal and action.

The Aptitudes Module enables an agent to choose

an action in terms of its perceptions, skills and rep-

resentations. In terms of the current goal, the Skills

Module provides preferences on every action the ro-

bot may do. The Aptitudes Module chooses among

these actions what will be the next action to reach

the goal. Many decision functions can be considered;

e.g. an arbitrary policy (the action having the high-

est preference is chosen) or a Monte Carlo method-

based policy, which is chosen for our example, since

it has already been successfully applied to foraging

tasks (Topin et al., 1999). Therefore, the Aptitudes

Modules can be summed up in a Monte Carlo deci-

sion function on the preference vector (the list of ac-

tion preferences for an agent) provided by the Skills

Module. In the same manner, the Cooperation Mod-

ule provides preference vectors in order to solve the

NCS which are described in section 3.

2.1 Internal Functioning

During the perception phase of the agents’ life cycle,

the Perceptions Module updates the values of the sen-

sors, which directly implies changes in the Skills and

Representations Modules. Once the knowledge is up-

dated, the decision phase results in an action choice.

During this phase, the Aptitudes Module computes

from knowledge and proposes action(s) or not. At

each time t, a robot chooses between different actions

that are proposed by the two decision modules (Skills

and Cooperation). At time t, each action act

of the

robot r

is evaluated. For each action, this value is cal-

culated in terms of perceptions, representations and

reﬂexes in the case of a nominal behavior:

nomi

(act

, t) =wp

(act

, t) + wm

(act

, t)+

(act

)

with:

• V

nomi

(act

, t) represents the value for the action

act

at time t for the robot r

• w p

(act

, t) represents the calculated value in

terms of perceptions,

Table 1: Speciﬁcation of the nominal behavior

Perceptions Effects

¬car ∧ cBox ր wp

(pick, t)

¬car ∧ ¬cBox ∧ sBox ր wp

(forward, t)

¬car∧¬cBox∧ ¬ sBox∧¬inCZ ր wp

(hCZdiri, t)

¬car ∧ ¬cBox ∧ ¬sBox ∧ inCZ ր wp

(backward, t)

ր wp

(forward, t)

ր wp

(lef t, t)

ր wp

(right, t)

car ∧ cLZ ր wp

(drop, t)

car ∧ ¬cLZ ր wp

(hLZdiri, t)

with:

• car: r

is carrying a box,

• cBox: r

is close to a box,

• sBox: r

is seeing a box,

• inCZ: r

is in the claim zone,

• cLZ: r

is close to the laying zone,

• cLZ: r

is close to the laying zone,

• hCZdiri: the move to perform to go to claim zone,

• hLZdiri: the move to perform to go to laying zone,

• ր: increasing.

• w m

(act

, t) represents the calculated value in

terms of memory,

• w r

(act

, t) represents the calculated value in

terms of reﬂexes.

All the V

nomi

(act

, t) are grouped in a vector,

called action preference vector. In the same manner,

the Cooperation Module detects if the agent is faced

up to a NCS or not. In the former case, the Coop-

eration Module proposes an action that subsumes the

actions proposed by the Aptitudes Module. In the lat-

ter case, the action proposed by the Aptitudes Module

is chosen and, then, the agent acts by activating effec-

tors and/or changing its knowledge. As for aptitudes,

an action preference vector, V

coop

(act

, t), is gener-

ated by the Cooperation Module, by regrouping eval-

uation of the actions. Once these values have been

calculated by the two modules for each action of a ro-

bot, the vector on which the Monte Carlo drawing will

process is a combination of the two vectors in which

the cooperation vector subsumes the nominal vector:

(t) = V

nomi

(t) ≺ V

coop

(t)

2.2 Nominal Behavior

The nominal behavior is described with rules that

modify the values in the V

nomi

preference vec-

tor. This vector is obtained by adding values from

perceptions (wp

(act

, t)) and values from reﬂexes

(wr

(act

, t)). Memory is not necessary to imple-

ment a this behavior. Table 1 shows values to increase

in the wp

(act

, t) to achieve the two disjoint goals:

reach claim zone (¬car) and reach laying zone (car).

Reﬂex values are static and also depend on percep-

tions and more precisely on the direction of the ro-

bot. As for ants, robots may prefer moving forward

COOPERATIVE SELF-ORGANIZATION TO DESIGN ROBUST AND ADAPTIVE COLLECTIVES

237

then backward (Topin et al., 1999). For example, val-

ues for wr

(act

, t) can be: wr

(forward, t) =

50; wr

(lef t, t) = 10; wr

(right, t) = 10;

(backward, t) = 0. Thus, even if a goal leads

a robot to a wall, the robot can move by side, as ants

do to forage and to avoid dead ends. But, this mech-

anism is not sufﬁcient to avoid deadlocks in long nar-

row corridors in which robots cannot cross. The goal

is more inﬂuential than reﬂexes. As a consequence,

deﬁning cooperation rules is necessary to enable all

robots to achieve their tasks without deadlock.

2.3 Cooperative Attitude of Agents

The AMAS theory identiﬁes several types of NCS

(Capera et al., 2003), resulting from the analysis of

the cooperation deﬁnition which is close to the sym-

biosis notion. An agent is cooperative if: all perceived

signals are understood without ambiguity (c

per

) and

the received information is useful for the agent’s rea-

soning (c

dec

) and reasoning leads to useful actions to-

ward other agents (c

act

). Therefore, a NCS occurs

when ¬c

per

∨ ¬c

dec

∨ ¬c

act

. We identify seven NCS

subtypes that express these conditions:

• incomprehension (¬c

per

): the agent cannot extract

the semantic contents of a received stimulus,

• ambiguity (¬c

per

): the agent extracts several inter-

pretations from a same stimulus,

• incompetence (¬c

dec

): the agent cannot beneﬁt

from the current knowledge state during the deci-

sion,

• unproductiveness (¬c

dec

): the agent cannot pro-

pose an action to do during the decision,

• concurrency (¬c

act

): the agent perceives another

agent which is acting to reach the same world state,

• conﬂict (¬c

act

): the agent believes the transforma-

tion it is going to operate on the world is incompat-

ible with the activity of another agent,

• uselessness (¬c

act

): the agent believes its action

cannot change the world state or it believes results

for its action are not interesting for the other agents.

Cooperative agents must avoid or repair these NCS,

if they occur. Designing such agents focuses on NCS

speciﬁcation –a kind of exception-oriented program-

ming in which designers focus on exceptions.

3 COOPERATIVE

SELF-ORGANIZATION

Beyond two robots, acting to transport boxes in a

same environment, the nominal behavior is no more

adequate. Indeed, a robot is equipped with skills to

achieve its tasks, but not to work with other robots. In

a constrained environment, spatial interference zones

appear. If two robots, a ﬁrst one carrying a box and

moving to the laying zone and a second one moving

to the claim zone to pick up a box, meet in a corridor,

the circulation is blocked.

3.1 Reactive Cooperation

Two main NCS can be reactively solved, without re-

quiring memory:

A robot is blocked. A robot r

cannot move for-

ward because it is in front of a wall or another ro-

bot r

moving in the opposite direction

. In this

case, if it is possible, r

must move to its sides (left

or right). This corresponds to increasing values of

the cooperative action vector related to side move-

ments: V

coop

(t, right) and V

coop

(t, lef t). If r

can-

not laterally move, two other solutions are openned.

If r

has an antagonist goal, the robot which is the

most distant from its goal will move backward (in-

creasing V

coop

(t, backward)) to free the way for

the robot which is the closest to its goal (increasing

coop

(t, forward) even if it may wait). Robots can

evaluate which is the most distant since they know

their goals and the associated zones. If r

has the

same goal than r

, except if r

is followed by an an-

tagonist robot or if r

moves away from its goal (vis-

ibly it moves to a risky

region), r

moves backward;

else r

moves forward and r

moves backward.

A robot is returning. A robot r

is returning

a consequence of a trafﬁc blockage. If it is possible,

moves to its sides (and is not returning anymore).

Else, r

moves forward until it cannot continue or if it

encounters another robot r

which is returning and is

closer to its goal than r

. Table 2 sums up the cooper-

ative behavior in this situation. If there is a queue of

robots, the ﬁrst returning robot is seen by the second

one that will return too. Therefore, the third one will

return too and so on until there are no more obstacles.

These two rules correspond to resource conﬂicts

(on corridors) or uselessness (when robots move

backward and away from their goal) situations. These

rules, which are simple to express, ensure that robots

cannot block each other in corridors, and robots do

not need to communicate. But, this cooperative atti-

tude only solves problem instantly, creating returning

movements and then implying time loss.

If r

moves in another direction than the opposite di-

rection of r

, it is not considered as blocking because it will

not block the trafﬁc anymore on the next step.

It is risky in the sense it may lead to the occurrence of

a lot of non cooperative situations such as conﬂicts.

A robot is considered as returning while it has no

choice of side movements.

ICINCO 2005 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

238

Table 2: Speciﬁcation of "a-robot-is-returning" NCS.

Condition Action

ret ∧ f R ր V

coop

(t, right)

ret ∧ f L ր V

coop

(t, left)

ret∧¬(f L∨ f R)∧ant∧toGoal∧

cGoal

ր V

coop

(t, backward)

ret∧¬(f L∨ f R)∧ant∧toGoal∧

¬cGoal

ր V

coop

(t, f orward)

ret∧ ¬(fL∨fR)∧ant∧¬toGoal ր V

coop

(t, backward)

ret ∧ ¬(f L ∨ f R) ∧ ¬ant ր V

coop

(t, f orward)

with:

• ret: r

is returning,

• fR: right cell is free,

• fL: left cell is free,

• ant: in front of an antinomic robot,

• toGoal: r

is moving to goal,

• cGoal: r

is closer to its goal than its opposite one,

• ր: increasing.

3.2 Anticipative Cooperation

It is possible to specify cooperation rules to antici-

pate blockage situations in order to make the collec-

tive more efﬁcient : these rules are optimization coop-

eration rules. Previous rules enable robots to extract

from blockage. A robot is in such a situation because

it was crossing a zone frequented by antinomic robots.

So as to prevent this situation and to avoid repeating

their past non cooperation failures, robots must mem-

orize locations of risky areas (from which antinomic

robots come) and avoid them. Thus, an anticipation

rule can be speciﬁed:

A robot sees an antinomic robot. If a robot r

per-

ceives a robot r

having an antinomic goal and if r

can move to its sides it does else it moves forward.

Nevertheless, this reactive anticipation presents

a major problem: once a robot has avoided the

risky zone, no mechanism ensures that it will not

go in it again, led by its goal. Robots can be

equipped with a limited memory of the risky zones

(in the Representations Module). Each time t a

robot r

experiments an anticipation situation fac-

ing a robot r

, it memorizes a tuple (or virtual

marker) hposX(r

, t), posY (r

, t), goal(r

, t), wi in

which posX(r

, t) and posY (r

, t) represent the co-

ordinates of r

at the moment t. goal(r

, t) repre-

sents the goal r

was achieving at time t. w repre-

sents a repulsion value. The higher this value is, the

more the robot will try to avoid the zone described

by the marker when it is achieving another goal than

goal(r

, t). Therefore, the robot inspects all its per-

sonal markerswhose distance is less than its percep-

tion limit (to fulﬁll the locality principle). A marker

with a weight w and situated in the direction dir at

a distance d induces that V

coop

(t, dir

opp

) will be in-

creased of w (dir

opp

is the opposite direction to dir).

As the memory is limited, tuples that are added

Figure 1: Average number of returned boxes in terms of

simulation time and standard deviation for 15 simulations

for different behaviors: individualist, cooperative unblock-

ing, cooperative anticipative and hardcoded behavior.

must disappear at runtime. The weight w decreases

of a given value δ

(called forgetting factor) at each

step. Once w = 0, the tuple is removed from the

memory. This method corresponds to the use of vir-

tual and personal pheromones, and, as ants do, robots

reinforce their markers: a robot moving to a position

corresponding to one of its marker with another goal,

re-initializes the marker. But contrary to the ant ap-

proach, no stigmergy or physical medium are needed.

4 EXPERIMENTS AND

DISCUSSION

The expounded model has been implemented and

simulated in the environments shown in ﬁgures 3, 4

and 5, with the different entities : boxes (non bordered

circles), robots without boxes (light grey bordered cir-

cles) and robots carrying boxes (dark grey bordered

circles). This environment is made up of two rooms

(25 × 30 cells) separated by two long and narrow cor-

ridors (30 × 1 cells). 300 robots are randomly placed

in the claim room. These robots can perceive at a dis-

tance of 5 cells, and can make a move of one cell at

each step. If they can anticipate conﬂicts, their mem-

ory can contain 1500 tuples with an initial repulsion

value w = 400 and a decrease value δ

= 1.

Reaction vs. Anticipation. Figure 1 shows a com-

parison between the average numbers of transported

boxes for 15 simulations (300 robots, 2 corridors, 5-

ranged perception), corresponding to the nominal be-

havior (individualist), a hardcoded one and two co-

operative ones: the cooperative unblocking behavior

(see section 3.1) and the cooperative anticipative be-

havior (see section 3.2). By adding blockage antici-

pation, the collective becomes more efﬁcient (at least

30% more boxes are transported). According to the

AMAS paradigm, we can experimentally observe that

the local resorption of NCS leads to the collective

functional adequacy. Nevertheless, equipping agents

COOPERATIVE SELF-ORGANIZATION TO DESIGN ROBUST AND ADAPTIVE COLLECTIVES

239

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 20000 40000 60000 80000 100000

Steps

Robots

Moving to claim zone

Moving to laying zone

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 20000 40000 60000 80000 100000

Steps

Robots

Moving to claim zone

Moving to laying zone

Figure 2: Incoming robots for the top corridor for two dif-

ferent behaviors: unblocking behavior (left) and anticipa-

tive unblocking behavior (right).

Figure 3: Positioning of all the virtual markers (dark

squares) for all the robots and the two goals.

with cooperative behavior is not as efﬁcient as hard-

coding by giving non adaptive passage points: claim

zone, then corridor 1, then laying zone, then corridor

2, as shown in ﬁgure 1. Finally, the global adaptive

behavior is not sensible to initial state as shown by

the standard deviation, which is negligible.

Emergence of Corridor Dedication. Figure 2

shows the corridor-usage for the two cooperative be-

haviors, i.e. the number of incoming robots for a cor-

ridor and for the two cooperative behaviors: unblock-

ing behavior (left) and anticipative unblocking behav-

ior (right). In the case of anticipative behavior, we can

observe the emergence of a sense of trafﬁc. Robots

collectively dedicate corridors to particular goals. In

fact, markers of all the agents are positioned only at

one corridor entry for one direction as shown in ﬁgure

3. This view is only for monitoring purpose: robots

do not perceives all the markers, only their owns. We

can assign the emergent property to this phenomenon

because robots do not handle any notion of corridor

– unlike some previous works (Picard and Gleizes,

2002). Thus, just with local data, robots established a

coherent trafﬁc behavior that leads to an optimization

of the number of transported boxes.

Robustness in Difﬁcult Environments. Some sim-

ulations have been done in the environment with dead

ends of ﬁgure 4. Robots are able to manage such

difﬁculties by using directions at a higher abstraction

level. For example, the forward direction is not sim-

ply interpreted as going straight forward. If the robot

has only one free direction, left for example, going

Figure 4: Positioning of all the virtual markers (dark

squares) for the goal reach laying zone in a difﬁcult envi-

ronment (with deadends).

Figure 5: Positioning of the virtual markers (dark squares)

in a dynamic environment with two closed corridors.

forward will become going left. As a consequence,

a dead end problem is easily avoided. But, robots

do not distinguish corridors, since they are too close

and markers are not precise enough. In our exam-

ple, corridors are separated by only 9 cells, which

is less then two times the perception distance of ro-

bots. Therefore, marked areas intersect and robots

cannot precisely detect which corridor to avoid. Thus,

there is no corridor dedication, as shown in ﬁgures 4.

However, the collective behavior is robust enough so

that no deadlock appears, even if the collective be-

comes less efﬁcient, because the learning process is

disabled. Solving this problem implies either mod-

ifying parameters such as distance of perception or

repulsing force of markers in function of the envi-

ronment (which is too environment-dependent), or

adding learning capabilities on these parameters by

adding new NCS rules.

Adaptation to Dynamics. Simulations have been

done with an environment with four corridors. At

each 10,000 step period, two corridors are randomly

chosen and closed to add non determinism and dy-

namics. Here again, the collective is less efﬁcient, but

there is no deadlock. Of course, if corridor closing

is too frequent, robots cannot adapt and dedicate di-

rections to corridors. In fact, 300 robots need about

2000 steps to adapt. Figure 5 shows that only entries

of opened corridors are marked and some robots can

be captured in closed corridors, and are then useless.

During each closing period, the two opened corridors

are exploited and a direction is affected. Moreover,

ICINCO 2005 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

240

Figure 6: Compared efﬁciency (boxes/time) between a sim-

ulation in a static environment with two corridors and an-

other one in an dynamic environment with 4 corridors

which 2 corridors are randomly closed every 10,000 steps.

the effect of the environmental dynamic become neg-

ligible with a great number of steps. Figure 6 shows

the efﬁciency for two different environment (static or

dynamic). The efﬁciency of the system in the static

one is more stable but equivalent to the efﬁciency of

the system which evolves in the dynamic one.

Discussion. The AMAS cooperative agent ap-

proach is relevant for several reasons. Firstly, unlike

ant algorithms (Bonabeau et al., 1997), robots do not

physically mark their environment with pheromones,

but memorize personal markers. Secondly, contrary

to competition-based (Vaughan et al., 2000) or altruis-

tic (Lucidarme et al., 2002) approaches, robots do not

need direct communication to inform close robots or

exchange requests and intentions. Thirdly, coopera-

tive behavior encoding is insensitive to the number of

robots, to the topography and to the dimensions of the

environment. Fourthly, no global feedback is needed

to lead the system to functional adequacy, which pre-

vents the system to reach local extrema. Finally, ob-

tained collectives are robust and adaptive, even if per-

ception capabilities are very limited. Nevertheless,

ADELFE does not provide any guidance to instan-

tiate these values. For instance, the initial weights

for markers and the forgetting factor have been ad-

justed to the time robots spend to cross the entire

environment. This might be completely different in

a more complex environment with more or less cor-

ridors which can dynamically open or close. Some

simulations have been done with such environments,

and the affected values seem correct unless corridors

are too close to each other or frequency of closure is

too fast. These values also may be learnt at runtime,

which is one of our perspectives.

5 CONCLUSION

In this paper, we have shown the relevance of co-

operation as a local criterion for collectives to self-

organize to be more adapted to a speciﬁc task. Con-

sidering the ignorance of the global task and the

environment, the self-organizing collective reaches

an emergent coherent behavior, which is then more

robust to environmental risks. Our simulation ap-

plication tackles a simple problem in a simple sta-

tic environment in which the collective achieves its

global task. Simulations in difﬁcult and dynamic en-

vironments conﬁrm the relevance of cooperative self-

organizing collectives. Finally, this application has

been developed to confront the ADELFE cooperative

agent model to a task that requires adaptation and ro-

bustness. However, this application is very speciﬁc,

in the sense it only concerns quasi-reactive non com-

municative robots. In the case of agents able of com-

municative acts, other kinds of NCS are possible.

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