This paper shows that, in some situations, con-flict can deliberately be left in an autonomy-basedmulti-agent system. This study, supported byexperimental results, has two major outcomes.First, it proves that conflict does not necessarilyalter the global outcome of the system in a qual-itative way. Second, it shows that it is possibleto effect the way the global task is achieved byappropriately modifying the environment of theagents.
IntroductionOur work fits in the framework of Bottom-Up Artifi-cial Intelligence (Brooks 1986), (Brooks 1991) and particularly, in that of Autonomous Agents (Pfeifer1995). We are concerned with collective phenomenaand their issues and more precisely, the way to carryout solutions that allow an autonomy-based multi-agentsystem to achieve a global task by virtue of emergenceand self-organization. Emergence offers indeed a bridgebetween the necessity of complex and adaptive behaviorat a macro level (the one of the system) and situation-based interactions at a micro level (the one of everyagent) (Forrest 1990). We are concerned with the studyof systems made of autonomous agents, looked at fromthe point of view of their adaptive capabilities. Forthat, we take up a methodology which follows an engi-neering trend that can be characterized by:
1. a bio-inspired approach, drawing its models fromevolutionary biology and the study of animal so-cieties, and participating in the concept of em-bodiment of intelligence now surfacing in artifi-cial intelligence (Robert, Chantemargue, & Courant1998), (Lerena & Courant 1998);
2. the relinquishing of supervised control and stringenthierarchical data structures in favor of decentralizedcontrol strategies based on interactions through influ-ences. These strategies, hence requiring autonomouscomponents are expected to lead to solutions throughemergent features (Chantemargue et al. 1998b);
3. aa epistemological stance that fits in with the rootsof cognitive science, in which can be found the theory
of Varela (Varela, Thompson, & Rosch 1991).
Our work is supported by two types of experiments,namely multi-agent simulations applied to collectiverobotics, aml collective robotics applications involv-ing real robots. This paper will (i) focus exclusivelyon a multi-agent case study, which consists of study-ing through intensive simulations how a pool of op-erationally autonomous agents regroups objects thatare distributed in their environment, and (ii) addressthe specific question of conflict which, according to acommon-sense idea, is bound to happen in every sys-tem composed of multiple entities. In this paper, wetake up an approach in which nothing is explicitly un-dertaken to eliminate conflict in the system. However,the results we obtained show that in our context andto some extent, the system is able to cope with con-flict by itself. This paper is organized as follows: thefirst section starts by briefly reporting how conflict hasbeen attempted to be avoided and solved till now in theframework of Artificial Intelligence and Distributed Ar-tificial Intelligence. The second section describes ourexperimental testbed and highlights our approach onconflict. The next section gives the most significantexperimental results for our purpose. The last sectionsummarizes our point of view regarding conflict andconcludes this paper.
Conflict in Artificial Intelligence and
Distributed Artificial Intelligence
There are indeed numerous reasons for which conflictmay arise, depending on the context of the applicationand on the type of entities that are considered. Forinstance, entities may have limited access to resources;entities may have knowledge conflicts, due to problemsof incompleteness, uncertainty or non reliability in theirown knowledge databases (see for instance (Kwong,Wong, & Low 1998), (Cholvy 1998), (Lamontagne Benhamou 1998)). When the term conflict is evoked, itis very likely to relate to a problem of concurrent accessto resources. As far as we are concerned, we considerconflict as a divergence at the level of goals between en-tities in the system: therefore, for us, conflict is linkenedto antagonism (Ferber 1995). An access to a given re-
source can itself be classified as a goal (or sub-goal)and is consequently included in this interpretation ofthe term. Note that this notion of conflict could be ex-tended so as to encompass sources of goal divergences,as in cases of knowledge conflict. Generally, it is arguedthat if conflict is not appropriately solved, the systemmay run into serious trouble (it may not fulfill the goalsfor which it was designed). If it appears to be true thatconflict has to be planned ahead in certain contexts suchas operating systems, it however seems paradoxical inthe context of autonomous agents, wherein approachesto system development are typically bottom-up, start-ing from atomic entities, whose composition of behav-iors is hard to be predicted by the designer.
Conflict is somehow addressed by coordination. Co-ordination is defined as the management of depen-dencies between activities (Malone & Crowston 1994).Work generally concentrates on peculiar aspects of co-ordination, among which the most commonly addressedtopic is cooperation. In (Ferber 1995) an interactiontaxonomy for goal-oriented agents is put forward: in-teractions are classified according to the goals of theagents, their resources and their skills. This taxon-omy leads to three categories of situations: indifferenceand cooperation situations encompass situations wheregoals are compatible (with the different combinationsfor resources and skills, namely sufficient and insuffi-cient), whereas antagonistic situations group togetherall possible situations in which goals are incompatible(indiscriminately of the status of resources and skills).In (Ferber 1995), numerous methods for handling coop-eration situations are discussed (see (Chaib-Draa 1996)as well). These methods, according to Mataric’s defini-tion (Mataric 1992), imply information exchanges andactions performed by a couple of agents in order to helpsome others. We refer to them as explicit cooperation,that’is, a set of interaction organization methods devel-oped for foreseen situations. However, what is remark-able is that antagonistic situations are never addressed:it seems as if they were considered out of scope.
In fact, approaches to address the problem of con-flict mostly consisted in replicating techniques for theprevention of conflict that were developed in the disci-pline of operating systems, and in fitting them to Dis-tributed Artificial Intelligence. Our approach is quitethe reverse: we are concerned with conceiving systemsin which conflict is tolerated.
An experimental multi-agent testbedOur simulation tackles a quite common problem in col-lective robotics which is still given a lot of concern:agents seek for objects distributed in their environmentin order to regroup all objects. However, the way weaddress this problem is not classic: the innovative as-pect of our approach rests indeed on a system inte-grating operationally autonomous agents, that is, ev-ery agent in the system has the freedom to act. Moreprecisely, every agent decides by itself which action totake on the basis of its own perception, which is strictly
local and private. Therefore, there is not in the sys-tem any type of master responsible for supervising theagents, nor any type of cooperation protocol, thus al-lowing the system to be more flexible and fault toler-ant. In that, this work relates to other work in theframework of collective robotics (see (J.C. Deneubourget al. 1991), (Bonabean & Theraulaz 1994), (Gaussier& Zrehen 1994), (R. Beckers and O.E. Holland andJ.L. Deneubourg 1994), (Martinoli & Mondada 1995)and (Martinoli & Mondada 1998)) in which the focusis on the collective capabilities of a multi-robot systemto achieve clustering tasks (the system typically createsseveral clusters of objects in the environment) and/oreventually regrouping tasks (the system typically cre-ates a single cluster containing all the objects of theenvironment) on the basis of a stigmergic1 coordinationbetween robots.
We implemented our simulation in the Swarm Sim-ulation System (developed at the Santa-Fe Institute,USA) (Langton, Minor, & Burkhart 1996). In our sim-ulation, the environment is composed of a discrete twodimensional square grid, a set of objects and a set oftransparent obstacles. A set of agents is present in thisenvironment: agents roam (by avoiding obstacles), pickup and drop objects. At the outset of an experiment,objects are (randomly) distributed in the environmentthat may contain obstacles (randomly set or set at chosen fixed location), with at maximum one objectper cell. An experiment will be considered completedwhen all objects present in the environment will be re-grouped by the agents onto a single cell (in this case,we will speak of a stack of all objects).
An agent possesses some sensors to perceive the worldwithin which it moves, and some effectors to act inthis world, so that it complies with the prescriptionsof simulated embodied agents (Ziemke 1997). An agentconsists of several modules, namely perception, state,actions and control algorithm. These (almost self-explanatory) modules depend on the application andare under the user’s responsibility. The control algo-rithm module defines the type of autonomy of the agent:it is precisely inside this module that the designer de-cides whether to implement an operational autonomyor a behavioral autonomy (Ziemke 1997). Operationalautonomy is defined as the capacity to operate with-out human intervention, without being remotely con-trolled. Behavioral autonomy supposes that the basisof self-steering originates in the agent’s own capacity toform and adapt its principles of behavior: an agent, tobe behaviorally autonomous, needs the freedom to haveformed (learned or decided) its principles of behavior its own (from its experience), at least in part.
For our purpose, and for sake of simplicity, we chose
1To our knowledge, Beckers et al. (R. Beckers and O.E.Holland and J.L. Deneubourg 1994) were the first to exploita stigmergic coordination between robots. Stigmergic coor-dination means literally "incitement to work by the productof the work".
to implement operationally autonomous agents. Eachagent decides by itself which action to take, accordingto local information. There is no master responsible forsupervising the agents in the system, thus allowing thesystem to be more flexible and fault tolerant. Agentshave neither explicit coordination features for detectingand managing antagonistic situations nor communica-tion tools for negotiation. In fact they "communicate"in an indirect way, that is, via their influences in the en-vironment. Under these constraints, several variants ofcontrol algorithm for our agents have been implementedand tried out. However, in this paper, we will focus onthe following control algorithm: if an agent that doesnot carry an object comes to a cell containing N objects,it will pick one object up with a probability given byN to the power of -Alpha, where Alpha is a constantgreater than or equal to zero; if an agent that carriesan object comes to a cell containing some objects, itwill systematically drop its object. If the cell is empty,nothing special happens and the agent will move to an-other cell. Note that an agent can not carry more thanone object at a time. Such a simple control algorithmallows to explicitly modulate the probability of pickingobjects up as a function of the local density and it is asufficient condition for the system to regroup objects.In (J.C. Deneubourg et al. 1991), the authors indeedshowed in their model that a mechanism that involvesthe modulation of the probability of dropping objects asa function of the local density was sufficient to generatean observed sequence of clustering.
The State module encompasses the private informa-tion of the agent and of course depends on the controlalgorithm of the agent. In our case, it consists of theinformation relative to whether the agent carries or notan object plus other internal variables that include thestates of their random number generators.
Agents can be endowed with several types of objectperception and different moving strategies, thus lead-ing to several families of agents. Yet the perception ofother agents and/or obstacles in the environment is thesame for all families in the sense that a cell contain-ing an obstacle or an agent is implicitly perceived as acell where the agent can not move to. Note that twoagents can not come to the same cell; this induces spa-tial conflict. An agent endowed with what we refer toas a basic object perception, perceives only the quantityof objects that is present on the cell on which it stands.Such agents are endowed with random move capabili-ties to roam in the environment: at every step, a movedirection is randomly drawn. Agents of this type willbe referred to as basic agents. A variant is as follows:at every step, the agent, instead of randomly drawinga direction, is given a probability of 0.1 to randomlydraw a direction and a probability of 0.9 to keep its di-rection. This family of agents is referred to as inertialagents. A last family of agents is that of agents withcamera: every agent is given an artificial eye (pin-holecamera model (R. Horaud and O. Monga 1993) with theclassical five intrinsic parameters and three out of the
six extrinsic parameters, namely two translations outof three and one rotation out of three). So that, everyagent, through its camera, is able to perceive objects(and objects only, not obstacle and not other agents) (part of) the environment and goes towards the objectwhich is the closest to its optical axis, thus avoidingwandering around in an area without interest.
Every agent can be tuned in numerous ways (Alpha,the lens of the camera) so that we have available a largenumber of individual behaviors. In a previous work,we conducted some studies on finding the appropriateparameters so as to optimize the global behavior of thesystem when varying the number of agents.
An agent is said to be regrouping agent if it is able toregroup all the objects into a single stack on a cell, ina finite time, when acting alone in the environment, forany initial configuration. Experimenting environmentswhere some regrouping agents concurrently work is ex-pected to yield a single stack containing all the objects.However this result does not appear as a goal embod-ied into the agents, but is generated by the recurrentinteractions of the agents. It can be interpreted as aglobal goal, but such an interpretation is generally thedescription made by an external observer spying on theexecution of the experiment.
In our experiment, conflict is naturally induced, dueto the nature of the agents we consider. Even if thereis only one agent in the system, the action of the agentat a given time can lead to an observed contradictorygoal when compared to a previous goal suggested by apreceding action: the agent can indeed pick an objectup from stack A and drop it on stack B, and then later,can do exactly the opposite actions, namely pick anobject up from stack B and drop it on stack A. Whenseveral agents are present in the system, the differentcombined actions of all the agents will as well induceconflict.
ResultsFor a given size of the environment and a fixed numberof objects, we have run an intensive number of exper-iments for two families of agents, namely basic agentsand agents with camera. For basic agents, the size of theenvironment is 9 by 9 cells, there are 10 objects and wehave run 400 experiments. For agents with camera, thesize of the environment is 25 by 25 cells, there are 20objects and we have run 1500 experiments. For everyfamily, Alpha was set to 0.3 and experiments consistedin varying (i) the distribution of objects in the environ-ment and (ii) the number of agents in the system, andin measuring the cost2 of the system to achieve the taskof object regrouping. Moreover, the same experimentshave been repeated with a simple obstacle present inthe south-west part of the environment (see figures and 2).
2The cost of the system is defined as the number of iter-ations necessary to the system to achieve the task.
Figure 1: A 9 x 9 cell environment with 3 basic agents,10 objects and a simple obstacle: red squares (grey ifprinted in B/W) represent objects, green squares (lightgrey if printed in B/W) represent agents, black squares(dark grey if printed in B/W) materialize the obstacle.
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Figure 2: A 25 x 25 cell environment with 3 agents withcamera, 20 objects and a simple obstacle.
Preliminary results were presented at the time of theECAI’98 workshop on Conflicts (see (Chantemargue al. 1998a)): these results were obtained with very sim-ple environments (no obstacle), but they already intro-duced some features of the collective system, namely thefact that implicit cooperation takes place in the system,and the fact that conflict is naturally induced in thesystem. These results conform to the results presentedin (R. Beckers and O.E. Holland and J.L. Deneubourg1994). Our system has been deeply studied since. First,we quantified the different types of conflict that arise inthe system. Second, we analyzed the influence of obsta-cle on the outcome of the system (i.e. the location of thefinal stack). We present hereafter the most significantresults.
The first result yielded for all tried parameters, isthat the collective system achieved the global task ofobject regrouping. Figure 3 (respectively figure 5) dis-plays the cost for agents with camera (respectively ba-sic agents) versus the number of agents in the system3.
3Vertical bars on all charts indicate standard deviations.
Figure 4 (respectively figure 6) displays the speedup the system for agents with camera (respectively basicagents) versus the number of agents in the system. Thespeed-up for n agents is defined as the ratio of the meancost for one agent to the mean cost for n agents.
Speed-up charts show how the performance of thesystem scales with the number of agents. To some ex-tent, the more the number of agents in the system, thebetter the performance of the system. This illustratesa feature in our system, namely that of cooperation:agents participate in achieving the global task withoutbeing aware of it and without any explicit cooperationprotocol, but just in virtue of their design and the con-text in which they operate. A form of implicit cooper-ation takes place in the system through the recurrentactions of the agents. Apart from the fact that the ob-stacle increases the cost in the system (figures 3 and 5),it does not really alter the property of cooperation (fig-ures 4 and 6).
In the case of basic agents, the speedup is approx-imately linear (even supra-linear) up to 4 agents (fig-ure 6). The control algorithm of these agents is ex-tremely sub-optimal with respect to the task; the con-text given by the presence of a few agents appears toimprove the efficiency of the control algorithm. This isalso true (but linearity only) for the case of agents withcamera in the presence of an obstacle: a single agentis greatly perturbed by the obstacle (due to its design,it can be persistently obstructed by an obstacle whengoing towards an object); the "’noise" generated by thepresence of other agents attemmtes this perturbation.Notice that in our experiments, the obstacle can hardly"trap" more than one agent at a time (due to its geom-etry).
The different types of conflict that may arise in oursystem are referred to ~s spatial conflicts and (sub-)goal conflicts. Spatial conflicts re,present the numberof times (per iteration per agvnt) an agent has beenperturbed by other agents in its neighborhood whenmoving. Figure 8 (respectiw,ly figure 10) displays thespatial conflicts that were measured in the system ver-sus the number of agents for agcnts with camera (re-spectively basic agents). (Sub-)goal conflicts (or uselessoperations) have been <Iuant iii,,d by measuring the ag-gregate number of extra operat ions done by the agentsin the system. N-1 pick-up operations are theoreticallyenough to regroup N objc,cts ~mlt~ a cell containing al-ready an object; the mmdwr of ,,xtra operations in thesystem will be determined by measuring the total num-ber of pick-up operations in the system minus the theo-retical number. Figure 7 (respectively figure 9) displaysthe (sub-)goal conflicts that were measured in the sys-tem versus the number of agents for agents with camera(respectively basic agents).
In the case of basic agents, the number of spatial con-flicts increases linearly with the number of agents: thisis expected due to their moving strategies. In the caseof agents with camera, the use of the camera stronglyreduces the parts of the space used for moving, thus in-
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creasing strongly the number of spatial conflicts as thenumber of agents grows.
In the case of basic agents, the number of (sub-)goalconflicts decreases in the system with the number ofagents ranging from 1 to 6. This is probably due to thefact that the control algorithm for these agents is veryrudimentary and therefore not optimized for a singleagent to act in the system. This relates to the supra-linearity observed in the speedup.
We have further run 400 experiments with a systeminvolving inertial agents with Alpha set to 0.3. The sizeof the environment is 9 by 9 cells and the number of ob-jects is 10 (experimental conditions identical to thoseof basic agents). Figures 11 and 12 display respectivelythe cost and the speed-up that were obtained. Figure 13displays the (sub-)goal conflicts that were measured the system versus the number of agents. Figure 14 dis-plays the spatial conflicts that were measured in the
system versus the number of agents. As for basic agentsand for the same reasons, the number of spatial conflictsincreases linearly.
We have also run 400 experiments (data not shownhere) with a system involving agents with camera withAlpha set to 0.3, for which the size of the environmentis 9 by 9 cells and the number of objects is 10 (exper-imental conditions identical to those of basic agents).Compared to basic agents, agents with camera stronglyreduce the cost. Moreover and especially for two orthree agents in the system, they reduce the number ofuseless operations. On the other hand, the range oflinearity in the speed-up is significantly reduced (espe-cially in the absence of obstacles). There are at leasttwo reasons for this optimization. The most obviousone is the use of the camera to guide movement. Theother one, less obvious, is the fact that agents keep theirdirection for a while. This last feature is found in the
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moving strategy of inertial agents. Compared to ba-sic agents, inertial agents significantly reduce the costand the number of useless operations. Furthermore, asthey exhibit a larger range of (supra-)linearity in thespeed-up, they improve the robustness of the system.
There is nowhere in the agent something encodedthat specifies where to regroup objects in the environ-ment: the location of the stack containing all the ob-jects at the end of a regrouping experiment is indeedthe result of the agents’ interactions; it depends on thenumber of agents, the number of objects and their lo-cations, the presence of obstacles and their locations.This illustrates another feature in our system, namelythat of self-organization. The presence of obstacles inthe environment influences the location of the stack, notonly due to obvious spatial constraints: it may modifythe spatial distribution of the final stacks.
In our experiments, even though we can bet on theglobal task to be achieved (from a thorough examina-
tion of the control algorithm of every agent), we can notreally preempt the manner that will be used to achievethe task nor the exact location of the final stack con-taining all the objects, due to the non determinism inthe system’s actions. With the environment depicted infigure 15 (11 by 11 cells, 20 objects and a complex ob-stacle), we have run 600 experiments involving inertialagents with Alpha set to 1, so as to study the influenceof such an obstacle on the spatial distribution of thefinal stack. Note that in this environment, the numberof free cells (that may contain objects) in the north partis the same as the one in the south part. Results on thedistribution of the locations of the stacks containing allobjects at the end of experiments suggest that certainconfigurations of obstacle do influence the outcome ofthe system. Figure 16 displays the frequencies of thelocations of the final stacks: the frequency of buildingthe stack in the north part of the environment is sig-nificantly higher than that of building it in the south
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ConclusionIn this paper, simulations of a simple system of object-regrouping agents have been presented. In our system,agents decide by themselves over time the action to takein relation to their internal state and their perception.The collective behavior (at the system level) is implic-
Figure 16: Location frequencies of the final stacks
itly driven by the individual behaviors (at the agentlevel): we can speak of a certain behavioral autonomyat the level of the system, though the autonomy is op-erational at the level of each agent. There is no super-visor in the system and the global task to be achieved,viz regrouping objects, is not encoded explicitly withinthe agents; the environment is not represented withinthe agent and there is no explicit cooperation proto-col between agents. Therefore in our experiments, the
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global task is achieved by virtue of implicit coopera-tion, where self-organization plays a role. Advantagesof such an approach are flexibility, adaptivity and faulttolerance, since agents and obstacles can be added toor removed from the system to some extent withoutrunning severely into trouble.
We pointed out different kinds of conflict. The sys-tem was observed under the effects of these forms ofconflict, instead of explicitly handling to avoid them.The results we obtained suggest that, despite the in-crease of spatial conflict, the cost can quickly be de-creased; in particular the less individual behaviors areoptimized, the higher are the chances that a strong formof cooperation (supra-linearity) takes place, and thisappears to be true in spite of several forms of conflictthat are natural to the system. Furthermore, differentconfigurations of obstacle can be used to influence thedistribution of the location of the final stacks. Findingsome means to control an autonomy-based multi-agentsystem so as to compel it to fulfill some specific taskswould indeed be very profitable.
AcknowledgementsThis work is financially supported by the Swiss NationalFoundation for Scientific Research, grants 20-05026.97and 21-47262.96.
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