The call of duty: Self-organised task allocation in a population of up ...

Robotics and Autonomous Systems 30 (2000) 65–84

The call of duty: Self-organised task allocation in a population of up totwelve mobile robots

Michael J.B. Kriegera,1, Jean-Bernard Billeterb,∗,2

a Institute of Ecology, University of Lausanne, 1015 Lausanne, Switzerlandb Laboratoire de Micro-informatique, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland

Abstract

Teams with up to 12 real robots were given the mission to maintain the energy stocked in their nest by collecting food-items.To achieve this mission efficiently, we implemented a simple and decentralised task allocation mechanism based on individualactivation-thresholds, i.e. the energy level of the nest under which a given robot decides to go collect food-items. Theexperiments show that such a mechanism — already studied among social insects — results in an efficient dynamical taskallocation even under the noisy conditions prevailing in real experiments. Experiments with different team sizes were carriedout to investigate the effect of team size on performance and risk of mission failure. ©2000 Elsevier Science B.V. All rightsreserved.

Keywords:Collective robotics; Task allocation; Division of labour; Self-organisation

1. Introduction

In human and other social groups with advancedlabour division, life is organised around a series ofconcurrent activities. For a society to function effi-ciently, the number of individuals (team size) involvedin these activities has to be continuously adjusted suchas to satisfy its changing needs. The process regulat-ing team size — and thus modulating labour division— is called task allocation. It can be evident whencentralised and embodied in a special agency (like aforeman dispatching men on a working site) or it can

∗ Corresponding author. Tel.: +41-22-7400094; fax: +41-22-7400094.E-mail address:[email protected] (J.-B. Billeter).

1 Present address: Department of Entomology and Department ofMicrobiology, University of Georgia, Athens, GA 30602, USA.

2 Laboratoire de Micro-informatique, EPFL, http://diwww.epfl.ch/lami

be less visible when decentralised (as with neighboursproviding unsupervised help after an earthquake). Be-hind the diversity of possible task allocation mecha-nisms lays a common structure: they all act at theindi-vidual level, prompting individuals either to continueor to change their activities (Fig. 1). The conditionthat triggers the change to another activity may be asimple rule of thumb or a complex decision-makingprocedure.

Task or role3 allocation has been extensively stud-ied in social insects (e.g. [6,10,13,15,26–28,32,33]).The study of task allocation in social insects isparticularly interesting since their labour division and

3 The wordstask, activity and role may often be used one forthe other, as in “My task, activity, role, is to sweep the yard”.Still, taskspecifies “what has to be done”,activity “what is beingdone”, androle “the task assigned to a specific individual withina set of responsibilities given to a group of individuals”.Castedefines a group of individuals specialised in the same role.

0921-8890/00/$ – see front matter ©2000 Elsevier Science B.V. All rights reserved.PII: S0921-8890(99)00065-2

66 M.J.B. Krieger, J.-B. Billeter / Robotics and Autonomous Systems 30 (2000) 65–84

Fig. 1. Individual choice between two activities.

its regulation are organised by surprisingly simple androbust means. Task allocation within insect colonieswas considered a rigid process. The different activitieswere associated with different castes and caste poly-morphism was related to genetic or internal factors[11]. At the same time, other observations indicatedthat individuals could change activity during their lifespan [27,32], suggesting other than genetic factorsbeing relevant for task allocation. These findings havelet to reformulate the caste definition based purelyon morphological or genetic criteria to incorporateage or simple behavioral differences [13,27]. Thus,recent research on task allocation in social insectsconcentrates on behavioral flexibility and stresses theimportance of external and decentralised factors likepheromones or individual encounters [5,25]. One ofthe most inspiring models to explain this decentralisedand flexible task allocation found in social insects isthe activation-threshold model.

In the activation-threshold model, individuals re-act to stimuli that are intrinsically bound to the taskto be accomplished. For instance, neglected brood orthe corpse of dead ants diffuse an odour of increasingstrength. When this stimulus reaches an individual’sthreshold value, the individual reacts by adopting therelevant activity (in our example: grooming the broodor carrying the corpse out of the nest) or by increas-ing its likelihood to do so. This is a proximal mech-anism: individuals closer to the work to be done aremost likely to be recruited. Moreover, if the individualsdo not have the same threshold value, the recruitmentis gradual, which may allow regulation of the teams’sizes [6,26,27]. Indeed, Bonabeau et al. [4] have shownthat such a simple activation-threshold model “. . .

can account for the workers’ behavioral flexibility”. 4

Similarly, models in sociology have shown that sim-ple reaction-threshold differences among individualsmay lead to complex social dynamics [9,30]. The pur-pose of the experiments described below was to testthe efficiency of the activation-threshold mechanismfor task allocation in practical robotics.

The regulation of a group of robots engaged in sev-eral concurrent activities involves regulating the teammembers’ activity in real time (dynamical task allo-cation). A variety of mechanisms may achieve taskallocation, however, when working with real mobilerobots whose perceptions, communication and actionsare reckoned to be limited, it is advisable to selecta mechanism for its simplicity and its robustness. Agood candidate for a robust and simple task alloca-tion mechanism is the activation-threshold mechanismdescribed above [6,26,27]. Its task-related recruitingstimuli increase when the tasks to be accomplishedare neglected, acting as a feed-back. In a team ofNagents whose choice of activities is limited to two,neglecting the first activity (because too many indi-viduals are engaged in the second activity) causes thestimulus for the first activity to increase, promptingindividuals to change from the second to the first ac-tivity; and conversely (Fig. 2). Choosing appropriateactivation-thresholds is crucial for the performanceof the robot team since individuals with the sameactivation-thresholds and exposed to the same stim-uli switch activity at the same time, yielding gen-erally a poor regulation. Hence, one of our objec-tives was to show that simply implementing differentactivation-thresholds is sufficient for an effective taskallocation mechanism in robotic experiments.

4 The idea of activation-threshold might seem a truism since anychange can be brought back to the fact that a variable crossed athreshold! What the model wants to stress is theorigin and thesimplicity of the activation variable directly tied to the recruitingactivity. In the case of corpse carrying witnessed among someant species, the stimulus is a natural by-product of the corpsedecomposition, namely oleic acid. We are all familiar with thistype of mechanism: when there is a smell of gas, we go checkthe gas-range; when there is a smell of cheese, we put the cheeseaway into the refrigerator. The point, however, is that social insectsseem to regulate all their colony activities in this way, whereas,among humans, the dynamical allocation of workforce betweenthe different trades is a rather complex procedure including con-siderations of aptitudes, tradition, interest, openings, wages, etc.

M.J.B. Krieger, J.-B. Billeter / Robotics and Autonomous Systems 30 (2000) 65–84 67

Fig. 2. Individual choice between two activities with a fixedactivation-threshold. Neglecting activity 1 causes the stimulus foractivity 1 to increase, prompting individuals to change from ac-tivity 2 to activity 1; and conversely.

From the biologist’s point of view, the purpose ofthese experiments is to contribute a piece of heuristicevidence that complex social systems may be organ-ised on decentralised organisation principles. Centralto sociality is labour division, with its correlates ofspecialisation, cooperation and task allocation. As wehave seen above, social insects are thought to organ-ise an important aspect of labour division, i.e. taskallocation, in a decentralised manner where each in-dividual’s decision is made according to a simple setof rules based on local information only. Many com-plex patterns and collective behaviours observed atthe colony (macroscopic) level emerge as the aggre-gated result of the decentralised interactions at theindividual (microscopic) level. This mode of organ-isation, termed self-organisation [19], could accountfor many collective phenomena found in social in-sects [8]. Other authors used successfully mathemat-ical models of self-organisation to model either spe-cific behaviours (e.g. [35,37]) or whole insect colonies[3,20,21]. Yet it is difficult to prove unequivocally thatself-organisation is the main mechanism operating in

social insect societies and that all complex collectivebehaviours emerge from interactions among individu-als with simple stereotyped behaviours.

Our experiments intend to bring heuristic evidence,and thus shed some light on two questions: first, canwe imagine plausible mechanisms of automatic anddecentralised control for insect societies; and secondly,do these mechanisms account for or lend themselvesto the gradual evolution from a solitary individual sys-tems to sociality? Such a gradual evolution implies thatthe transition from the ancestral, solitary state to a so-cial system is beneficial. Hence, individuals in simpleaggregations have to have a better pay-off than solitaryindividuals, and individuals in groups with coopera-tive interactions have to outperform individuals in ag-gregations. Since not all animals live in social systemsit follows that these conditions are not always given.One element which has proven to influence social or-ganisation are environmental factors. Among them,the distribution of food and its availability was identi-fied as one of the key features [1,7,17,29]. Therefore,we also examined the influence of different food dis-tributions on social organisation. However, it shouldbe stressed that our robots do not mimic any specificsocial insect species and therefore, no binding conclu-sion can be obtained by the comparative study of ourrobots’ behaviour and the behaviour of social insects.

2. The robots’ mission

2.1. The mission

The robots’ mission was to search and collect“food-items” in a foraging area (Figs. 3 and 4) andbring them back to the “nest” (Figs. 3 and 4) inorder to keep the nest-energy at a safe level. Theirenergy consumption was activity-related: it was lowwhen they were inactive in the nest, increased whenthey moved around and reached a maximum whenthey were carrying a food-item. For the robots toachieve their mission efficiently, i.e. using globallyas little energy as possible, we dispersed their indi-vidual activation-thresholds to avoid that the robotsleave the nest simultaneously (for comments on theactivation-threshold distribution, see Section 5.1). Theactivation-thresholds were equidistributed between3/4 and full initial nest-energy. This simple task allo-


Fig. 3. The experimental set-up. Experiments were carried out on a 9.24 m2 surface with a nest and a foraging area. The entrance ofthe nest was signalled by a light beacon. Next to the entrance, the robots unloaded the collected food-items into a basket. Depending onthe experiment, the food-items were either grouped in two patches of 12 food-items each (clumped food-items) or placed singly at sixlocations (isolated food-items).

cation mechanism resulted in a good modulation ofthe number of individuals engaged in the two possi-ble activities: staying in nest (inactive), and foraging(active). All robots were able to execute either of thetwo tasks and, depending on the situation, were ableto switch from one to the other. They had no priorknowledge about the number and the distribution pat-tern of the food-items, or about the robot team’s size.

2.2. Basic mission cycle

The basic mission (Fig. 5) can be described withthe following pseudo-procedural instructions:1. Wait in nest

• If a robot ahead leaves the waiting line, compactthe waiting line by moving forward.

• Keep listening to control-station’s radio messagesthat periodically update the nest-energy level.

• Radio to the control-station the energy you havebeen consuming while waiting in the line. In thesame time refill your personal energy store.

• Leave the nest when the radioed nest-energylevel is lower than your personal activation-threshold.

2. Leave nest• Leave the waiting line and move to the exit-lane.• If there are other robots, slow down and give way.• Follow the exit-lane; at its end turn left and leave

the nest.(Once the robot has left the nest, it is not updatedanymore about the current nest-energy level, norcan it inform the control-station about its energyconsumption. During this time the robot dependsentirely on the energy of its personal energy store.At the same time the robot keeps track of its energyconsumption.)

3. Look for food-items• Start a random search for food-items. Or, if you

already know where to find one, try to returnto the spot using odometry (a helpful but not avery robust localisation method, since any freespinning of the wheels will cause the odometry


Fig. 4. An experiment under way (for schematic representation see Figs. 3 and 5).

Fig. 5. Mission cycle.


to be inaccurate). If you have reached the spotwhere you previously detected a food-item butyou do not detect one, start a random search.

• If you have used up your personal energy storereturn to the nest (ignoring step 4 and 5).

• When you detect a food-item, load it.4. Load food-item

• Turn toward food-item, recede a bit, open thegripper, lower the arm, move forward until grip-per’s optical barrier is broken.

• Close the gripper, raise the arm.5. Evaluate site

• Check the vicinity for the presence of morefood-items.

• If you detect one, turn on your odometry.6. Return to nest

• Head toward the nest using the light beacon at itsentrance.

• When reaching the nest’s entrance, radio yourenergy consumption and recharge the personalenergy store.

(Recharging is a data exchange with no visible be-haviour associated.)

7. Unload food-item• Go to the basket and unload your food-item.• If the nest-energy level is higher than your

activation-threshold, stay in the waiting line, oth-erwise exit the nest. If you stay in the nest, eraseany information about locations of food-items

Back to 1

2.3. Mission cycle with information exchange

In a second series of experiments, we introduceda simple coordination among the robots. Robots thatdetected a food source were able to recruit and guideother robots to this food source (robots can record theposition of food-item patches with their odometry).This was inspired by the tandem recruiting-behaviourobserved in the antCamponotus sericeus[12]. Tworeasons lead us to chose such a behavior based re-cruitment: first, it represents a type of communicationwithout symbolisation which probably established it-self very early during social evolution and secondly,such a mechanism scales up without problems (i.e. canbe used with larger groups), whereas radio transmis-sions relaid by a central base create communicationbottlenecks.

Recruitment was executed just before the robot wasabout to return to the food patch where it previouslyfound food-items. The recruiting itself was rather sim-ple; the recruiting robot approached the robot at thehead of the waiting line, which was the signal for thewaiting robot to follow (Fig. 6). To incorporate in-formation exchange among the robots the followingadditions to the mission cycle were made:• To the robots waiting in the nest:

– If you are heading the waiting line, you are a po-tential follower: be ready to be asked to tandem.

– Once you have been asked to tandem, follow theleading robot until you lose it. When you havelost it, start a local search for the food-items.

• To the recruiting robots:– If you know where to find more food-items, try

recruiting the robot heading the waiting line, byapproaching the one to be recruited to a closedistance (about 5 mm).

– Go slowly toward the food source. When youhave reached it, decouple the tandem by makinga fast move forward, wait a while and go backto collect food-items. (By making a fast moveforward the leading robot gets out of the sensoryfield of the follower, which serves as a signal toindicate the arrival at the food patch.)

3. Experimental setup

3.1. Data acquisition

Radio communication was strictly used for control-ling the experiment and for sending data from therobots to the control station for later analysis. The op-erator could initialise the robots from his computer, aswell as start, suspend, resume or stop an experiment.The messages were not broadcast simultaneously toall robots: every robot was individually addressed anda message was considered received only when echoedproperly to the radio base and displayed on the controlstation screen. Every 10 to 20 seconds a data requestwas initiated from the control station to the robots. Therequest signal was radioed together with nest-energy,the only information used by the robots to allocatetasks. The robots were programmed to consider andupdate this external variable while inside the nest, butto ignore it when outside, reflecting the fact that they


Fig. 6. Tandem recruitment. (a) Recruiting robot (r) backs up toward the waiting robot (w) at the head of the waiting line. When w’sproximity sensors detect r, w goes into follower mode. (b) Recruited robot (w) follows recruiting robot (r) to the food patch.

do not know the evolution of nest-energy while work-ing outside the nest. In return, the robots updated thecontrol station on their current activity and energy con-sumption for the statistical analysis.

3.2. Experimental procedure

The experiments were carried out on a 9.24 m2 sur-face tiled with 64 printed boards (0.38 m× 0.38 m)(Figs. 3 and 4) with copper strips alternatively con-nected to the two poles of a direct current power sup-ply. The floor was bordered by a wall. Along thewall, a black line was painted on the floor to facilitatethe distinction between the wall and the food-items(for a detailed description see Section 3.5). The nest,whose entrance was signalled by a lamp, was also en-closed with black footed walls. Inside the nest and inits close proximity, black lines were used as tracksfor easy navigation (Fig. 4). Next to the entrance, therobots unloaded the collected food-items into a bas-ket (Figs. 3 and 4). The food-items were small plasticcylinders (3 cm diameter× 3 cm height) with narrowstrips of infrared reflecting tape. Depending on theexperiment, they were either grouped in two patchesof 12 food-items each (clumped food distribution), orplaced singly at six locations (dispersed food distri-bution). All food-items were replaced soon after theywere seized by the robots.

We conducted three types of experiments (Table1): food search in an environment with a dispersedfood distribution, food search in an environment witha clumped food distribution both without recruitmentand finally food search in an environment with aclumped food distribution with recruitment. Each type

Table 1Each type of experiment was repeated eight times (the experimentwith group size one was dropped in Series C for an obviousreason: a single robot cannot recruit another robot)

Recruitment Food distribution Group size

Series A No Dispersed 1 3 6 9 12Series B No Clumped 1 3 6 9 12Series C Yes Clumped 3 6 9 12

of experiment was carried out with groups of one,three, six, nine and twelve robot teams, with the ex-ception of the experiments with recruitment, where theexperiments with group size of one were omitted sincerecruitment involves at least two robots. All experi-ments were repeated eight times (112 experiments intotal) and had a duration of 30 minutes. Before the startof the experiment, all robots were positioned inside thenest. The only deliberate difference among them wastheir activation-threshold whose values were equidis-tributed between 3/4 of and full initial nest-energylevel. In order to allow comparisons between differentteam sizes, the initial nest-energy was proportional tothe number of robots participating in the experiment.A typical experiment with six robots is shown in Fig. 7.

3.3. Statistical data analysis

Two series of analysis were carried out. First, theeffect of the two different food distributions (clumpedversus dispersed) was investigated using the twotypes of experiments without recruitment and, sec-ondly, the effect of recruitment (recruitment versusnon-recruitment) was investigated using the two typesof experiments carried out in the environment with a


Fig. 7. A typical experiment with six robots. (a) Nest-energy; (b) number of active and inactive robots. At the beginning (a), none of therobots is active. As nest-energy decreases (b), the robots progressively leave the nest. At time 800 s (c), all six robots are active. Theirharvest is good, which results in a nest-energy higher than the initial nest-energy (d). As a consequence the robots switch to the inactivemode and stay in nest, as all of them have done by time 1200 s (e). But as nest-energy decreases again (f), the robots resume their foodsearch. At the end of the experiment all but one robot are inactive in the nest (g).

clumped food distribution. Statistical tests were con-ducted with ANOVAs [34]. Performance was calcu-lated as the inverse of the total energy used during thecourse of the experiment. Robustness was measuredas the lowest nest-energy recorded during the exper-iment. Values closer to zero indicate a higher risk ofsystem collapse since the system was considered tohave crashed when nest-energy dropped below zero.To assess the relative amount of work done by eachteam member a skew measure [22] was used. This

measure allows to quantify the skew in individualcontributions to a global task and ranges from zeroto one. A skew of one indicates that one team mem-ber was doing all the work whereas a skew of zeromeans that all team members contributed equally tothe global task. The skew can be calculated with thefollowing formula:

S =(

N − 1∑p2

i

)/(N − 1) ,


where N is the number of individuals in the groupandpi the relative contribution of team memberi.

3.4. The robots

We used Khepera5 robots with three additionalmodules: a gripper turret, a custom-made detectionmodule, and a radio turret (Fig. 8). The Khepera’s ba-sic module is a miniature mobile robot designed as aresearch tool at the Laboratoire de Micro-informatiqueof the Swiss Federal Institute of Technology at Lau-sanne [18], and now produced by K-Team SA.6 Forour experiments, we redesigned the Khepera’s basicmodule, adding four floor contacts plus a regulator forcontinuous power supply (allowing long experimentswith additional turrets) [16], three floor-oriented IRsensors for floor readings and a castor wheel (Fig. 9).The main specifications of the Khepera’s basic mod-ule are:

Diameter 55 mmMotion 2 DC motors with incremental encoder

(about 10 pulses per mm of advance)Power Rechargeable NiCd batteries or externalAutonomy About 45 minutes (maximal activity,

no additional module)Sensors Eight infrared proximity and light

sensorsProcessor Motorola 68331RAM 256 KbytesROM 128 or 512 Kbytes

3.5. Additional modules

The gripper turret is a standard Khepera modulewith an arm moving from the front to the back, plusthe gripper whose jaw can seize objects up to about55 mm. An optical barrier detects the presence of ob-jects between the jaws, and conductive surfaces (notused in our experiments) measure the electrical con-ductivity of the object seized.

The detection modulewas custom-made featuringtwo detection units: an ambient light detector and an

5 Robot Khepera: http://lamiwww.epfl.ch/Khepera/#khepera.6 K-team: http://diwww.epfl.ch/lami/robots/K-family/K-Team.html.

optical barrier (light modulation photo IC). The am-bient light detector was used by the robots to navi-gate back to the nest which was signalled by a lightbeacon. The optical light barrier was used to distin-guish the three basic objects present in our experi-ments: walls, food-items and other robots. Distinc-tion between the three basic objects was achieved inthe following way: When the standard IR sensors de-tected the presence of an object, the robot made twoadditional readings: floor reflection and optical bar-rier status. If the floor reflection was low, signallingblack painting, the robot was near a wall. An unbro-ken optical barrier indicated that another robot — theonly object high enough to reflect its beam — wasfacing the robot. If the floor reflection was high (ab-sence of black painting), and the optical barrier wasbroken (absence of other robots), the robot was facinga food-item. The programs used to detect the three ba-sic objects were run continuously and in parallel, oc-casional misinterpretations were usually resolved bythe frequent double-check procedures included in theprogram.

Theradio moduleis a standard Khepera turret usinga low power 418 MHz transceiver [16]. A communi-cation protocol allows complete control of the robot’sfunctionality through an RS232 serial line.

3.6. Control architecture

Goal of the robots’ control architecture (Fig. 10)was to achieve the desired functionality by the properconnection of the three units: Sensory, Motor and Pro-cessing unit. It can be considered as a black box anddoes not claim any biological relevance to social in-sects.

The Sensory unit took measurements in the envi-ronment and sent associated signals to the Process-ing unit. Apart from the sensors described in Sections3.4 and 3.5, the robot also received sensory feed-backfrom its own motor actions through incremental en-coders for the wheel motors, and potentiometers forthe arm and gripper. The Motor unit executed thecommands sent by the Processing unit. Four differentmotors were addressed: left wheel, right wheel, grip-per’s arm and gripper itself. Motor actions were as-sociated with an energetic cost — purely mathemati-cal — which was subtracted from the robot’s energy


Fig. 8. (a) A Khepera robot with three additional modules: a gripper turret (bottom), a custom-made detection module (middle), and aradio turret (top). (b) A Khepera robot loads a “food-item”.


Fig. 9. Modified base. Contacts for continuous power supply (a), floor-oriented IR sensors (b) and castor wheel (c).

level (physiology). The Processing unit consisted oftwo parts, the Decision unit for activating and deacti-vating small programs, and the programs themselves(Fig. 10). The Decision unit receives inputs from threesources:• the physiological variable set;• the conceptual tags (= classified sensor inputs);• the drives.

The only physiological variable considered in ourexperiments was the robot’s energy level, and the onlydrive used was hunger.

At anytime, depending on the inputs, the Decisionunit decided to either activate or deactivate a pro-gram. For instance, when a robot had left the nest,the program “Follow nest tracks” was deactivatedand “Search for food” was activated or when a robotreached the nest “Return to nest” was deactivated and“Follow nest tracks” was activated. The programsthemselves had one or several inputs and generated a

corresponding output (for details, see below). Oncea program was activated, it ran concurrently withall other activated programs until deactivated (thisis facilitated by the multi-tasking capabilities of theKheperas). Some programs had a higher priority andunder certain conditions could override other runningprograms. The programs were categorised into fourdistinct classes depending from which unit they re-ceived their inputs and to which unit they sent theiroutputs.1. Input: Sensory unit, output: Processing unit (“Per-

ception”)These programs classified the inputs they receivedfrom the Sensory unit into conceptual tags like “ob-stacle”, “dark floor” or “object in the gripper”. Eachconceptual tag was considered a user pre-definedconcept.

2. Input: Processing unit, output: Processing unit(“Thoughts”)


These programs received one or several conceptualtags as an input and generated another conceptualtag as an output. Example: When both the proposi-tions “there is an obstacle” and “the floor is dark”are confirmed, the Processing unit generates theconcept “wall”.

3. Input: Processing unit, output: Motor unit (“Inten-tional Actions”)These programs used conceptual tags from the Pro-cessing unit to engage specific motor actions. Forexample, after having positively checked the propo-sition “there is a food-item in the gripper”, therobot closed its gripper and lift its arm to transportposition.

4. Input: Sensory unit, output: Motor unit (“Re-flexes”)Reflexes were programs which had to be exe-cuted fast. They received inputs directly from the

Fig. 10. Control architecture of the robots. The control architectureis made out of three main parts: the Sensory unit, the Processingunit (consisting of a Decision unit for activating and deactivatingprograms, and the program themselves), and the Motor unit. TheSensory unit translates the outside world into internal variables,the Processing unit uses these variables to create more complexvariables or to instruct the motor unit to perform an action, andthe Motor unit translates internal commands into a physical action.Depending on the inputs (conceptual tags, drives, physiology), theDecision unit decided to either activate or deactivate programs.The programs were categorised into four distinct classes dependingfrom which unit they received their inputs and to which unit theysent their outputs (for more details see Section 3.6). SIS = sensoryinput signal, CT = conceptual tag, MAC = motor action command.

Sensory unit and generated immediate motor ac-tion. No concepts were generated. Example: Theobstacle avoidance routine.

4. Results

Our experiments showed that an artificial, com-plex system can be regulated using a simpleactivation-threshold as the only control parameter.Nest-energy, the variable to be regulated, was stableand stayed in the experiments with the three, six andnine robot teams well above the activation-thresholdof the robot with the lowest activation-threshold (Fig.11). Only in the experiments with the teams of 12robots, a steady decrease in nest-energy was observed(Fig. 11). Moreover, the activation-threshold allowsshifting from a single individual to a multi-individualsystem without any additional changes. This mech-anism has proven well adapted to task allocation inrobot teams.

4.1. Effect of group size and food distribution onperformance

The effect of the group size and food distributionwas tested using a 2-way ANOVA. The size of therobot team had a significant effect on their perfor-mance (2-way ANOVA, group size: df = 4,1,F = 4.72,P= 0.002). The relative performance, where the bestrobot team has a performance of 100%, was 88.9%,99.5%, 100%, 91.5% and 91.6% for teams of one,three, six, nine and twelve robots, respectively. In bothenvironments the one robot teams had the lowest per-formance whereas the three and the six robot teamshad the highest performance. Performance among thegroups of one, nine and twelve as well as betweenthe groups of three and six was however, not sig-nificantly different (Fisher’s PLSD, 5%). When thefood-items were grouped in patches the robots had asignificantly better performance (2-way ANOVA, fooddistribution: df = 4,1,F = 12.87,P< 0.001). The rela-tive decrease in performance in the environment withdispersed food-item was 7.7%. Yet the difference inperformance among the various group sizes was dif-ferent for the two food distributions. The relative in-crease in performance for robot teams of three and sixwas more pronounced in the environment with dis-persed food-item distributions (Fig. 12).

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Fig. 12. Performance relative to the one robot teams in an environment with clumped and a dispersed food distribution with no informationsharing. Performance was measured as the inverse of the total energy used and the normalised for the number of robots.

4.2. Effect of information sharing and group size onperformance

When the location of the food patches were trans-mitted by recruiting and guiding a team member to thepatch, the performance of the group increased signifi-cantly (2-way ANOVA, information sharing: df = 3,1,F = 39.93, P< 0.001). The increase in performancewas 13%. Again, group size had a significant effecton performance (2-way ANOVA, group size: df = 3,1,F = 6.87,P< 0.001) with the best performance in thethree and the six robot teams.

4.3. Interferences in an environment with clumpedfood-item distribution

Interferences among robots was defined whenevera robot tried to perform a task, but was hinderedby another robot. The proportion of time spent insuch interferences increased significantly with in-creasing group size (2-way ANOVA, group size:df = 3,1, F = 6.33, P= 0.003). The mean proportion

of time spent in an interference was 0.4%, 0.6%,1.0%, 2.3% for teams of three, six, nine and twelverobots, respectively. However, a post hoc analy-ses revealed (Fisher’s PLSD, 5%) that only thetwelve robot team spent significantly more time ininterferences.

4.4. Effect of group size and food distribution onrobustness

The size of the robot team had a significant ef-fect on the minimal nest-energy recorded (2-wayANOVA, group size: df = 4,1,F = 5.41, P< 0.001).Groups with a larger number of robots had a higherminimal nest-energy (Fig. 13). Except for the twelverobot team, which had a higher minimal nest-energythan the minimal nest-energy recorded for onerobot team but a lower compared to all other groupsizes. The effect of the food distribution on theminimal nest-energy recorded was not significant(2-way ANOVA, food distribution: df = 4,1,F = 3.18,P= 0.079).


Fig. 13. Minimal nest-energy recorded during the experiments with no information sharing for the teams of different group size. Theminimal nest-energy was normalised for the number of robots. Error bars indicate the 95% confidence interval.

4.5. Effect of information sharing and group size onrobustness

Information sharing had a positive effect on the ro-bustness of the robot teams. The minimal nest-energyrecorded during the experiment was higher in teamswith information sharing, with an average of 2147and 1870 in the experiments with and without in-formation sharing, respectively. This difference washighly significant (2-way ANOVA, information shar-ing: df = 3,1, F = 11.77, P= 0.001). Again, groupswith a larger number of robots had higher minimalnest-energies with the exception of the twelve robotteams (2-way ANOVA, group size: df = 3,1,F = 3.10,P= 0.034).

4.6. Work skew among the robots

Due to their different activation-thresholds, therobots spent unequal amounts of time in the activeforaging state. This skew in activity among the teammembers was expressed using the skew index. Largergroups had better share-out of their work load indi-cated by the mean work skew of 0.370, 0.345, 0.197and 0.172 for the three, six, nine and twelve robot

teams, respectively. This difference in work skewamong the teams of different group sizes was signifi-cant (2-way ANOVA, group size: df = 3,1,F = 13.03,P< 0.001). In contrast, information sharing had nosignificant effect on the work skew (2-way ANOVA,information sharing: df = 3,1,F = 0.421,P= 0.519).

4.7. Time active

Information sharing decreased significantly thetotal time the robots spent in the active (working)state (2-way ANOVA, information sharing: df = 3,1,F = 6.86,P= 0.009). Robots with information sharingspent on average 48% of their time in an active statewhereas the robots without information sharing 56%.However, this was not true for all team members(Fig. 14). When the robots were categorised accord-ing to their activation-threshold into three thresholdclasses (high, middle and low) the robots with thelowest thresholds spent significantly more time inthe active state as the robots of the same thresholdclass with no information sharing (ANOVA, df = 1,F = 4.76,P= 0.031). This was due to recruitment fromother team members when inactive in the nest.


Fig. 14. Proportion of time spent in an active (working) state depending on the threshold class and information sharing. The robots werecategorised according to their activation-threshold in one of the three classes (high, middle, low). Error bars indicate the 95% confidenceinterval.

5. Discussion

5.1. Threshold control

During our experiments the nest-energy never de-creased below zero. This held under a variety of differ-ent experimental settings such as various group sizes,different food distributions and presence or absence ofinformation sharing. This result suggests that complexsystems as our artificial ant colony can be regulatedwith a single control parameter in a decentralised way;it also indicates that this mode of task allocation canbe favourably used in practical robotics.

Apart from its efficiency and simplicity, theactivation-threshold mechanism presents a secondadvantage: it allows to control single as well asgroups of robots. Simply choosing a differentactivation-threshold for each robot results in an au-tomatic adjustment in number of active robots to thecurrent work load. This has positive implications forfuture robot applications. Imagine a system whereseveral robots could work collectively on a given task.Due to financial or other reasons, only one robot isengaged at the beginning. Later, when more robots areadded to the system, no special arrangements besidechoosing different activation-thresholds have to be

made to move from a single to a multi-robot system.Likewise, when the number of robots is reduced eitherby individual failures or by allocation of some robotsto other work areas, no changes have to be made in thecontrol program of the robots. This might even repre-sent a more substantial advantage since robot teamscould be left unsupervised, individual breakdownshaving little effect on such a coordination scheme.

As already mentioned, the individual activation-thresholds were equidistributed between a lowerand an upper value. Using other distributions be-tween these two limits might modify the regula-tory characteristics of the mechanism. Although wedid not pursue the experiments in this direction,we speculate that any reasonable distribution ofactivation-thresholds would yield equivalent results.There is no reason to consider equidistribution best;we chose it for its simplicity. Also, on account of thenoisy context of practical robotics, the exact values ofactivation-thresholds are but of minor interest. Amongother possible activation-threshold distributions, therandom distribution is of special interest since thereis no need to preset the thresholds by an opera-tor. In our experiments, we had to preset a specificactivation-threshold for each robot at the beginning ofthe experiments. In contrast, a random distribution of


activation-thresholds would allow to fix a same lowerand upper limit for all robots from which each robotdraws individually its activation-threshold.

5.2. Performance

The size of the robot team had a significant effecton their performance, with teams of three and sixperforming better than single robots or larger groups.This finding is caused by a trade-off between thepositive and the negative effects of robot–robot in-teractions. Robots were programmed to avoid eachother which results in better coverage of the for-aging arena when several robots are present. Thisis because each robot will avoid an area where an-other robot is already foraging. This effect causedsingle robots to perform less efficiently than smallgroups of robots. However, when the number ofrobots increases, those robot–robot encounters havealso negative consequences. First, robots avoidedmore often areas with food-items because on av-erage more robots were already present at loca-tions with food-items. This was especially impor-tant in the environment where the food-items weregrouped in patches. Secondly, robots seized simul-taneously the same food-item more often, causingone of the robots to leave empty handed. Finally,larger groups spent more time in interferences at theentrance or inside the nest (see also Section 4.3).Thus, single robots could not benefit from the posi-tive effect of robot–robot interactions found in smallgroups, whereas in large groups the negative effectof the robot–robot interactions overthrew the positiveones.

A second result was that the optimal group size wasdifferent for each of the two food distributions. Thissuggests that under some environmental conditions thebenefit of living in group of a particular size is largewhereas under other conditions the benefit is modest.Observed animal groups’ sizes, which are assumed tohave evolved and optimised, can be correlated to eco-logical factors (e.g. [7,14,17]). Furthermore, the rel-ative increase or decrease in performance from onegroup size to another was different in the two envi-ronments (Fig. 12). For example the decrease in per-formance from a six to a nine robot team was largewith the dispersed food distribution but relative smallwith the clumped food distribution. This indicates that

under some ecological conditions, a change in groupsize is very likely to happen whereas under other con-ditions this shift is unlikely to occur.

5.3. Robustness

The risk of mission failure was measured as theminimal nest-energy recorded during the experiments,since a nest-energy below zero would have ended theexperiment. Our results show that the larger the sizeof the team, the lower the risk of mission failure. Thisresult holds for all group sizes with the exception ofthe twelve robot team. The twelve robot team hada lower risk than the one robot team but a higherrisk than the three, six and nine robot teams (Fig.13). The risk of mission failure however, should notbe confounded with the performance of the system.Performance was measured as the inverse of the totalenergy used and hence measures the teams’ efficiencyof accomplishing the task (keeping the nest-energy ata safe level). In contrast, the risk of mission failureindicates how close the system was to a nest-energyof zero anytime during the experiment. The apparentcontradictory result of the three and six robot teamhaving the best performance but not the lowest risk ofmission failure stems from the fact that smaller teams’nest energies fluctuate more widely.

In the experiments with groups of three, six andnine robots, the nest-energy usually stayed above thelowest activation-threshold (Fig. 11). As a result, atleast one of the robot was still inactive in the nestand hence, the system did not reach its full capacity.A different picture emerged in the experiments withtwelve robots. Even if the final nest-energy neverfell under half the initial nest-energy (Fig. 11 (a)),the energy curve showed in all three experimentalset-ups a tendency to steadily decrease. This suggeststhat in longer experiments the nest-energy wouldhave reached zero and hence the system would havecrashed. From our observations it was the interfer-ences between the robots that made the system lesseffective. Indeed, a detailed analysis of the robot’sbehaviour in the patchy environment (with and with-out information sharing) revealed that the time spentin interferences increased with increasing group size.This shows that a given experimental set-up (sizeof the environment, number of food-items) supportsonly a limited number of robots, around 12 with the


mission we chose for our experiments. This is similarto a phenomenon found in ecology termed carryingcapacity, which is defined as the maximum populationsize that can be supported by a given environment[2].

5.4. Information sharing

Sharing the information of the location of thefood patches by recruitment had a positive effecton performance, resting time and robustness. Theincreased performance was due to the fact that notall robots had to search for their own food patch,which resulted on average in more efficient food re-trievals. Thus, the robot teams needed less time tomaintain the nest-energy. However, this was not thecase for all team members. The robots with a lowactivation-threshold had to work significantly moreunder this scheme since they were more likely to berecruited for work when inactive in the nest. Thisphenomenon is useful since it allows teams organisedwith gradual activation-thresholds to distribute thework load more evenly among their members.

The increased robustness originated from theearly recruitment of inactive robots. In the experi-ments without recruitment the robots left the nestonly when the nest-energy was below their personalactivation-threshold. This mechanism caused a largedelay between the signal (low nest-energy) and theresponse (retrieving a food-item) which in turn re-sulted in greater fluctuation of the nest-energy. Thisdelay was much smaller in the experiments with re-cruitment since some robots became already active(by recruitment) at nest energies where they normallywould have stayed inactive in the nest.

5.5. Scaling up

As mentioned above (Section 2.3) informationexchange by tandem recruitment scales up easilywith the number of robots. The same holds for thefixed-threshold dynamical task allocation, especiallyif the activation-thresholds are drawn randomly be-tween two preset limits. Whether the number of activ-ities scales up as easily as the tandem recruitment andthe activation-thresholds remains to be investigated.

5.6. Why not settle for a simulation?

Demonstrating by simulation that a fixed activation-threshold mechanism can properly regulate teams ofsimulated robots is not enough for practical robotics.Computer simulation is a powerful and essential toolfor robotics. Still there is no warranty that an algo-rithm tested with simulation will work practically withrobots. First, real robot–robot and robot–environmentinteractions are more complex and unpredictablethan their simulation. Secondly, a real environment,however simple, is subjected to its own dynamicsand puts the robots up to a set of constraints usuallyimpossible to list and model. Sometimes, especiallywhen the robot’s activities are restricted to movingon a smooth surface, simulation yields excellent re-sults. But as soon as the interactions between robotsand their environment increase, for instance whenthe robots seize objects or when the lighting condi-tions are not constant, practical experiments rapidlydiverge from their simulations. Even if not mentionedby technical articles, nor seen on videos, autonomousrobotics experiments are frequently marked by tech-nical problems. Only mechanisms proven effective insuch difficult environments should be considered. Theultimate test, in experimental robotics, is the practicaltest. In addition, experimentation is rich in unantici-pated interactions which will not occur in simulations,most of them negative, some of them positive. Thelatter can prove useful enough to be integrated intothe mission’s strategy.7 However, it should be men-tioned that exploitable unexpected phenomena remainrare. Emergences — their noblest variety — do notpop up on request.

5.7. Related work

In her seminal work, Parker [23] studied dynamicaltask allocation in a group of robots whose mission wasto collect pucks in an arena. To choose between the

7 A classical example is the robot programmed to aim at a lightsource, and devoid of an obstacle avoidance mechanism. Versinoand Gambardella [36] tell how, after having inadvertently leftan object between the robot and the light source, they saw therobot turn around it without bumping into it! Explanation: enteringthe shadow cone, the robot automatically turned toward a moreluminous zone to the right or to the left. This emergence wouldnot have taken place in a shadow-less simulation.


various tasks involved in their mission, the robots con-sulted their individual “motivation” which integratedfive factors: sensory feedback, inter-robot communica-tion, inhibitory feedback from other active behaviours,robot impatience and robot acquiescence. This generalpurpose architecture, called ALLIANCE, lends itselfto many variations since every motivation factor maybe further developed including learning [24]. In ourresearch, we took a more restrictive approach, usingthe simplest possible mechanism to achieve task al-location. The mechanism we propose functions witha single parameter, the activation-threshold. The onlybroadcasted information used by our robots was theperiodical update of the nest’s energy.

The question of labour division in collectiverobotics8 was also studied by Schneider-Fontan andMataric [31] who engaged two, three and four robots inan arena divided in as many equally-sized contiguousregions. Each robot is territorially attached to regioni,where it collects and carries the pucks to regioni−1,where roboti−1 will then transport them to regioni−2, and so on. Eventually, the pucks reach region 1where robot 1 will carry them to their final destina-tion, a spot in region 1. The goal of this mission was toclean all regions of their pucks and move them all totheir final destination (a spot in region 1). The authorscompare the efficiency of accomplishing this task inrelation to the different group sizes used in their ex-periments. Their best results were achieved with threerobots, which shows “that increased group sizes can,in embodied agents, negatively impact the effective-ness of the territorial solution”. We witnessed a sim-ilar phenomenon in our experiments: the best resultswere achieved with intermediate team sizes. Territo-riality, which “produces a physical division of spaceand all associated resources”, seems to be an effectiveway to reduce interferences between robots [31].

6. Conclusions

From the robotics point of view, we demonstratedthat dispersing the individual activation-thresholds ofrobots is an efficient way of allocating tasks in teamsof real robots.

8 A 15-minutes video entitled “Task allocation in collectiverobotics” depicts and comments our experiments. For copies (pri-vate use only), contact [email protected]

From the biological point of view, we demonstratedthat complex social systems can be regulated in de-centralised way. This adds further evidence to the hy-pothesis that social insect colonies are regulated in aself-organised manner. Moreover, groups of three andsix robot teams had a better performance than a sin-gle robot illustrating that a transition from a solitaryindividual to a social group would have been favouredin our experimental set-up. Even though the relativeadvantage of a given group size depends entirely onthe system we demonstrated that there are favourableconditions where such a transition is possible.

Acknowledgements

We thank Professor J.D. Nicoud’s LAMI (Mi-croprocessors Systems Laboratory, EPFL) for itssustained help, and K-team SA for providing partof the hardware. We thank Laurent Keller, AlcherioMartinoli and Cristina Versino for comments on themanuscript. We are especially grateful to Edo Franzi,André Guignard, Alcherio Martinoli, Philip Maechlerand Christian König. This work was funded by grantsfrom the Fonds UNIL-EPFL 1997 (to J.D. Nicoudand L. Keller) and the “Stiftung für wissenschaftlicheForschung” (to M.J.B. Krieger).

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Micheal B. Krieger obtained his Masterin Biology from the University of Basel,Switzerland. He received his Ph.D. fromthe University of Lausanne, Switzerland in1999. He is currently a Post-Doctoral As-sociate in the Department of Entomologyand Microbiology, University of Georgia,USA, where he continues to work on as-pects of social organisation of ants.

Jean-Bernard Billeter obtained hisdiploma in Electrical Engineering at theSwiss Federal Institute of Technology inZurich (ETHZ). After numerous years outof the academic world, he joined EPELfrom 1994 to 1998 to work on collectiveintelligence. He is currently working onexhibition robotics projects.

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