Social Inhibition Manages Division of Labour in Artificial Swarm Systems

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1 Socal Inhbton Manages Dvson of Labour n Artfcal Swarm Systems Payam Zahadat 1, Karl Cralshem 1 and Thomas Schmckl 1 1 Artfcal Lfe Lab of the Department of Zoology, Unverstätsplatz 2, Karl-Franzens Unversty Graz, 8 Graz, Austra payam.zahadat@un-graz.at Abstract Ths paper presents a novel and bo-nspred algorthm for dstrbuted dvson of labour n swarms of artfcal agents (e.g., autonomous underwater vehcles). The algorthm s nspred by dvson of labour va local nteractons n socal nsects. The algorthm s successfully mplemented n vrtual agents and smulated robot swarms and demonstrates a hgh adaptvty n response to changes n the workforce and task demands n the swarm level as well as a hgh specalzaton to tasks n the agents level. Introducton In the feld of swarm ntellgence and collectve robotcs, socal nsects are promsng sources of nspraton due to ther capabltes n self-organzaton and and self-regulaton n the colones. Dvson of labour s one of the promnent characterstcs of socal nsects such as honey bees (Seeley (1982); Huang and Robnson (1992)) and ants (Hölldobler and Wlson (28); Julan and Cahan (1999)). The nsect colones mantan plastcty that adapts the dvson of labour to the status of the colony and, n parallel, also to envronmental stuatons, e.g. to the number of workers or taskdemands. The flexblty and quck response to the changes n the status of the colony and envronment n one hand and specalzaton of workers for the tasks n the other hand are nterestng propertes of the methods drvng behavour n the colones. Several models have been proposed to explan the mechansms of dvson of labour n socal nsects, e.g. foragngfor-work (Tofts (1993)), response-threshold renforcement (Bonabeau et al. (1997); Theraulaz et al. (1998)), and common-stomach models (Karsa and Schmckl (211)) (for a good revew of such models see Beshers and Fewell (21)). These models have been also used as nspraton for dstrbuted algorthms n applcaton areas such as swarm robotcs. For example, n Gross et al. (28) and Labella et al. (26), models of ants-foragng behavour have been mplemented for mantanng dvson of labour n a group of robots performng an object retreval task or response-threshold renforcement model (Bonabeau et al. (1997); Theraulaz et al. (1998)) that s nspred by wasps s appled for swarms of robots (e.g. n Whte and Helferty (2); Yang et al. (29)), or n Schmckl et al. (27) a trophallaxs-nspred strategy whch s nspred by food exchange of honeybees and ants s appled to a smulated robot swarm. In ths paper, we are nterested n a mechansm of dvson of labour that s nspred by behavours of honey bees (Huang and Robnson (1992, 1999)). A honey bee undertakes dfferent tasks durng ts lfe-tme n a process of behavoural development. In earler weeks of ts adult lfe, a honey bee performs nursng, then t performs other tasks nsde the hve, and only n ts fnal weeks t leaves the hve for foragng (Johnson (2)). Ths behavoural development can be delayed, accelerated, or even reversed n response to changes n colony or envronmental condtons. Socal nhbton s proposed (Huang and Robnson (1992)) as a conceptual method for mantanng ths adaptve behavour of the colony. In ths method, tasks are consdered n an ordered sequence. The behavoural development of an ndvdual that determnes when the worker swtches to the neghbourng task n the sequence s regulated va local nteractons wth other ndvduals. In ths paper, a dstrbuted algorthm of dvson of labour based on local communcaton s nspred by socal nhbton. The algorthm consders the spatalty of the taskregons that restrct the possble local nteractons between the ndvduals as t s more realstc regardng many applcaton areas and also the bologcal system. For example, n a honey bee colony, the workers of the tasks whch are early n the sequence stay nsde the hve whle the workers of the tasks later n the sequence work outsde the hve. The very early workers do not have much contact wth the out-of-thehve workers. In other words, the nteractons are restrcted to some extent to the ndvduals of the tasks whch are next to each other n the sequence. Despte the bologcal source of nspraton of the proposed algorthm, we am for applcatons n swarm robotcs. In partcular, where there s a spatal clusterng of the robots based on ther tasks that lmts the local communcatons 69 ECAL 213

2 to the robots of the same or neghbourng tasks. The proposed algorthm s smple and easy-to-mplement. It s mplemented n swarms of vrtual agents as well as swarms of smulated robots that perform several tasks. The behavour of the swarm n response to the changes n the number of agents n each task and the task-demands are nvestgated representng adaptablty that s acheved by the algorthm. Socal Inhbton In honey bee colones, dvson of labour s manly based on the age of the workers. Ths mechansm s called temporal polyethsm. In temporal polyethsm, there s a correlaton between the age of the workers and the tasks they perform; e.g. older workers perform tasks outsde of the hve and younger workers perform tasks wthn the hve (Wlson (1971); Robnson (1992)). The behavoural development of the bees s assocated wth ther physologcal development such that the physologcal age of a bee ndcates the man task that t performs (Wnston (1987); Beshers et al. (1999)). As t s shown n dfferent studes (e.g. Huang and Robnson (1996)), honey bee colones are flexble to changes n age dstrbuton of the colony and task demands. For example, n a colony of young honey bees, the age n whch a bee starts foragng (an outsde task) s lower than n a normal colony. It means the behavoural development n such colony s accelerated. On the other hand, presence of older bees delays or nhbts the development of physologcal age of other bees n the colony. Another example s the behavour of the colones when the hve workers are removed. In ths case, the development of physologcal age decreases and nverts resultng n transformaton of out-of-hve workers nto nsde-the-hve workers. Huang and Robnson (1992) proposed that worker-worker nteractons drve mechansms of hormonal regulaton n bees resultng n a socal nhbton that explans temporal polyethsm and adaptablty of the colony to dfferent age dstrbutons. The concept s then used n other researches toward developng models of socal nhbton, e.g., Beshers (21); Naug and Gadagkar (1999); Gadagkar (21). In ths work for some reasons Naug and Gadagkar (1999); Gadagkar (21) are not used as a source of nspraton. Prevously Suggested Algorthm: Evoluton Maps One of the models of socal nhbton followng Huang and Robnson (1992) s the model of evoluton maps proposed by Beshers (21). In ths model, a map whch s a set of curves descrbng changes n the physologcal age of the ndvdual s ntroduced. A state varable x represents the physologcal age of every ndvdual. In addton to that, the ndvduals also contan an auxlary varable y. In every tme-step (day for bees), an ndvdual has a number of nteractons wth others. y s a weghted average of x values of all the nteracted ndvduals. The weghts are set based on the task the ndvdual s performng. Every curve of the map descrbes changes of x based on ts current value and the value of y. In the reported work (Beshers (21)) two tasks are mplemented. A threshold s set to ndcate whch task s chosen by the ndvdual based on ts x value. The threshold s augmented wth hgher and lower margns provdng more stablty for the system. The curves are derved based on expermental data from real bees. Although the model mght be extendble to more tasks, global-range nteractons (nteractons between ndvduals rrespectve to the task they are performng) would be a necessary condton for the stablty of the model. The reason s that f the nteractons are restrcted, e.g. to the neghbourng tasks n the task-sequence, the y value s no longer an estmaton of the x n the whole system and wll have nstantaneous changes when an ndvdual swtches between two tasks leadng to endless back and forth swtchngs. Apart from the complexty of generatng a proper map, the global-range nteracton s usually not the case n both nsects and robotc tasks, snce workers of dfferent tasks are usually separated spatally and nteractons are restrcted to ndvduals of the same or neghbourng tasks. New Proposed Algorthm One of the propertes that we are nterested n them are the ablty of the decentralzed algorthm to dvde the swarm nto groups relatve to the task-demands whle the system s flexble to changes n the demands and workforce. In addton, the number of swtchngs between dfferent tasks should be lmted due to practcal costs (e.g., a robot may need to spend some energy to change ts workng area n order to perform a dfferent task). Therefore, specalzaton of the ndvduals s also of our nterest. In the proposed model, every ndvdual contans a state varable x as ts physologcal age. Ths varable s restrcted to a defned range of (x mn,x max ). There s a number of tasks wth ther assocated demands. The tasks are ordered n a sequence such that an ndvdual can only swtch to the prevous or the next task n the sequence. An ndvdual chooses a task based on ts x and a set of defned thresholds that separate the tasks (see Fgure 1). The thresholds are used together wth lower and upper margns. For an ndvdual that s performng task, n order to swtch to task +1, ts x value should exceed th :+1 + upper margn. For an ndvdual that s performng task, n order to swtch to task 1, ts x value should become lower than th 1: - lower margn. The lower and upper margns prevent the ndvduals from nstant back and forth swtches between two consecutve tasks due to nosy changes n x. The man dea of the algorthm s to spread the x values of the whole swarm unformly over the range of (x mn,x max ). Wth such a unform dstrbuton of x throughout the swarm and settng the thresholds such that the range s splt nto segments relatve to the task-demands, the requred number ECAL 213 6

3 x mn task 1 task 2... task n x th 1:2 th 2:3... th n 1:n x max Fgure 1: x changes wth small steps n a range of (mn x, max x ). A task s assgned to the ndvdual when ts x varable passes the respectve thresholds. x mn task 1 : 2% task 2 : % task 3 : 2% x th 1:2 th 2:3 x max Fgure 2: An example unform dstrbuton of x and proper thresholds that splt the range relatve to the task-demands. In ths example, eght agents are dvded nto three tasks. The relatve demands for the three tasks are 2%,%, and 2% respectvely. of agents wll be assgned to each task (see Fgure 2). Regulaton of x values n the swarm occurs through local nteractons between the ndvduals. Every ndvdual contans two varables that keep track of ts experence n the swarm. In an deal case, these two varables stand for the closest hgher and lower x values belonged to other ndvduals n the swarm. In practce, these varables have to be estmated durng nteractons. Let these varables be x low and x hgh. In the deal case ther varables are as follows: x low = arg mn( x x ), where x <x x x hgh = arg mn( x x ), where x >x x The value of x s updated for each agent n the drecton towards the average of ts x low and x hgh, as follows: x + δ f x x low <x hgh x x = x δ f x x low >x hgh x (2) x ± X otherwse where δ s step-sze whch s a constant parameter wth a small value n terms of the sze of segments for every task. In the current mplementaton X δ U(, 1). Snce there s no global nformaton about the x values n the swarm, agents update ther x low and x hgh values gradually durng tme and n every nteracton wth another agent. Say agent nteracts wth agent j. x low and x hgh are updated as follows: x low = x j x low f x low <x j <x otherwse (1) (3) x hgh = x j x hgh f x <x j <x hgh otherwse x low and x hgh also slowly drft away from x n every tme-step n order to be adaptable to changes n other agents x values as well as the envronment: x low x hgh = x low = x hgh ϕ + ϕ where ϕ s a value smaller than δ n Eq. 2. After every update of x, an ndvdual consders swtchng to the prevous or next tasks n the task sequence. For an ndvdual wth task, new task s chosen as follows: task +1 f x > th :+1 + l u new task = task 1 f x < th 1: l b (6) task otherwse where th 1: and th :+1 represent the threshold values between task 1 and task, and task and task +1 respectvely. l u and l b are the upper and lower margns for the thresholds. The Algorthm The followng actons are performed by any agent n every tme-step of runnng: 1. update x low and x hgh usng Eq.. 2. f there s an nteracton wth agent j: (a) update x low and x hgh usng Eq. 3 and Eq. 4. (b) update x usng Eq. 2. (c) update the assgned task usng Eq. 6. Experments A number of experments are performed n order to nvestgate the performance of the proposed algorthm, ts adaptvty to changes, and specalzaton of the agents to the tasks. In the frst set of experments a swarm of vrtual agents s smulated and the nteracton between the agents performng the same task or n the adjacent tasks occur based on defned probabltes. The senstvty of the algorthm to the chosen values for the step-sze δ s also nvestgated. In the second experment, a smulated swarm of movng agents (robots) s nvestgated and the nteractons are based on the locaton of the agents n the arena n every tme-step of the smulaton. Vrtual swarm experments The algorthm s frst tested n a number of vrtual swarms of agents. In all of the followng experments a sequence of fve dfferent tasks s consdered. Every experment s repeated for (4) () 611 ECAL 213

4 2 ndependent runs. Every run s smulated for tmesteps whle each agent runs the proposed algorthm. Interactons are possble between the agents of the same task or neghbourng tasks. In every tme-step of the smulaton, 3 nteractons are sampled from a unform dstrbuton over all the possble nteractons. All the agents are ntalzed by x mn for the state varable x. Expermental settngs of the algorthm are represented n Table 1. Investgaton of the algorthm wth fxed settngs In the frst experment the demands for the fve tasks are equal. The progress of the number of robots n each task over tme s represented n Fgure 3 (left). Snce the agents start wth the same ntal value for x (x mn ), they all start wth task1. By occurrng nteractons durng tme the x values are spread n the range and the swarm s splt for performng dfferent tasks. In the second experment the demands for the fve tasks are %, 4%, %, 3%, % respectvely. Fgure 3 (rght) represents the results. All the runs reached the stable desred status for both experments. The experments were also repeated whle the possble nteractons between the agents of neghbourng tasks were lmted to a fracton of the agents n each task nstead of the whole agents and smlar results were acheved (data not shown). Investgaton of adaptvty to changes n task-demands In order to nvestgate adaptablty of the swarm to changes n the task-demands, another experment s performed startng wth equal demands for every task. The task demands are then changed at tme-steps 2 and 4. Fgure 4 (left) represents the results for ths experment. As the fgure demonstrates, the swarm mmedately reacts to the changes n the demands. The reason s that the x values of the swarm are spread almost unformly n the range (n the deal stuaton they are spread unformly). By changng the task-demand, the thresholds over the range of x are changed such that the range s splt relatve to the new settngs. Therefore, proper fractons of agents are reassgned for dfferent tasks whle the x values do not need to change. Investgaton of adaptvty to changes n work-force In the next experment the adaptablty of the swarm to the changes n the number of agents presented n each task s nvestgated. In order to do that, the experment starts wth a swarm of 3 agents. In tme-step, 2 agents ncludng all the agents n task2 and taks3 are removed from the swarm. Later on n tme-step 3, more agents are ntroduced n the swarm n the task1. Fgure 4 (rght) represents the behavour of the swarm n response to these changes. As the fgure demonstrates, the swarm reacts to these changes by swtchng the tasks of the proper number of agents. The mechansm behnd ths reacton s as follows: When a number of agents are removed from the system (or new agents are ntroduced), the unformty of the dstrbuton of x n the swarm s volated. The agents wth x values close to the low-densty (or hgh densty) regons n the dstrbuton react to ths stuaton by shftng ther x value towards the regon (or n opposte drecton). The process contnues untl the dstrbuton becomes unform agan. Investgaton of specalzaton In order to nvestgate specalzaton of the agents for the tasks n the swarm, the number of non-necessary task-swtchngs of every agent s evaluated durng the run-tme. The settngs are the same as the frst experment: fxed equal demands for all the fve tasks. Snce all the agents start wth task1 due to ntal value for x, a certan number of swtchngs from a task to the next one s necessary for a certan number of agents. Moreover, any swtchng to a prevous task (swtch-back) s not desrable. Fgure represents the frequency of swtch-backs durng tme-steps for all runs and agents for dfferent values of step-sze (δ). Investgaton of the effects of step-sze The step-sze δ n Eq. 2 s a predefned parameter n the current mplementaton of the algorthm. Therefore, the senstvty of the algorthm to ths parameter s nvestgated by repeatng the frst experment wth dfferent values for δ. Fgure 6 represents a comparson for dfferent values. The man fgure demonstrates the medan error of the task allocaton (number of agents n wrong tasks) over tme. The nlne fgure compares the tme requred for reachng a swarm-state stablzed n maxmum of % error. As t s represented n Fgure 6, for very small values of δ, error decreases slowly. It s more quck for mddle values. For hgh values of δ, the error decreases quckly regardng the man fgure, but regardng the nlne fgure the tme to reach the stable status wth maxmum of % error s hgh. In addton, the szes of quartles are bg ndcatng that n dfferent runs dfferent values are calculated for the tme-toreach. The nstablty of the hgh values s also vsble n Fgure that represents the frequency of swtch-backs for dfferent δ for all the runs durng tme-steps. In ths fgure, for δ =.1 there was not a sngle swtch-back n all the runs. As δ ncreases, the frequency of swtch-backs also ncreases. In short, f the step-sze (δ) s too small, the system s less reactve, and convergence takes longer. But f the value s too bg, the system gets nstable and results dffer from case to case. Smulated robot experment In ths experment a smulated robot swarm runnng the proposed algorthm s nvestgated for ts behavour and adaptablty to the changes n the workforce and task demands. A square arena s set up wth a lght source located n one sde (see Fgure 7). A swarm of robots s supposed to be splt ECAL

5 3 t1 t2 t3 t4 t 3 t1 t2 t3 t4 t 2 2 Number of Robots 2 Number of Robots Tme Tme Fgure 3: Medans of the number of agents n each task over tme for 2 ndependent runs. All of the runs reached the stable soluton for both experments. Tasks are represented by t1, t2, t3, t4, t. The left fgure represents fve tasks wth fxed equal demands. The rght fgure represents fve tasks wth fxed demands of %, 4%, %, 3%, % respectvely. Number of agents n both experments are 3. T me 2 4 th 1:2 2 th 2:3 4 2 th 3: th 4: Swarm Sze T me 3 th 1:2 th 2:3 th 3: th 4: Swarm Sze t1 t2 t3 t4 t 3 t1 t2 t3 t4 t 2 2 Number of Agents 2 Number of Agents Tme Tme Fgure 4: Medans of the number of robots n each task n 2 runs. All of the 2 runs reached the soluton for both experments. In both experments the swarm starts wth 3 agents. The left fgure represents changes n the demands n tme-steps 2 and 4. The rght fgure represents changes n the number of robots. In tme-step, 2 agents ncludng all the agents n second and thrd task and randomly chosen agents are removed from the system. In tme-step 3, agents are added to the system n the frst task. 613 ECAL 213

6 Step-szes (δ): Error Tme-to-reach Step-szes (δ): Tme Fgure 6: Comparson of error over tme and also tme-to-reach the stable status for nne dfferent values of step-sze δ based on 2 ndependent runs. Man fgure represents the medan of the number of agents n wrong tasks (errors) over tme for 2 runs. Inlne fgure represents the boxplots of the tme to reach a swarm state that s stable wth maxmum one error out of 3 agents (more than 9% correct task-assgnment) (*:p <.1 for all pars of δ except (.1,.7) where p <.2; Wlcoxon sgned-rank test, unpared date, two.sded -hypothess). Box-plots ndcate medan and quartles, whskers ndcate mnmum and maxmum, crcles ndcate outlers. Frequency Number of swtches Step-szes (δ): Fgure : Frequency of number of swtch-backs n tme-steps for all the 3 agents and 2 runs. The fgure represents the frequency for dfferent values of step-sze δ. Table 1: Expermental settngs for the proposed socal nhbton algorthm vrtual scenaros robot scenaro x mn x max δ.3.1 ϕ δ/3 δ/3 l u,l b 1 1 up nto three regons of the arena n order to cover the arena wth dfferent denstes. Every robot has a lumnance sensor percevng the brghtness of the lght sensor. The three regons are located n dfferent dstances from the lght source and the robots dentfy them based on ther brghtness. Each robot s able to rotate or move forward. When a robot decdes to swtch the task, t moves uphll or downhll the lumnance gradent untl t reaches the approprate workng regon. Robots move randomly n ther workng regon and do not leave t unless they decde to swtch the task. A robot can nteract wth another robot whch s located n ts communcaton range by exchangng the x values. The arena s of sze and the communcaton-range s fve tmes bgger than the robots dameter. Every robot n the smulaton performs the followng: If the robot s n the regon of ts assgned task: ECAL

7 Perform a random walk nsde the task-regon. Otherwse (the robot s out of ts task-regon): turn towards the proper task-regon based on the brghtness gradent and step forward. regulate the state varables: 1. update x low and x hgh usng Eq.. 2. f there s a robot j n the communcaton range: (a) update x low and x hgh usng Eq. 3 and Eq. 4. (b) update x usng Eq. 2. (c) update the assgned task usng Eq. 6. At the begnnng of the experments, the number of robots s 16 and the task-demands are 2%, %, and 2% respectvely whch means 4, 8, and 4 robots are desred for each task-regon. At tme-step 2, all the 8 robots n task2 are removed from the arena but the proportonal demands are fxed. At tme-step 4, the demands are changed to 2%, 2%, and % respectvely. The experment s repeated for 2 ndependent runs. Fgure 8 represents the progresson of the number of robots n each task over tme. As t s demonstrated n the fgure, the swarm reacts properly to the changes n the number of robots by swtchng a proper number of robots from task1 and task3 nto taks2. The system also quckly responds to the changes n the task-demands by swtchng two robots from task2 to task3. Fgure 9 represents the frequency of swtch-backs durng the frst tme-steps of all the runs. The fgure represents that about.47% of the robots have not a sngle swtchback durng the whole evaluaton-tme and very few robots had more than swtch-backs representng specalzaton for the robots n the tasks they perform. Concluson Ths paper ntroduces a novel decentralzed, self-organzed and self-regulated dvson of labour n artfcal swarms nspred by temporal polyethsm n honey bees. The algorthm s based on local communcaton whle the communcatons need to be possble only between the agents that perform the same task or neghbourng tasks. The logc behnd the algorthm s smple and t s easy to mplement whle the nterestng propertes are mantaned for the swarm. Experments nvestgatng the behavour of the swarm n response to changes n the swarm members or task-demands represents that the algorthm provdes a hgh adaptvty for the swarm. In addton, t s demonstrated that the agents are specalzed n the tasks and unnecessary swtchngs between the tasks are lmted. The senstvty of the system to a predefned parameter of the algorthm (step-sze) s also nvestgated ndcatng that there s a trade-off between the speed of approachng the soluton and stablty of the swarm. In the future the algorthm wll be extended for more complcated requrements and wll be used n real-robot scenaros. Fgure 7: A screenshot of the robot arena. Three dfferent task-regons are located based on ther dstances from the lght source. Number of Robots T me 2 3 th 1: th 2:3 7 7 Swarm Sze t1 t2 t Tme Fgure 8: Medans of the number of robots n each task n 2 runs. The system starts wth 16 robots whle the demands for the three tasks are 2%, %, and 2% respectvely. At tme-step 2, all the robots n the second task are removed from the arena. In tme-step 3, the demands change to 2%, 2%, and % respectvely. Tasks are represented wth t1, t2, t3. 6 ECAL 213

8 Frequency Number of swtches Fgure 9: Frequency of number of swtch-backs n the frst tme-steps for all the 16 agents and 2 runs. J., and Pasteels, J., edtors, Informaton Processng n Socal Insects, pages Brkhuser Basel. Huang, Z. Y. and Robnson, G. E. (1992). Honeybee colony ntegraton: worker-worker nteractons medate hormonally regulated plastcty n dvson of labor. Proc Natl Acad Sc U S A, 89(24): Huang, Z. Y. and Robnson, G. E. (1996). Regulaton of honey bee dvson of labor by colony age demography. Behavoral Ecology and Socobology, 39(3): Johnson, B. (2). Dvson of labor n honeybees: form, functon, and proxmate mechansms. Behavoral Ecology and Socobology, 64(3): Julan, G. E. and Cahan, S. (1999). Undertakng specalzaton n the desert leaf-cutter ant acromyrmex verscolor. Anm Behav, 8(2): Karsa, I. and Schmckl, T. (211). Regulaton of task parttonng by a common stomach : a model of nest constructon n socal wasps. Behavoral Ecology, 22: Acknowledgements Ths work s supported by: EU-ICT project CoCoRo, no ; EU-IST-FET project SYMBRION, no ; EU-ICT project REPLICATOR, no ; Austran Federal Mnstry of Scence and Research (BM.W F); EU- ICT project ASSISI bf, no References Beshers, S. (21). Socal nhbton and the regulaton of temporal polyethsm n honey bees. Journal of Theoretcal Bology, 213(3): Beshers, S. and Fewell, J. (21). Models of dvson of labor n socal nsects. Annu. Rev. Entomol, 46: Beshers, S., Robnson, G., and Mttenthal, J. (1999). Response thresholds and dvson of labor n socal nsects. In Detran, C., Deneubourg, J., and Pasteels, J., edtors, Informaton Processng n Socal Insects, pages Brkhuser Basel. Bonabeau, E., Sobkowsk, A., Theraulaz, G., and Deneubourg, J.-L. (1997). Adaptve task allocaton nspred by a model of dvson of labor n socal nsects. In Bocomputng and emergent computaton: Proceedngs of BCEC97, pages World Scentfc Press. Gadagkar, R. (21). Dvson of labour and organzaton of work n the prmtvely eusocal wasp ropalda margnata. In Proceedngs of the Indan Natonal Scence Academy - Part B: Bologcal Scences, volume 6 of 67, pages Gross, R., Nouyan, S., Bonan, M., Mondada, F., and Dorgo, M. (28). Dvson of labour n self-organsed groups. In SAB, pages Hölldobler, B. and Wlson, E. (28). The Superorgansm: The Beauty, Elegance, and Strangeness of Insect Socetes. W. W. Norton and Company, New York. Huang, Z.-Y. and Robnson, G. (1999). Socal control of dvson of labor n honey bee colones. In Detran, C., Deneubourg, Labella, T. H., Dorgo, M., and Deneubourg, J.-L. (26). Dvson of labor n a group of robots nspred by ants foragng behavor. ACM Trans. Auton. Adapt. Syst., 1(1):4 2. Naug, D. and Gadagkar, R. (1999). Flexble dvson of labor medated by socal nteractons n an nsect colony a smulaton model. Journal of Theoretcal Bology, 197: Robnson, G. E. (1992). Regulaton of dvson of labor n nsect socetes. Annu Rev Entomol, 37: Schmckl, T., Möslnger, C., and Cralshem, K. (27). Collectve percepton n a robot swarm. In Şahn, E., Spears, W. M., and Wnfeld, A. F. T., edtors, Swarm Robotcs - Second SAB 26 Internatonal Workshop, volume 4433 of LNCS, Hedelberg/Berln, Germany. Sprnger-Verlag. Seeley, T. D. (1982). Adaptve sgnfcance of the age polyethsm schedule n honeybee colones. Behavoral Ecology and Socobology, 11: Theraulaz, G., Bonabeau, E., and Deneubourg, J.-L. (1998). Response threshold renforcement and dvson of labour n nsect socetes. In In Proc. Royal Socety of London, volume 26 of, pages Tofts, C. (1993). Algorthms for task allocaton n ants. Bull. Math. Bol., : Whte, T. and Helferty, J. (2). Emergent Team Formaton: Applyng Dvson of Labour Prncples to Robot Soccer. Engneerng Self-Organsng Systems, pages Wlson, E. O. (1971). The nsect socetes. Belknap Press of Harvard Unversty Press. Wnston, M. (1987). The bology of the honey bee. Harvard Unversty Press. Yang, Y., Zhou, C., and Tan, Y. (29). Swarm robots task allocaton based on response threshold model. In Gupta, G. S. and Mukhopadhyay, S. C., edtors, ICARA, pages IEEE. ECAL