The Economic Metaphor of Italian Politics for the coordination of a colony of ERS-7 Robot in the ROBOCUP multi-agent environment

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1 SETIT rd Internatonal Conference: Scences of Electronc, Technologes of Informaton and Telecommuncatons March 27-31, 2005 TUNISIA The Economc Metaphor of Italan Poltcs for the coordnaton of a colony of ERS-7 Robot n the ROBOCUP mult-agent envronment A. Chella *, R. Sorbello *, M. Gentle, L. Martorana and M. Palermo * Dpartmento d Ingegnera Informatca - Unverstà d Palermo - Italy chella@unpa.t, sorbello_rosaro@unpa.t Abstract: In ths paper, we modfed E-MIP archtecture [10][3][4][5][6], an archtecture that we developed tang nspraton from the poltcal organzatons of democratc governments, and whch provdes a soluton for the coordnaton of a robot colones n dangerous envronments, to allow a team of robots to play soccer. The development of an evoluton of Economc Metaphor of Italan Poltcs s now outlned. Ths new approach proposes a mechansm to mae a new coalton caused by the falure of the government strategy and by a general neffcency of the whole colony durng the reachng of the msson targets, such as goals scored, faults commtted and other soccer parameters. The robot agency s able to adapt ts behavor to hghly dynamc stuatons, choosng from tme to tme the best coalton capable to apply the most sutable strategy for the current stuaton. Key words: Mult-agent systems, robotc soccer, hybrd archtecture. 1 Introducton A Robots colony can be effcently used for many dffcult tass, because t can complete an assgned tas more rapdly than a sngle agent can by separatng the tas nto sub-tass and executng them smultaneously. Two man methods have been proposed n the lterature: the frst one s the centralzed approach whle the second one s the dstrbuted approach [2] [9]. If we suppose to use the second approach, we need to decde how we can mae the robots able to get organzed and, moreover, how can they regenerate ths organzaton durng the tme? In ths report, we descrbe a method for coordnatng a team of robots nvolved n playng soccer, based upon a metaphor of poltcs, usng economc methods for coaltons regeneraton. In ths paper we revsted E-MIP archtecture [3][4][5][6], an hybrd and dynamc archtecture to coordnate a robot team that we have been developng n the last years, ntroducng a new economc-based approach for the regeneraton of the coalton accordng to the current trend of the team durng the match, and to the performance obtaned under the prevous strateges appled by the varous governments, allowng each robot to dynamcally choose the best one. Our economc approach too nspraton from the wors of many researchers, le [1][8]. The proposed soluton s an hybrd snce t adopts a centralzed, but at the same tme dstrbuted among the government members, delberatve planner and several agents wth reactve and delberatve capabltes. 2 Mathematcal Model The approach adopted n E-MIP archtecture consders a colony composed of H robot and M poltcal partes. A set of three ssues, expressng ndvdual features, s assocated to each robot. Every ssue can have a lmted set of values: 0 (don't care), -1 (absolutely not) and 1 (absolutely yes). Every party can be represented by the values of the ssues that an deal robot should have to belong to that party. For the applcaton n robotc soccer we choose the followng ssues: Attac: Atttude to attac Defense: Atttude to defence Aggressveness: atttude to commt faults Every ssue s weghted through a non negatve coeffcent representng the ntensty of the ssue. The heterogenety of the robots nsde the colony s descrbed by a Roles Matrx whch shows the capablty for a robot to cover a role n the government; for example one robout couldn t be able to cover the goaleeper role, whle another one couldn t be able to c the ball n order to score a goal. The archtecture foresees at the hghest level of abstracton the four macro-states showed n fgure 1,

2 that wll be explaned n detal n the followng sectons. Fgure 1: Hghest Level FSA 2. Coalton Formaton: The formaton of the poltcal coalton whch consttutes the new government s made wth the support of a lnear space, called poltcal deology space. Ths space represents all the robots and the partes belongng to the robot ssues space. The mappng between the two spaces s performed by a mappng functon whch groups the robots showng the same vote durng the votng process. The axs of coaltons s dvded nto 3 bg strps whch represent the deologes of the left, center and rght poltcal trends. A postve value of the mappng functon dentfes a rght party whle a negatve one dentfes a left party; values closer to zero dentfy rght-center or left-center partes accordng to the sgn. A graphcal example of representaton s showed n fgure Electon Ths frst state can be dvded nto sub-states, each one representng a dfferent phase of the entre process; we wll descrbe these states below: 1. Votng Process: The votng process s dvded n two steps. The frst step s Cluster Identfcaton, based on Vorono tessellaton. In the E-MIP archtecture, the cluster dentfcaton groups the robots of the colony on the bass of the membershp's party; ths choce s based on the consderaton that every robot has a poltcal orentaton dependng on the closest poltcal party n the three-dmensonal space. Fgure 2 shows the graphcal result of the clusterng process referrng to an example made up of 11 robots and 3 partes. Fgure 3: Scalng Process A relaton analogous to the calculaton of the relatve dstances leads to the determnaton of the poltcal mass of each robot, whch represents ts weght nsde the voted party. m, = d d,, f voted, 0 otherwse (1) where the ndex descrbes all the robots of the colony whch expressed a vote for the party. Also the partes represented n the poltcal deology space are characterzed by a mass center dependng on the poltcal masses assocated to the robots whch expressed a vote for that party; such a center of mass s obtaned usng the analogous concept of the classcal physcs: Fgure 2: Clusterng The second step s the Vote Extracton, represented by a Montecarlo random extracton of a number ncluded n nterval [0,1]. Ths nterval s dvded n ts turn nto M sub-ntervals, each one assocated to the M partes. The sze of these sub-ntervals s proportonal to the relatve dstances of the robot from each party. r CM = m, m r, (2) where the ndex descrbes all the robots of the colony whch voted the party.

3 When the scalng process s fnshed, the coalton whch wll consttute the new government wll be formed by the wnnng party, that s the most voted one, added by adacent partes untl more of 50% of total votes s reached. 2.2 Determne Roles Next step s the dentfcaton of the robots whch wll assume the government roles, that s: Prme Mnster (PM), Mnster of Defence (MD) end Mnster of Communcatons (MC). Frst the robots of the coalton are fltered through the Role's Matrx cuttng the ones unable to execute the tass concernng such a role. Second, followng rules are used to assgn the poltcal roles: the PM s chosen between the robots belongng to the wnnng party, whle the MD and the MC are chosen between the robots belongng to the wnnng coalton, whch has not assumed a prevous governatve role. The PM role s then assgned to the robot closer to the center of mass of the coalton, the MD role s assgned to the robot postoned to the rght extremty of the coalton, and the MC role s assgned to the robot postoned to the left extremty of the coalton. A graphcal example of the role assgnment process s depcted n fgure 4. to a contnuous nterval whose extremes (lower and superor) are assocated to the lmt left and rght strateges. Each parameter wll be affected by the partes belongng to the wnnng coalton, each of whch wll act on the bass of the weght assumed n the coalton. Its value s then calculated as weghted average of the parameters of the coalton partes: p c = a p (3) where refers to the partes whch form the coalton. The weght a assocated to the -th party s obtaned tang nto account the votes whch t receved wth respect to the total votes of the coalton. For example, n case of progressve government, the dsposton of the robots n the feld could be the one represented n fgure 5. Ths formaton s due to a more aggressve strategy, whch leads the robots to tae poston dstant from ther goaleeper, n order to attac the opponent team. The purpose of ths strategy s to score one more goal than the opponent team. Fgura 4: Roles Assgnment 2.3 Conduct Busness The robots formng the new government wll adopt a behavor n the msson's management accordng to the strategy of the wnnng coalton. Ths strategy s a combnaton of two extremes, representng pure left and pure rght deologes, and dynamcally changes n accordance wth the weght gven to the two component n the formaton of the government coalton. A strategy s characterzed by a set of parameters whch dentfy the varous aspects of the robot's behavor. For our applcaton, that s robotc soccer, we consdered the dsposton of the robots n the feld, the atttude to pass the ball, the dstance from the opponent goal from whch a robot can shoot and the tactc that must be used to steal the ball to the opponent team. Each parameter has values belongng Fgure 5: Progressve Government Instead a conservatve coalton would select a dfferent strategy, postonng ts members n a more defensve formaton, as shown n fgure 6. In ths case, the tas s to tae one goal less than the opponent team. Fgure 6: Conservatve Government

4 2.3 Coalton Regeneraton Ths macro-state contans a fundamental part of the process, snce t allows the robots to change ther poltcal poston n the robot ssues space adaptng to dynamc changes of the external condtons. It s composed by three sub-states: Tral Balance: as we sad n the prevous sectons, we adopted an economc method to evaluate msson results; followng ths approach, we provded every robot ctzen wth a startng captal, called equty, that he can ncrease or decrease n accordance wth msson development. Also the government s provded wth an equty, ncremented from msson to msson by means of, le we wll see, the taxes. The frst step for each robot s consttuted by drawng up a balance of the actvtes carred out durng the msson, n terms of costs and rewards. To acheve ths goal each robot converts the acheved goals nto monetary unts (MU), n order to compare them, by means of a seres of reward functons that we developed for ths purpose. All data relatve to the development of the msson, must be converted n MU. In partcular, n our model for robotc soccer we too nto account the followng factors: goals scored, faults commtted, successful passes, goals taen, number of asssts and number of saves for the goaleeper. After completng ths converson, each robot ctzen draws up an economc report, gven by the dfference between costs and rewards, achevng a proft or a loss named Operatng Income (OI). In case of proft, each robot must pay a certan percentage of t to the government, n order to smulated what happens n the real lfe. The result after ths payment s the Net Income (NI): NI = OI TaxRate OI (4) Ths result s used by the robot to calculate an economc performance ndex; the one we have chosen s ROE (that s Return On Equty), thus expressng the proft n terms of percentage of the nvested captal. NI ROE = (5) Equty In the end each robot sends ts report to the government members, whch collect and add them n order to obtan a total msson result, calculatng fnally the msson ndex, n the same way showed for the ctzen robot, but usng global data. Estmate Busness: In ths second step, robots must understand f the ndex value ust calculated represents a good result or less. Keepng nspraton from economc ndex analyss, we propose a comparson on hstorcal bass; n other words, each robots eeps trac of ts prevous performances, and then uses ths stored values to carry out the comparson. In partcular, he calculates an actualzed average ROE. For ths actualzaton process we ept nspraton from Value Based Economy [7]: AvROE = t+ = 1 1 t ROE t ( 1+ γ ) δ (6) Where γ s the nterest rate appled for the actualzaton of the old values (that can be set by the government n accordance wth ther poltcal trend) and δ represents the number of legslatures passed from the begnnng of the msson. In the end, to dynamcally create a mert range, each robot dvdes the ROE axs n a certan number of subntervals, centered around the average value obtaned. The factors that dvde the nterval are represented by a percentage shft from ths central value. So, accordng to the current ROE value obtaned, each robot nows what s the mert strp whch he belongs to. Fgure 7: Economc Comparson of Msson Index Analogously, government members follow the same procedure, usng for that purpose the values related wth prevous global performances, apart from the poltcal trend of those coaltons. They wll then able to classfy ther wor aganst the others one, and to now whch s ther mert strp. Accordng to ths result, the government dstrbutes to all the ctzens a dvdends, whch could balance a possble ndvdual loss. It s to note le the dvdend s equal for each robot, and not proportonal to ts performance. In fact t s not a reward, but only a stmulus to convnce all the ctzens to confrm ther poltcal dea (f they already belonged to the wnnng coalton) or to change t (f they were of the opposte party). Update Poltcal Poston: Ths last state s responsble for the effectve updatng of the postons of the robots n the robot ssues space. Le we ntroduced n the frst sectons, each party represented n the poltcal deology space s characterzed by a mass center dependng on the poltcal masses

5 assocated to the robots whch expressed a vote for that party. Therefore, every robot maes the dfference between ths center of mass and ts own poston, obtanng the poltcal gap. The robots wll use ths value to update ther poston, approachng or dsmssng the governng coalton mass center coverng a certan percentage of ths gap, proportonally to ther satsfacton or dssatsfacton degree, gven by the mert strp whch they belong to. Moreover, the converson of the numerc value obtaned (the belongng mert strp) nto a mert one, s made through the formulaton of a udgement, by means of a cogntve representaton of the government coalton by the robotc agent. So t's defned an mage of the partes based upon obtaned results. Cogntve mage s determned by means of the nteracton between a percever-determned mage and a stmulus-determned one. The frst one s related wth the belongng of the agent to the government coalton, and t s obtaned from the electve process precedng the msson, whle the second one represents the ncrease, or the decrease, of each robot's economc welfare. Ths s ndcated through the mert strp. The mass center becomes then the nucleus and the coalton becomes the force feld that contans all the poltcal masses that expressed a favorable vote. To send away the poltcal mass of a robot from the nucleus, t s necessary to apply a force whose ntensty must wn the attractve feld that the nucleus generates. In other words, t s necessary to wn an deologcal ndolence generated by coalton mass center. The movement towards or by the wnnng party s expressed by the followng equaton: Fgure 8: Update of Poltcal Postons Concluson One of the fundamental and nnovatve feature of the Economc Metaphor of Italan Poltcs Archtecture s ts dynamc socal structure. It s a good balance between the cost of formng a coalton and the soluton qualty that t obtans, and also t s capable, mang use of economcal theores, of regeneratng at each tme the best coalton, thus mantanng optmal results for the whole msson. We propose to apply ths last verson of our archtecture to a team of AIBO ERS-7 robots, vsble n fgure 9, n order to play next edtons of RoboCup competton. ( s) rcm r' = s r + 1 (7) Where s s the scalng factor that determnes the entty of the translaton. It depends on the belongng mert strp, whch determnes the entty of the movement c, on the poltcal deology of the robot, whch determnes the correcton factor, and on the bonus gven by the government n the end of the msson. Its mathematcal expresson s the followng: c s = bonus (8) Ths process s better depcted n fgure 8, where the robot on the left s outsde the government coalton, and then he needs a stronger force to get near to the wnnng party. Fgura 9: AIBO ERS-7 Robot The tests that we already carred out nsde Msson Lab software[1][2][3][4], where n fact concerned wth mssons of bombs searchng and defusng. As we sad, these tests demonstrated as the performances obtaned by the colony were optmal, snce the robots dynamcally adapted ther poltcal postons to the results of the msson, votng from tme to tme the coalton whch granted the best results. Then, we thn that the Metaphor of Poltcs wll be able to grant the same optmal performances, but only the mplementatons on the AIBO robots and the subsequently partcpaton to a real competton wll provde the certanty of our frm belef.

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