ScienceDirect. Formation of Control Structures in Static Swarms

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1 Avilble online t ciencedirect Procedi Engineering 100 (2015 ) th DAAAM Interntionl ymposium on Intelligent Mnufcturing nd Automtion, DAAAM 2014 Formtion of ontrol tructures in ttic wrms Vlery Krpov, Irin Krpov* Ntionl Reserch University Higher chool of Economics, 20 Mysnitsky Ulits, Moscow, , Russi Abstrct Work solutions re prosed for problems of leder definition nd role distribution in homogeneous groups of robots. It is shown tht trnsition from swrm to collective of robots with hierrchicl orgniztion is possible using exclusively locl interction. The locl revoting lgorithm is centrl to the procedure for choice of leder while redistribution of roles cn be chieved by wve method. The bsis for this pproch is the sttic swrm model, which is chrcterized by the bsence of set control center nd represents the network fixed t some time intervl s set of loclly intercting gents The The Authors. Published by Elsevier by Elsevier Ltd. This Ltd. is n en ccess rticle under the BY-N-ND license ( Peer-review under responsibility of DAAAM Interntionl Vienn. Peer-review under responsibility of DAAAM Interntionl Vienn Keywords: swrm robotics; voting procedur; selecting group leder; roles distribution; locl interction 1. Introduction Active reserch into the cretion of systems of intercting robots hs been ongoing for nerly qurter of century. Approches such s collective, swrm nd flocking robotics hve been prominent in modern robotics nd the theory of multi-gent systems, but the overwhelming tendency of reserch in this re remins t theoreticl, model level. According to numerous reviews [15, 17], it is pprent tht this bsence of vlid, significnt results is not lest connected with the reltive neglect of number of importnt tsks. Reserch in the field of group robotics (to coin generlized nme for collective, swrm, flock etc. robotics) hs very frgmentry chrcter. One wrning sign is the obvious trnsfer of the center of grvity of reserch to swrm robotics, which cn be viewed s simpler, more bsic level of group robotics model. Among set of problems in swrm robotics tht remin insufficiently studied, two will be elborted here. The first of these is the problem of leder definition in * orresponding uthor. Tel.: E-mil ddress: vkrpov@hse.ru, ikrpov@hse.ru The Authors. Published by Elsevier Ltd. This is n en ccess rticle under the BY-N-ND license ( Peer-review under responsibility of DAAAM Interntionl Vienn doi: /j.proeng

2 1460 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) homogeneous group of robots, nd the second is role distribution mong members of the group under conditions of exclusively locl interction. Ledership. One of the bsic fetures of swrm robotics is the locl chrcter of interction of robots, with ech other nd with their environment [17]. This kind of interction is clled implicit communiction [15], which mens tht ech robot in the group intercts directly only with neighbours within some limited visibility rnge. In such systems, it usully follows tht robots mke decisions independently on further ctions, guided by some simple rules of locl interction. However, the overwhelming mjority of exmples of tsk solution in the field of swrm robotics concern the coordinted movement of swrm. For instnce, in the obvious nd rther simple tsk chrcterised s the Leder-Follower method in [13], it is considered tht there is n priori leder in the group who sets this movement. There re mny vrints of locl interction rules, from the formlistic [12] to the very exotic. For instnce, [3] describes the virtul spring-dmper model of flocking mobile robots behvior. The spring component of the model defines the force of ttrction to the leder (not follower to follower), nd the dmper component defines the repelling force. Another especilly technicl pproch hs been prosed in [4], in which one of the robots must become the 'leder' of the group by mximizing the vlue of its communictive output. The min issue of this method is tht it leds to ppernce of set of leders, nd number of them depends on the tology of the swrm. A similr technicl pproch ws offered in [6], in which the gent with the gretest weight ws ppointed s leder. The difference between the leder nd other members of the group (or flock) ws tht the leder did not use the rule move to the nerest neighbour. This pproch provided solution to the problem of coordinted movement, turning swrm into flock. In very interesting project described in [11], utonomous robots used rther simple Fish Behvior interction rules for collision-free driving, in which ll robots were equipped with set of complex sensors. This pper dels minly with the priori set leder, or with techniques tht void defining the leder under the conditions of some specific objective. However, in number of works, swrm leder is elected. In [8], group leder selection is bsed on timizing power consumption, mking it necessry to know the distnces between robots nd the power consumed by trnsfer of the messge from one robot to nother. In [16], swrm trffic control using the center of msses or the geometricl centre of swrm is described. This method requires tht coordintes of gents, their speed nd their direction of movement must be known. Another pper [10] describes loclized mechnism for determining the informtion potentil on ech node, bsed on locl process informtion nd the potentil of neighbouring nodes. In tht instnce, the node with the minimum potentil ws considered to be the leder, but we re interested here in the problem of leder identifiction in more generl cse, in terms of mechnisms of locl informtion interction. Role distribution. For solution of the bsic problem of the coordinted movement of robots, it is sufficient tht there is leder. However, more complex chllenges solved by group of robots require differentition of their functions nd, generlly speking, distribution of tsks between robots; this is perhps one of the most problemtic concepts of swrm robotics. In reviews mentioned bove [15, 17], tsk distribution in robot groups ws considered rther declrtively t best, some physicl models, methods of distributed plnning, timiztion nd other generl mechnisms re mentioned [5]. In prctice, one usully dels with either the centrlized control systems or with homogeneous groups without functionl differentition. For exmple, [9] describes n ssembly system model with self-orgnizing behviour (Bionic Assembly ystem BA). The behviour of ech mobile robot in this system depends on its internl stte nd on the stte of the system. A centrl computer plns the globl production of BA, synchronizing the supply of prts nd so on, becuse differentition of functions nd distribution of tsks is not considered n ctul problem by swrm robotics. Insted, it is usully tken tht the swrm hs to solve only simple, mss problems like coordinted movement. This certinly reduces the importnce of the swrm pproch nd goes stright to the min declred thesis of swrm robotics s n pproch to the solution of complex behviourl tsks using set of simple technicl devices robots. In the present cse, it is considered tht the problems of leder formtion nd role distribution re extremely importnt for the develment of swrm robotics. This pper considers some wys in which these tsks might be solved, using such model the orgniztion of group of robots, s sttic swrm.

3 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) Tsk definition The tsk is formulted s follows. onsider set of simple devices (robots or gents) cpble of directing locl interction between neighbours. The question is whether it is possible to formulte conditions under which it will be possible for such system to solve more complex problems, both t the behviourl level nd t the levels of informtion processing, decision-mking, nd so on. In other words, it is necessry to define the conditions of emergence of synergetic effects or emergent prerties. There re two min clsses of swrm models: micro- nd mcro-level models. The first of these is bsed on the models of the behviour of individuls; the second clss is bsed on description of the swrm s whole. For exmple, t the micro-level, models of finite-stte mchines re widely used, nd t the mcro-level, hydrodynmics models re common. Hybrid models combining both pproches re less often pplied. For exmple, Bermn et l. describe model of the dynmics of environment stte in [1] tht defines the behviour of members of swrm (gents). The resoning in the present study generlly belongs to the micro-level clss becuse our interest is in the mechnism of locl interction of robots in swrm (s in [14]). To begin, consider the structure of n gent, where the min objective is set of some simple devices. implicity here mens some principl limittion of cognitive bilities (sensors, clcultions nd memory). Further, some serious restrictions will be plced on the robots communiction portunities, in which ech robot cn communicte with no more thn some limited number of its neighbors. It will further be ssumed tht the robots hve fixed number of communictions ports (i.e. contct points tht form informtion chnnels) for exmple, robots must be connected physiclly to ech other s communiction ports for communiction s orgnized in Fig. 1. ommunictions Port ommuniction hnnel 2 1 Agent 3 4 Fig. 1. Robots with four communictions ports nd their communictions. 3. ttic wrm One of the models describing the orgniztion of gret number of loclly intercting gents or robots is the soclled sttic swrm. This rrngement is chrcterized by the bsence of control centre nd represents the given network fixed t some time intervl s set of gents [7]. The min feture of sttic swrm is tht t some moment, insted of set of seprted gents, the computing structure is completely defined, enbling the solution of difficult clculting nd dt processing tsks. It follows tht sttic swrm cn be considered s n object with qulittive prerties other thn simple set of gents. The min prerties of sttic swrm re n ctivity, loclity of interctions nd functionl heterogeneity. Activity. ertinly, unlike the computer network, the network of gents hs to be cpble of perceiving signls from the environment, nd of producing some effector functions (such s motion, for exmple) in order to hve n impct on the outside environment. Loclity of interction. An importnt feture of sttic swrm is essentilly the locl nture of interction: gents communicte only with their neighbours.

4 1462 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) Functionl heterogeneity. The solution of complex tsks (i.e. mnifesttion of emergent prerties of system) ssumes heterogeneity exists in the group in terms of differentition of functions crried out by gents: strtegic nd tcticl mngement, gthering nd informtion processing, reliztion of effector functions, nd so on. The orgniztion of the mechnism of this functionl heterogeneity is therefore n importnt question. The following tsk will be considered. Let there be set of gents (robots) cpble of locl informtion exchnge between nerest neighbours. Further, t some timepoint, the sttic swrm must relize certin procedure for role distribution; some individul must ct s control centre, nother must serve the dt processing function, nother hs to collect informtion from the externl environment, nd so on. The generl principles of role distribution cn be bsed on the following obvious resoning: node (gent) with mximum number of links (neighbours) becomes cndidte for the control centre role. Its nerest neighbours re nlyzers of informtion; they prepre informtion for decision-mking. Nodes locted on the periphery of network re responsible for gthering informtion. An exmple of such network of gents is shown in Fig. 2. B B A B B E D Fig. 2. An exmple of the orgniztion of network. Here, node A becomes min control center; its nerest neighbours (B) re ssigned the role of nlyzer; nd peripherl nodes () will ct s externl sensors. Lbels, E nd D designte other roles. The min question, then, is how these node-gents will choose the centrl, min node. There re severl possible wys to orgnize such vote. 4. Voting tsk onsider the following formultion of the voting tsk. Let there be set of gents with limited communiction portunities, so tht gents re cpble only of directing locl interctions between neighbours. The tsk requirement is tht gents must choose leder by voting. All further ssumptions re bsed on the fct tht the tology of network is unknown nd tht ll resoning must hve n especilly locl chrcter (i.e. considered from the point of view of the gent tking prt in voting). At some timepoint, gents receive globl signl tht the vote is beginning. At this moment, ech gent estblishes communiction chnnels with its neighbours, nd generlly directed grph is formed. The grph s node is n gent; incoming edges re interpreted s the bility to receive dt from source nodes. In this wy, communiction chnnels re formed. Let sttic swrm be fixed (i.e. ssume tht its tology will not chnge further). Ech gent is described s A (, L,, W )

5 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) where α = gent s identifier or nme; L = list of gent-neighbors from whom the gent α cn receive informtion (incoming edges); = cndidte s identifier, for whom the gent α votes; W = weight of cndidte, i.e. the number of votes which, in the gent s inion, should be given to the cndidte. The essence of voting procedure is tht ech gent defines for whom its neighbours vote. Depending, then, on the weight of the cndidte for whom the neighbour votes, the gent cn chnge its inion nd vote for the sme cndidte. Figure 3 presents one step of this voting scheme. The node lbels indicte the following: the gent s identifier α is the numertor, nd vlues nd W represent the cndidte s identifier nd weight. c c :W c ) b) c c :W c b b :W b :W d d :W d b :W +1 c :W c +1 d d :W d Fig. 3. One voting step: ) = strt condition, b) = votes finl distribution. Assume tht gent α votes for cndidte nd gent c votes for cndidte c. If weight W is less W c then gent α cn chnge its inion nd revote, dding one more voice to the weight of the new cndidte. The probbility tht gent i will chnge their inion under the influence of the inion of gent j (n ponent) cn be defined s follows: p ij Wi W W i j Tht is, the tendency to chnge inion nturlly depends on the degree of conviction or weight of the cndidte. The distribution of voices of cndidtes nd their weight t n initil timepoint is lso implemented quite nturlly; ech gent votes for itself (declres itself the cndidte), nd the weight of this decision is equl to the number of this gent s neighbours. Algorithms for the gent s voting behviour re given below. Algorithm G1(α). Agent s decision-mking 1 α gent the cndidte for whom gent α votes W cndidte s weight L list of gent s cndidtes Procedure G1(α) To choose mong neighbours of the ponent with mximum weight A : A W L, mxw i il

6 1464 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) To clculte vlue of probbility of chnge of inion: p W W W To chnge inion with probbility p : W W 1 end procedure G1(α) It is possible to roughen the decision-mking lgorithm, forcing the gent to chnge its inion on the cndidte if there is stronger ponent in its environment. If prity is observed between scles of inion of the gent nd the strongest ponent, the choice of decision cn be crried out probbilisticlly. Algorithm G2(α). Agent s decision-mking 2 Procedure G2(α) To choose mong neighbours of the ponent with the mximum weight A : A W L, mxw i il if W >W then -- The ponent is "stronger". We chnge the inion: W W 1 else if W =W then -- Forces re equl. We chnge the inion -- with probbility 0.5 p rnd() -- Rndom vlue from 0 to 1 if p > 0.5 then W W end if end if end procedure 1 A common voting scheme might look like this: Algorithm V( A ). Voting A set of gents

7 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) α gent the cndidte for whom the gent α votes W cndidte s weight L list of gent s cndidtes eoj flg of end of voting procedure procedure V(A) eof flse for ll αa do -- Agents initiliztion W dim( L ) end for while not eoj do -- Min cycle of vote for ll αa do -- ycle on ll gents G1(α) end for Definition of conditions of completion of voting procedure eoj end while end procedure V(A) In this lgorithm, the biggest problem is the item Definition of conditions of completion of voting procedure eoj. In the bsence of globl informtion on network s stte, the gent hs to mke the decision for itself tht voting is finished. Informtion received from the immedite environment is obviously not sufficient for this purpose, nd two vrints of gent behviour re therefore possible: 1. To consider tht voting must be completed in t most some certin number of steps, involving t ssessment of the number of voting lgorithm steps. 2. To relize some procedure for n exchnge of messges defining tht voting is completed, nd no gent further chnges their decision. The first vrint must prove convergence of itertive voting procedures. ome resoning cn be bsed by nlogy with schem for reching consensus [2]. DeGroot s pper defines consensus s mutul greement on subject mong group of pele (gents in our terminology). The min issue is tht with DeGroot s schem convergence cn be proved only for some prtil situtions. The second vrint lso implies the existence of some ssessed number of voting steps prompting the gent to send request defining voting procedure completion. The reliztion of procedures of this sort lso presents number of highly technicl difficulties in prticulr, n increse in network trffic, s ech gent must relize this procedure irrespective of the others. As further exmple of voting procedure, Figure 4 shows 3 steps in the voting procedure for solid group of robots. In the first step, ech gent votes for itself, so tht the number of cells designting "borders" of distribution of voices for the corresponding cndidtes is equl to the number of robots. The second step (revoting) shows n integrtion of res voting for chosen cndidtes. Finlly, in the sixth step, ll votes re ssigned to single cndidte, nd the voting procedure comes to the end. An exmple of the process of voting in extremely dverse conditions is shown in Figure 5, involving two clerly expressed zones connected by two isthmuses.

8 1466 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) Fig. 4. A voting procedure in solid group. teps 1, 2 nd Fig. 5. ycling voting procedure. teps 1, 3, 20 nd 37. In this sitution, cyclic process of distribution of voices cn be observed. At the 20th step of the vote, two stble res re formed, ech of which votes for their own cndidte, nd further process of cyclic revoting begins. It is clerly visible how preference res ctully trde plces in the 37th step. The process continues only s fr s step 51, when ll oscilltions st nd single cndidte remins. Justifiction of these lgorithms requires nswers to two min questions: (1) convergence of the lgorithms to one solution nd (2) estimtion of the number of voting steps. Unfortuntely, these questions currently remin en, s we cn spek only bout the results of modelling, ccording to which the process of voting converges. lerly, the number of voting steps did not exceed the number of robots in the group. entrlized voting. Problems with the schemes bove result in prticulr from the locl nture of the gents decision-mking. If ech gent knew the grph structure, definition of the leder would be quite routine tsk. In fct, it is possible to provide rther simple scheme of n exchnge of messges between gents, which with gurntee would llow receipt of the full grph structure. The number of steps does not exceed the number of robots N in group. To chieve this, it is enough for the robots to report to ech other everything they know bout the structure of the grph t the present time, s follows: At n initil timepoint, informtion bout the structure of the grph for ech gent is limited to knowledge of its neighbours. This incomplete grph is represented, for exmple, by the list of edges L i 0 sent by gent i to its neighbours. Hving received such list, ech gent combines it with their existing list for fuller picture in the form of new list: L t L i k t1 kz This is combintion of the lists received from ll neighbours from some re Z t the previous timepoint.

9 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) Through no more thn N steps, then, ech robot will hve ll the informtion bout the grph s structure. Further, ll of them elect the only leder, proceeding, for exmple, from resons of mximum connectivity, equidistnce nd so on. An obvious nd inerdicble deficiency of such scheme is very big flow of informtion, which should be reported to robot neighbours. The prcticlity of this scheme in rel systems is rther doubtful. 5. Tsk distribution In the bsence of morphologicl distinctions between gents, role distribution in sttic swrm is defined exclusively by the current tology of the system. The distribution process is presented s well-known procedure of control wve distribution. The inititor of distribution is the leder, whose role is designted s R 0. Direct neighbours of the leder receive n initil messge, ccording to which role R 1 is ssigned to them, nd so on. Thus, the role of robot i is defined by the roles in its environment: R i mx R 1 kz k The roles wve distribution is relized exclusively by locl interction, but there is one essentil problem. For successful functioning of system let M roles be required, with the process of distribution of wve consisting of L steps (Figure 6). R L... M R 3 R 2 R 1 R 0 L M Fig. 6. Actul (L) nd required role number (M). If M = L, there is no problem. If M < L, there re too mny performers with role R M. This is not good sitution, but it is not ftl becuse in sttic swrm we re not interested in role distribution timiztion (like [5]). If M > L, however, the sitution is worse, s there is deficiency of performers, which is extremely undesirble. Agents plying severl roles t once (combintion of speciliztions) cn cover the performnce deficit, so tht definition of the procedure whereby n gent should ssume dditionl functions seems simple. For exmple, if n gent with role number L hs no neighbours with roles bigger thn L, it mens tht this gent is t the periphery. Further, if we know tht M roles re needed, this gent hs to ssume roles from L to M. The prevention of ny deficiency cn lso be defined in dvnce. If there is group of N gents with mximum connectivity to ech gent s (the mximum number of neighbours), it is possible to estimte the minimum number of roles M. Estimtion of the M vlue is M ~ log N 6. onclusions imple nd effective methods hve been prosed for the solution of importnt problems of swrm robotics such s leder definition nd role distribution in group of gents. Efficiency is understood s the cceptbility of robots with limited cognitive bilities (insufficiency of sensory bilities, computing cpcities, communictions chnnels etc. in short, ll tht is peculir to swrm robotic). Despite their simplicity, reliztion of these mechnisms confirms the bsic possibility of formtion of very complex structures in the orgniztion of homogeneous groups, nd gin confirms tht distinctions between swrm, flock nd collective of robots re somewht rtificil.

10 1468 Vlery Krpov nd Irin Krpov / Procedi Engineering 100 ( 2015 ) The sttic swrm model is convenient wy of looking t swrm robot orgniztion. While it is limited to exclusively locl interction between gents, it offers ll the dvntges of system understood s network of connected gents, llowing solution of such problems s storge nd dt processing, coordinted movement nd so on [7]. In future work, we he to investigte the mechnism of logicl consequence in sttic swrms, hypothesizing tht logicl consequence procedures cn be implemented by exclusively locl interction methods. Acknowledgements We grtefully cknowledge the support of RFBR grnt No References [1] Bermn., Hlsz A., Kumr V., Prtt.: Bio-Inspired Group Behviors for the Deployment of wrm of Robots to Multiple Destintions. In 2007 Interntionl onference on Robotics nd Automtion. pp , IEEE, [2] DeGroot M. H., Reching onsensus. J. Amer. tt. Assoc., 1974, Vol 69, Issue 345, pp [3] Dewi T., Rism P., Oktrin Y. Wedge Formtion ontrol of wrm Robots. The 14th Industril Electronics eminr, Electronic Engineering Polytechnic Institute of urby (EEPI), Indonesi, 2012, pp [4] Gigliott, O., Mirolli, M., Nolfi,. ommuniction bsed dynmic role lloction in group of homogeneous robots. Nturl omputing, Volume 13, Issue 3, eptember 2014, pp [5] Klyev I., Kpustjn., Ivnov D. Decentrlized control strtegy within lrge group of objects bsed on swrm intelligence. Proc. of the 2011 IEEE 5th Interntionl onference on Robotics, Automtion nd Mechtronics, RAM 2011, pp [6] Krpov, V.E. Prtil mechnisms of ledership nd self-consciousness in swrm robotics. Proc. of the 13th Ntionl onf. on Artificil Intelligence KII-2012, Belgord, 2012, (Belgorod tte Technicl University, Belgorod, 2012), Vol. 3, pp [in Russin]. [7] Krpov, V.E. ontrol in sttic swrms. Problem definition. Proc. of the VII Interntionl science-prcticl conference on Integrted models nd soft computing in rtificil intelligence, Kolomn. (Fizmtlit, Moscow, 2013). Vol. 2, pp [in Russin]. [8] Kim,.-., hin, K.H., Woo,.-W., Eom, Y.., Lee, J.M. Performnce nlysis of entry-bsed multi-robot coertive systems in MANET. Interntionl Journl of ontrol, Automtion nd ystems, Volume 6, Issue 5, October 2008, pp [9] Kukushkin, I.K.; Ktlinic, B.; esrec, P.; Zdyb, D. & Kettler, R.: Modeling of mobile robot behvior for line-less Bionic Assembly ystem, Annls of DAAAM for 2012 & Proceedings of the 23rd Interntionl DAAAM ymposium, IBN , IN , pp , Editor B[rnko] Ktlinic, Published by DAAAM Interntionl, Vienn, Austri, [10] Louks Andres, Woehrle Mtthis, Gltz Philipp, Lngendoen Koen. On Distributed omputtion of Informtion Potentils. Proceedings of the 8th AM IGAT/IGMOBILE Interntionl Worksh on Foundtions of Mobile omputing, FOM' , Mdeir; Portugl; 19 July 2012, Article number 5. [11] Nissn EPORO Robot r "Goes to chool" on ollision-free Driving by Mimicking Fish Behvior - Advnced Robotic oncept Debuts t EATE JAPAN [12] Pvlovsky V.E., Kirikov E.P., Pvlovsky V.V. Modeling of behvior of big groups of robots in the environment with obstcles. Proc. of the scientific seminr "ontrol in distributed network-centric nd multi-gents systems". t.petersburg: "Koncern NII «Jelektrribor» ", 2010, pp [in Russin]. [13] ong, Y., Zho, W. Multi-gent system rendezvous vi refined socil system nd individul roles. WEA Trnsctions on ystems nd ontrol. Volume 9, Issue 1, 2014, pp [14] tefnuk V.L. Locl Orgniztion of Intellectul ystems. Fizmtlit, Moscow, p. [in Russin]. [15] Yogeswrn M. nd Ponnmblm. G. (2010). wrm Robotics: An Extensive Reserch Review, Advnced Knowledge Appliction in Prctice, InTech. pp [16] Yu, H., Jin, J., Wng, Y. Flocking motion of mobile gents with leder bsed on distnce-dependent djcency mtrix. Lecture Notes in omputer cience. 1st Interntionl onference on Intelligent Robotics nd Applictions, IIRA 2008; Wuhn; hin; 15 October 2008 through 17 October 2008; ode Volume 5314 LNAI, Issue PART 1, 2008, pp [17] Zhiguo hi, Jun Tu, Qio Zhng, Lei Liu, Junming Wei. A urvey of wrm Robotics ystem. Proc. of the Third Intern. onf. on Advnces in wrm Intelligence, henzhen, hin, V.1, pp