Cooperative Motion of Swarm Mobile Robots Based on Particle Swarm Optimization and Multibody System Dynamics

Transcription

1 Abtract Cooerate Moton of Swarm Moble Robot Baed on Partcle Swarm Otmzaton and Multbody Sytem Dynamc Qrong Tang and Peter Eberhard Inttute of Engneerng and Comutatonal Mechanc Unerty of Stuttgart Pfaffenwaldrng Stuttgart Germany [qrong.tang eter.eberhard]@tm.un-tuttgart.de Th aer addree the roblem of cooerate moton of a warm moble robotc ytem wth the uroe of earchng a target n a comlcated enronment. The oluton nred from Partcle Swarm Otmzaton and combned wth multbody ytem dynamc whch alo nclude the conderaton of robot hycal roerte lke ma nerta force acceleraton etc. The entre robot warm manly guded by th hycal PSO and an ndeendent obtacle aodance module acte when robot encounter any conflct durng mon. Th aer conder an artfcal warm moble robot ytem to erform earchng tak and each member of the ytem may nteract wth t neghbor or the enronment by lmted local communcaton ablty. Seeral grou of mulaton are et u for the erfcaton of the trategy and the reult how that th method create the dered behaor well. The mulaton exerment alo netgate the feature of fault tolerance of th trategy. Fnally a framework for the future alcaton on real robot brefly dcued. Introducton Th aer netgate and focue on the roblem of warm moble robot cooerate moton. Swarm robotc ha acheed gnfcant rogre beneftng from the deeloment of artfcal ntellgent and alo the great mroement of communcaton technology. Neerthele erformng more comlex tak t enroll many challenge whch on other hand alo extend the alcaton area of warm robotc ytem. Swarm moble robot are ued e.g. for odor or lght ource localzaton (Meng L Sun Ba and Zeng 9 Hereford Sebold and Nchol 7) and effcent collecton of ll ol (Kakal and Ventko 8 Frtch 9). A number of organzaton carred out reearche through many tratege. For examle Martnell Pont and Segwart n reearched on the roblem of multaneouly localzng all member of a team of robot. They oled the roblem by tratege of relate oberaton and fued the rorocete and exterocete data nto an extended Kalman flter. Xu and Chen (8) ued an artfcal moment method for warm robot formaton control. In recent year many reearcher focued on ung bo-nred algorthm for warm robotc. It can range from mall organm a mle a bactera (Gaarr and Proer 8) to large mammal lke whale (Camazne Deneubourg Frank Sneyd Theraulaz and Bonabeau ). The Partcle Swarm Otmzaton (PSO) wa orgnally ntroduced by Kennedy and Eberhart n 99. After that PSO wa deeloed ery fat and generated numerou arant due to t mle dea and eay rogrammable feature. Seeral grou of centt adoted th algorthm for warm moble robot. (Doctor Venayagamoorthy and Gude 4) dcued ung PSO for mult-robot earchng and they manly focu on otmzng the model arameter wthout conderaton of calablty. Hereford n 6 deeloed a dtrbuted Partcle Swarm Otmzaton algorthm nonconderng obtacle n

2 the enronment and lmted rotaton. Pugh and Martnol (8) reented an adate trategy for a grou of robot engaged n the localzaton of multle target but the earch algorthm manly baed on the chemotax behaor of bactera wherea PSO only ued to otmze the arameter. Crn n 9 utlzed the PSO algorthm for warm robot earchng and formaton control wth lmted communcaton range and noe. Atyab Phon-Amnuauk and Ho () ntroduced a arant known a AEPSO to work n eeral earch cenaro uch a bomb darmng and uror recung howeer AEPSO can not be etablhed a a general method that can handle the entre robotc earch doman. Other reearche lke (Chang Chu Roddck and Pan ) (Xue and Zeng 9) (Derr and Manc 9) contrbuted ome mortant aect to the warm robotc. Howeer there are tll few reearche focung on warm robotc on a ytem leel whch can handle the entre warm comletely and nclude robot hycal roerte. So n contrat to the aboe mentoned reearche th aer reent a detaled trategy for warm moble robot cooerate moton eecally for earchng tak on a ytem leel. It baed on the PSO algorthm and ue dea of multbody ytem dynamc whch nclude the conderaton of robot hycal roerte. Prelmnary work n th area can alo be found n (Tang and Eberhard 9 and ). The aer tructured a follow. Secton reent the extenon of the bac PSO to a mechancal PSO on a ytem leel by ntegratng hycal feature of a warm. Smulaton and reult are hown n Secton. Secton 4 decrbe the tratege for real hycal moble robot whch are focu of our ongong work. Fnally concluon are gen n Secton. A Sytem Leel Moton Model for Swarm Moble Robot Swarm robotc ytem uually cont of many dentcal or mlar mle nddual. Snce they hae ery attracte feature uch a fault tolerance calablty and adatablty arou method hae been rooed for controllng moton and related behaor. One knd of method clafed a bo-nred. Many knd of ocal anmal lke brd bee and fhe organze themele n a grou and mong a a ngle communty wthout a central control ntance. Comared to human a ngle anmal ha a low leel of ntellgence. They hae nether adanced communcaton technology (language) nor comlcated logcal nght (bran) but they can erform ery well when mong together. In lght of thee fact th tudy et u a control framework/model for warm moble robot moton baed on PSO a tycal bo-nred warm algorthm. In order to undertand and then ue uch a method t neceary to netgate and analyze the man feature and challenge of warm robotc ytem frt both n the ew of robotc and warm behaor.. Man Feature and Challenge of Swarm Robot A warm ytem an aggregaton of ome member. The man feature artcularly the adantage of warm robot are ummarzed a () collaboraton the whole warm robot ytem how ueror erformance comared to nddual een f each of the member can only erform mle acton () fault-tolerance.e. nddual falure wll not reult n the falure of the entre ytem () arallelm.e. comleton of tme and ace tak n arallel

3 (4) harng.e. ung mechanm of relate otonng and nformaton exchange. Other adantage lke calablty or adatablty are alo ueful n a warm robotc ytem.. Clacal PSO and Extenon PSO uually ued a a tradtonal otmzaton method whch nred from the ocal behaor of flock of brd. It ha been found to be comette n arou aect e.g. due to t mlcty. In PSO a warm cont of N member called artcle. The artcle cooerate wth each other. Each artcle n the ytem oee nformaton about oton and elocty n a n-dmenonal ace and they are generated wth an ntally random oton and elocty. For the alcaton n th aer (.e. ung PSO for warm moble robot) n=.e. only lanar cae are condered. Of coure t can be extended f neceary for examle to n=. Hgher dmenon make ene for an otmzaton roblem but are not hycally oble for robot. The terate roce qute mle n clacal PSO and can be wrtten for the -th artcle at the j-th dmenon a j j c r ) c r ( ) () j j ( elfbet j j warmbet j j t () j j max... N j () where Equaton () and () are the elocty and oton udate reectely. Equaton () lmt the elocty to a redefned maxmum max. The frt tem at the rght de of Equaton () the nerta art whch contan the coeffcent and ued for roceedng n the former drecton. Uually c and c n Equaton () are referred to a cognte and ocal calng factor whch are generated from the attracton to the reou bet oton of the current artcle elfbet j and the entre warm bet oton warmbet j reectely. The factor r and r are unformly dtrbuted random arable and range n [ ] where teraton te. Uually the tme te t n Equaton () omtted whch make the equaton hycally wrong but common n PSO lterature. Furthermore n clacal or tandard PSO the warm bet n Equaton () often relaced by a neghborhood artcle nhoodbet j. In order to ma warm moble robot conenently th wrtten n matrx notaton. Thu all N artcle wll be ummarzed a wth r r I cr r I c r elfbet r N I t r r I nhoodbet r I r N (4). () I Here I a unt matrx. The matrce for elocte and oton can be formulated a

4 Smlarly [ [ [ [ elfbet elfbet nhoodbet nhoodbet T ] T ] [ [ [ [ N ] T R... N N ] T R... N elfbet elfbet T elfbet elfbet] nhoodbet nhoodbet T nhoodbet nhoodbet] N. N elfbet... nhoodbet N... N N elfbet. ] T R N nhoodbet N ] T R N The tandard PSO and t arant are ued for many engneerng otmzaton roblem. Here three more thng mut be addreed and exlaned before tranferrng t onto robot. () PSO n th tudy ued for gudng the robot to earch target wthn a lane rather than dong general otmzaton. Thu how to adjut the otmzaton arameter not addreed n th tudy. () The reaon to ue a neghborhood mode here manly becaue the robot uually contan only lmted enory ablty and to mroe robutne. () In tandard PSO the artcle change oton n the earch ace n any drecton wth any elocte max max. It neer conder hycal roerte lke e.g. ma acceleraton or lmted force.. Integraton of the Phycal Proerte of Swarm Moble Robot nto PSO The hycal roerte of nddual robot member affect the erformance of the oerall warm ytem thu they mut be condered when one buld a moton model for warm moble robot. The trategy ued n th aer to relace the artcle n the PSO-baed algorthm by mechancal robot whch follow hycal law. Each member of the warm robotc ytem an ndeendent mechatroncal ytem. So one would lke to tart the deraton of moton from a hycal ont of ew. Conderng a real moble robot t wll hae one or eeral actuator to dre t. So the acceleraton are generated from force whch are generated by the actuator. Robot moe n a tme te t by t a t (8) where the robot oton gen n abolute coordnate and the mle Euler forward ntegraton method ued. Then the moton of robot goerned by a t. (9) Comarng Equaton (9) wth (4) one already can ee ome clue to ue PSO for gudng robot moton. In multbody dynamc one know that all the external nfluence actng on a rgd body can be ynthezed by a reultant force f and a torque τ. If the oton (6) (7) 4

5 ector of the center of ma of body decrbed n abolute coordnate and m t ma then due to Newton econd law we hae d ( m ) dt d dt ( m ) m m a f () where a the tranlatonal acceleraton of body. Accordngly another eental art of rgd body moton rotaton whch decrbed by Euler law d dt ( J τ. () o ωo ) o The nerta tenor rereented by J o ω o the angular elocty and τ o the torque. If one ue R a the rotaton matrx from the body coordnate ytem to the nertal coordnate ytem then Equaton () can alo be wrtten a J α ω J ω τ () where α rereent the angular acceleraton. Equaton () and () can be ummarzed by m I a f. () J α τ ω Jω The generalzed acceleraton for robot wrtten n a column ector contan both tranlatonal and angular nformaton whch rereented by a and α reectely. In a more general way f we defne a α (4) a the generalzed acceleraton for all N robot and k a the term whch come from Euler equaton a well a a defnton that q contan the nformaton of force and moment actng on all N robot then the moton of entre warm robot ytem can be formulated by M k q. () Here M a ma matrx whch oeng the mae and nerta for the N robot. A th tudy ue no lnk and jont.e. t a free ytem th ma matrx T M dag( mi mi mn I J J J N ) M (6) whch nclude both the nformaton of mae and rotatonal nerta of the entre warm ytem. Wth a generalzed force matrx F Equaton () alo can be wrtten by M ( q k) M F. (7) For degnng arorate controller for real robot one wrte Equaton (7) a a tate equaton y M F (8) where and are the tranlatonal and rotatonal oton elocty and acceleraton reectely.

6 In the mulaton enronment or n the real robot cenaro f one know the robot ntal tatu and ue an arorate ntegraton roce then the future tatu of warm robot ytem can be comuted.e. the moton of th ytem obtaned. There are many ntegraton method uch a Euler forward Euler backward Traezodal and o on. Here for examle through Euler forward ntegraton method the moton of warm robot wth tme can be comuted by y y ty where and are the tme ont t the choen tme te. It well known that the mle Euler forward algorthm nether ery table nor ery effcent. Howeer thee aect are not o crtcal here nce for gnal roded from enor of real robot the ntroduced naccurace are een hgher. Thu to mroe the readablty we wrte the formulae only for th mlet cae. Rewrtng Equaton (9) by nertng Equaton (8) and (9) yeld t M F (9). () Here combned wth ractcal alcaton of the robot cenaro th tudy make ome aumton. Here the robot are only dren by force there are no torque.e. τ. Second t aume that the robot hae an nerta tenor o that the term ω Jω n Equaton () anhe. Thrd n th tudy t aumed that the drng force f de- termned from followng three art f f f l ( l ( l wthn whch k k elfbet l ) nhoodbet ) l ( k ) are the force factor and ummarzed n N N k I l k I ln k I N ) R l dag( l k. () The force f f and f contan hycal meanng.e. f attracton force from the lat elf bet oton to the current robot oton roortonal to ther dtance f attracton force from lat bet oton of a robot who locate n a ecfed neghborhood doman of current robot oton roortonal to ther dtance f a knd of nerta force whch roortonal to t lat elocty and counteract a change n drecton. Wth the defnton of force nertng Equaton () to Equaton () the moton of the entre warm ytem can be formatted by ( I tm l M t M l N l ) elfbet nhoodbet Equaton () a mechancal PSO model whch ued to control the moton of the entre warm moble robotc ytem. Next a bref comaron between the hycal PSO model () and the clacal PSO (4) made. The correondng relatonh between Equaton () and (4) are (). () 6

7 I N tm tm tm l l l c r k c r. k Here ome ue mut be addreed. It eay to extend the model to -dmenonal and alo nclude the torque. The force defnton can alo be extended e.g. to defne an external force to teer the robot when erformng a earch tak. In Equaton () the force coeffcent l k ( k ) alo ge a oblty to nclude ome random effect. The tme te t choen accordng to ome aect. In the real robot alcaton t deend on the eed of embedded CPU and model robutne. Fnally ome correondence are lted n Table. Table : Mang from clacal PSO to warm moble robot earchng tem tandard (clacal) PSO warm moble robot earchng member artcle robot orgnal uroe general otmzaton method earch ome knd of target n enronment dcretene udate by dcrete terate te contnuou erceton globally locally communcaton can be global lmted n a local area wth lmted nteracton to eer robot and enronment otonng not neceary or ue an abolute relate otonng nagaton obtacle aodance ath lannng moton retrcton hycal roerte ealuaton mechanm ealuaton data way not neceary Smulaton and Reult deal unretrcted no ma no olume ealuaton of a ftne functon data can be tored wthout retrcton (4) correondng tratege for obtacle aodance ath lannng mut be condered lmted by nerta elocty and actuator ma olume etc. mut be condered detectng the trength of gnal whch come from target lmted nce the memory of each robot uually not large Next an examle reented where a warm of hycal robot guded by PSO. Th mle examle defned by mnmze F ( x y) ( x x ) ( y y ) () 7

8 ubject to 8 G ( x y) ( x ) y 49 G ( x y) y ( x ) 8 x ( y.) G( x y). x y. Here ( x y ) (4) taken a the target whch wll be earched by warm robot. The robot earch n an enronment unknown to them ncludng alo ome obtacle and mathematcal contrant. The mnmzaton roblem n the examle mathematcally qute tral but t uffcent to erfy the trategy decrbed n th aer. Th tudy conder warm moble robotc ytem and there a hycal meanng of functon F ( x y). In our examle F ( x y) ge a crcular read where the ource (target) locate at t center. Th tudy ue PSO wth augmented Lagrangan multler to ole the contraned roblem leae refer to (Sedlaczek and Eberhard 6) and (Tang and Eberhard 9) for detal of th method. Here t hould be emhazed that the contrant n Equaton (6) are dfferent from the obtacle n the enronment nce robot can acce or a contraned area durng ther earch wherea th not allowed for the obtacle. Aodng obtacle guaranteed by the robot enor and ther correondng roce module. The acceble contraned area n th tudy can be condered a ome knd of functonal lmt uch a e.g. robot ang through ome dangerou regon.. Smulaton Enronment and Obtacle Aodance Th tudy erfe the trategy n a mulated enronment before tranferrng to a real enronment wth real hycal robot. Due to the comlexty of real world t neceary to conder dfferent knd and hae of obtacle. Durng the earch robot are manly guded by Equaton () and an ndeendent obtacle aodance module actated f any conflct haen whch nclude robot to robot and robot to obtacle aroach. In th tudy the obtacle aodance model only ue the dtance enor to judge whether they locate n an area dangerou for collon. (6). Exerment Here the exermental tak to dre a mulated warm moble robotc ytem to earch a target n the mulaton enronment and moe them toward th target whle aodng obtacle encountered. In th ecton the general te wll be hown and then followed wth two mulaton exerment... General Ste The general rocee to erform th tudy n mulaton are goerned by followng te. Ste : Intalzaton et a grou of mulated robot (mechancal roerte ncluded) buld enronment (ma). 8

9 Ste : Integratng wth N n te the model () record the fnal ncrement end to controller. Ste : Controller recee ncrement and ge command to actuator after calculaton then actuator dre robot wth one tral hycal te. If collon occur call obtacle aodance module after deconmakng ge one real hycal te. Otherwe dre one real hycal te drectly. Ste : Check found target? If ye go to te 4 f no run agan from te to. Ste 4: End Here N n the number of ntegraton te. The number the choen tme te n ntegraton roce... Verfcaton of the Bac Feablty N n ha a cloe relatonh to The uroe of th frt exerment to erfy the feablty of the decrbed hycal PSO model n a general way. Bacally we want to how that the man feature n clacal PSO can be ued and realzed n a robot warm ytem. The mulaton enronment et a ame a n Fgure and we ue a crcle to rereent a olume robot. In th tudy we et arameter qute unuual comared to clacal PSO nce the model nclude mechancal roerte of each robot thu e.g. f the robot ma ncreaed the effect from attracton force wll decreae wthout further change. The mulaton done on a Matlab latform and n th exerment robot are mulated. Th exerment take run fnally 8 run can fnd the target by the mulated robotc warm wth a ery hgh recon although ome member are defned to fal durng mon. target 4 6 cubc lne 8 7 Fg. : Smulaton enronment Fgure ge an examle howng the ntal and fnal tatu of that run. From th fgure one can ee that the warm fnd the target whle aodng collon. So t oble that th model can be ued for controllng the moton of warm moble robotc ytem. Here the ecfed earch tme et to econd. Note that ome of the robot may tll locate n the contrant area whch near to the target whch allowed durng 9

10 the earch tme but not after conergence. In Table t how ome reult of run whch erfed the feablty of model () n a tattcal aroach. From th table one can ee that th model can qualfy the tak requred by a earchng warm robotc ytem although eeral run faled durng the earch mon. It mut be ecfed that th tudy et a ery trct accuracy. A tattc about all the run made n Table and Fgure. * (a) * (b) Fg. : Verfcaton of the bac feablty (a) ntal tatu at (b) fnal tatu at Verfcaton of Fault-Tolerance Due to many reaon uch a e.g. enronmental noe uneen terran and communcaton delay one or eeral robot can fal and get tuck. Neerthele the earch hould be comleted by the warm. Th ablty one of the man feature of a warm robotc ytem. Motated by th real world tuaton n the econd grou of exerment th tudy

11 randomly et eeral robot to be dead durng the earchng tak. So the man uroe of th econd exerment to erfy the fault-tolerance of the decrbed hycal PSO model. Table : Some reult of run for erfyng the feablty no. bet robot oton robot detach ucce no. bet robot oton robot detach ucce (. 4.) ye 46 ( ) ye (. 4.9) ye 47 (.8 4.) ye ( ) ye 48 (. 4.) ye 4 (.78.99) ye 49 ( ) ye ( ) ye (..9999) ye 6 ( ) ye (. 4.) ye 7 ( ) ye (. 4.48) no 8 (. 4.) ye (.9.999) ye 9 (..977) ye 4 ( ) ye ( ) ye ( ) no 9 (.6 4.6) ye 84 ( ) ye 4 ( ) ye 8 ( ) ye 4 ( ) ye 86 ( ) ye 4 ( ) no 87 (. 4.) ye 4 ( ) no 88 (.9.998) ye 9 ( ) ye 96 ( ) ye 9 ( ) ye 97 (.7 4.6) ye 9 ( ) ye 98 (.78 4.) ye 94 ( ) no 99 ( ) no 9 ( ) ye (. 4.) ye totally ucceful: 8 run addtonally no robot detach from warm: 6 run one robot detach from warm: 7 run two robot detach from warm: run three robot detach from warm: run uccefully fnd target and wthout robot detach from warm: run uccefully fnd target but wth one robot detach from warm: 7 run uccefully fnd target but wth two robot detach from warm: run uccefully fnd target but wth three robot detach from warm: run

12 Fg. : Illutraton of the bet robot oton ( run how robot body center) In the mulaton the number of robot reduced to nce faled robot wll ge a greater nfluence to a maller warm ytem. Seeral exerment were done n whch the quantty of dead robot et to 8 and 7. For each of thee cae one examle run dlayed wth t fnal tatu ee Fgure 4. 8 * * 6 7 (a) 4 (b) * * (c) (d) Fg. 4: Inetgaton of fault-tolerance for robot (a) wth dead robot (b) wth 8 dead robot (c) wth dead robot (d) wth 7 dead robot

13 In Fgure 4 examle wth 8 and 7 dead robot n the warm whch totally contan robot are llutrated. The dead robot are marked wth an ndex number. From th exerment one can ee that the dered hycal PSO model ha a trong fault tolerance nce u to 7 robot of the can fal and tll the remanng robot can work n normal tatu due to the learnng effect of PSO. The target and contrant teted n th tudy are qute tral but uffcent to erfy the trategy reented n th aer. The man contrbuton of th aer nether to erfy the feablty nor erfy the fault tolerance of th model but to buld a model for controllng a warm moble robotc ytem to earch a target n a ytematc way. 4 Prooed Stratege for Real Phycal Moble Robot The rooed real robot we want to ue the Feto Robotno Fgure. Bede ome commonly ued comonent n moble robot the Robotno oee three omndrectonal wheel whch make t oble to rotate n full 6 degree. There are alo 9 nfrared dtance enor. colour webcam controller battere exanon board ocket for I/O etc. motor encoder teel cha rotecte guard omn-drectonal wheel Fg. : Feto Robotno and t man comonent 9 nfrared dtance enor Communcaton requred by our model e.g. nce the robot need to know the bet robot n ther neghborhood doman. Howeer only hort dtance local communcaton requred. Unfortunately t not oble to erform communcaton between Robotno drectly o further more work need to be done to qualfy communcaton. One rooal can be to end nformaton frt to an external comuter and then end command from th comuter back to robot. Th already teted howeer uch knd of trategy not urued ultmately nce a decentralzed trategy referable. So another trategy to attach an addtonal module onto the Robotno to hae a wrele eral ort whch oularly ued by robot communcaton. There are many method deeloed for the otonng (localzaton) of robot but mot of them are ued for the alcaton whch nole only ngle robot. Th tudy reearche on the alcaton where a warm of moble robot work n collaboraton to erform a earch tak thu a method tuated for localzng the oton of all robot

14 member requred. Howeer the Robotno lack uch rece otonng ytem thu ome method lke e.g. RFID-Rado Frequency Identfcaton tag (Hähnel Burgard Fox Fhkn and Phloe 4) can be ued. Concluon In th work a warm robot moton model baed on PSO and multbody ytem dynamc ha been reented whch nclude the conderaton of robot hycal roerte. A one-to-one mang from artcle n clacal PSO to robot n th warm moble robotc ytem wa ued to erform a earch tak n cooerate manner. There ha thu far been farly lttle work n th feld baed on PSO and multbody ytem. It ha been hown that uch a hycal PSO model oble to be tranferred and ued for a warm moble robotc ytem. The dered model wa erfed by mulaton exerment wthn a comlcated mulated enronment and the reult how t feablty and fault tolerance. One natural future tak to conduct a ytem leel exerment wth a warm of real and mulated Robotno. Acknowledgement The author want to thank the Chnee Scholarh Councl (CSC) for uortng Mr. Qrong Tang to tudy n Germany a a doctoral tudent. Part of th work uorted by the Cluter of Excellence Smulaton Technology (SmTech) n Stuttgart Germany whch alo greatly acknowledged. All uch hel and uort are hghly arecated. Reference Atyab A. Phon-Amnuauk S. and Ho C.K. (). Alyng area extenon PSO n robotc warm. Journal of Intellgent and Robotc Sytem 8(): 8. Camazne S. Deneubourg J.-L. Frank N.R. Sneyd J. Theraulaz G. and Bonabeau E. (). Self-Organzaton n Bologcal Sytem. Prnceton Unerty Pre Prnceton. Chang J.F. Chu S.C. Roddck J.F. and Pan J.S. (). A arallel artcle warm otmzaton algorthm wth communcaton tratege. Journal of Informaton Scence and Engneerng : Crn Y.J. (9). Cooerate control of multle warm of moble robot wth communcaton contrant. In Otmzaton and Cooerate Control Stratege Lecture Note n Control and Informaton Scence age 7. Berln: Srnger. Derr K. and Manc M. (9). Mult-robot mult-target artcle warm otmzaton earch n noy wrele enronment. In Proceedng of the nd Conference on Human Sytem Interacton age 8 86 Catana Italy. Doctor S. Venayagamoorthy G. and Gude V. (4). Otmal PSO for collecte robotc earch alcaton. In Proceedng of the IEEE Congre on Eolutonary Comutaton age 9 9 Portland USA. Frtch D. (9). Steuerung elbtorganerender Mult-Roboter-Syteme für dynamche Sammelaufgaben am Beel der Bekämfung martmer Ölerchmutzungen (n German). Doctoral the Unerty of Stuttgart Germany. 4

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