Visually Built Task Models for Robot Teams in Unstructured Environments Abstract 1. Introduction

Transcription

1 Vsuall Bult as Models fo Robot eams Ustuctued Evomets Vve A. Suja ad Steve Dubows (vasuja Depatmet of Mechacal Egeeg Massachusetts Isttute of echolog Cambdge, MA 039 Abstact I feld evomets t s ot usuall possble to povde obotc sstems wth vald geometc models of the tas ad evomet. he obot o obot teams wll eed to ceate these models b pefomg appopate seso actos. Hee, a algothm based o teatve seso plag ad seso edudac s poposed to eable them to effcetl buld 3D models of the evomet ad tas. he method assumes statoa obotc vehcles wth cameas caed b atculated mouts. he algothm uses the measued scee fomato to fd ew camea mout poses based o fomato cotet. Issues addessed clude model-based multple seso data fuso, ad ucetat ad vehcle suspeso moto compesato. Smulatos show the effectveess of ths algothm.. Itoducto A mpotat goal of obotcs eseach s to develop moble obot teams that ca wo coopeatvel ustuctued feld evomets, such as show coceptuall Fgue [, 7]. Potetal tass clude eplosve odace emoval, de-mg ad haadous waste hadlg, eploato/developmet of space, evomet estoato, ad costucto [, 7, 5]. Fgue : Repesetatve phscal sstem he cotol of such sstems tpcall eques models of the evomet ad tas. I ustuctued feld evomets t s ofte ot possble to have such a-po models. I such cases, the obot eeds to costuct these fom seso fomato. A umbe of poblems ca mae ths o-tval. hese clude the ucetat of the tas the evomet, locato ad oetato ucetat the dvdual obots, ad occlusos (due to obstacles, wo pece, othe obots). If the sstems ae equpped wth cameas mouted o atculated mouts, tellget plag of the camea moto ca allevate poblems of the occlusos, povdg a accuate geometcal model of the tas ad evomet. If the sstem cossts of moe tha oe obot, plag the behavo of these mult-fomato shag sstems ca futhe mpove the sstem pefomace. Pevous wo plag of vsual sesg stateges ca be dvded to two aeas [, 8]. Oe of these s coceed wth seso postog placg a seso so that t ca best obseve some featue ad selectg a sesg opeato whch wll pove the most useful object detfcato ad localato. Reseaches have lmted the wo to model-based appoaches, equg pevousl ow evomets [4, 6, 9]. aget motos (f a) ae assumed to be ow. Bute foce seach methods dvde the ete vew volume to gds, octees, costat sets, ad seach algothms fo optmum seso locato, ae appled [5, 6, ]. Addtoall, the eque a-po owledge of object/taget models [8]. Such methods ca be effectve but ae computatoall epesve ad ot pactcal fo ma eal feld evomets, whee occlusos ad measuemet ucetates ae peset. he othe decto of eseach plag of sesos s seso data fuso combg complemeta data fom ethe dffeet sesos o dffeet seso poses to get a mpoved et measuemet [7, 8]. he ma advatages of mult-seso fuso ae the eplotato of data edudac ad complemeta fomato. Commo methods fo seso data fuso ae pmal heustc (Fu logc) o statstcal atue (Kalma ad Baesa fltes) [3,, 4]. Fo evomet ad taget model buldg both aeas pla e oles. Howeve, lttle wo has bee doe effectvel combg the capabltes of seso placemet plag ad seso fuso, to develop a sesg stateg fo model buldg to be used b obots ad obot teams ustuctued evomets. Some studes have cosdeed coopeatve obot mappg of the evomet [8, 3, 9]. Novel methods of establshg/detfg ladmas ad dealg wth cclc evomets have bee toduced fo doo evomets [8, 9]. I some cases, obsevg obot team membes as efeeces to develop accuate maps s equed [3]. Mappg has bee doe sequetal bute foce fasho [3, 9]. Reseaches have addessed the cocept of map buldg usg a sgle moble vso sstem [, 4, 0]. Ofte, seso models ad data ucetat ae ot full cosdeed [, 0, ] o eploato schemes ae ot developed [3, 4]. Stuctued evomet ad patal owledge assumptos ae also made [4, 4]. hs pape poposes a evomet ad tas model buldg algothm, to ovecome the ucetates obot ad camea locato ad oetato, fo obot teams coopeatvel wog a ustuctued feld evomet. It s assumed that dmesoal geometc fomato s elevat ad equed fo obots to pefom the opeatos, such as the costucto of feld

2 facltes. It s also assumed that the sstem cossts of two (o moe) moble obots wog a uow evomet (such as costuctg a plaeta stuctue see Fgue ). hee ae o phscal teactos betwee the obots. he vehcles ad taget ae statc. Each has a 3D vso sstem mouted o a atculated am. Sesg ad seso placemet s lmted, esultg occlusos ad ucetates. Aga, the objectve s to effcetl buld a geometcall cosstet dmesoal model of the evomet ad taget, avalable to all obots, to allow fo tass to be pefomed. hs volves locatg the obots ad mappg a ego aoud a taget wth espect to some taget fed efeece fame. he e dea s that the algothm bulds a evomet ad tas model b fusg the data avalable fom each dvdual obot, povdg both mpoved accuac as well as owledge of egos ot vsble b all obots. Usg ths algothm, the dvdual obots ca also be postoed optmall wth espect to the taget [0]. Howeve, ths s beod the scope of ths pape. Moble vehcles wth suspesos Ite-sstem commucato Idepedetl moble camea Fgue : Coopeatve mappg b obots. Algothm descpto.. Ovevew he fst step coopeatve model buldg s to vsuall costuct a model of the local evomet, cludg the locatos of the tas elemets ad the obots themselves. We assume that ol the geomet of the tas elemets (such as the pats of a sola pael that eeds to be assembled [7]) s well ow. Obstacles ad obot postos ae ot ow. Steeo Acque Steeo 3 -D Map Reposto Camea Pa Optmum Pose (ematc costats) Itale - Locate taget - setup commo ef. fame 3-D 3D Map Fuso Wold geomet model (w/ ucetat) Ratg fucto (RF ) Evaluated fo all camea pas Fgue 3: Outle of model buldg ad placemet algothm Fgue 3 outles the map buldg algothm. he algothm cossts of two majo pats. I the fst pat, the atculated cameas coopeatvel sca the ego aoud a taget geeatg a 3D geometc model, so that the obots ca locate themselves ad the obstacles the taget efeece fame. he secod stage cossts of usg ths model to fd a optmum pose fo the multple camea sstems to vew the taget(s). he 3D map s modeled as a pobablstc dsceted occupac gd. Eve voel the map has a value fo pobablt-ofoccupac that ages fom 0 (empt) to (occuped). A value of 0.5 dcates mamum ucetat occupac of the voel. he pocess s taled b vsuall fdg the taget ad obots a commo efeece fame. hs s doe b loog aoud ad matchg the ow taget elemet geometc model wth vsual data. Net, a ew camea pose s foud fo each of the cameas b defg ad evaluatg a atg fucto (RF) ove the ow evomet map subject to ematc costats of the seso placemet mechasms fo the dvdual obots. he, the cameas move to the ew poses ad acque 3D data. Based o the camea mout ematcs, the motos of the cameas ae ow. Note, t s assumed that the vehcles do t move, as lage camea motos would be dffcult to measue. Small motos of the obot base (due to suspeso complace) ad eos camea mouts lead to addtoal ucetates. hese ae accouted fo b measug commo featues dug the camea moto (secto.5). Fall, the ew data ad ts assocated ucetat ae fused wth the cuet evomet map esultg a updated pobablstc evomet map... Algothm talato As descbed above, a commo taget s to be located to establsh a commo etal efeece fame betwee the obots ad the evomet. Seachg fo the taget b movg the obot cameas ca be doe ma was (depedg o the taget popetes), such as ehaustve aste scag, adom walg, tacg space fllg cuves, ad model-based mage udestadg methods [, 8]. I ths stud, camea postog fo taget seachg s doe the same wa as camea postog fo evomet model buldg (descbed sectos.4)..3. Data modelg ad fuso At a tme, the cameas o each moble obot ca ol obseve a small pat of the evomet. Howeve, measuemets obtaed fom multple vewpots ca povde educed ucetat, mpoved accuac, ad ceased toleace estmatg the locato of the obseved object [7]. o fuse multple age measuemets of a featue b sesos, a statstcal model of seso ucetat s emploed (see Fgue 4). Cuet ad pevous age seso measuemets ad the ucetat models ca be tegated to gve a updated pobablstc geometc model of the evomet. Seso Measuemets Seso Ucetat Model Pevous 3-D Measuemets & Ucetat Pobablstc Geometcal Wold Map Updated wold model Fgue 4: 3-D age measuemet fuso wth seso ucetat A sgle age obsevato of a pot ( ) s modeled as a 3-D Gaussa pobablt dstbuto ceteed at, based o two mpotat obsevatos. Fst, the use of the

3 mea ad covaace of a pobablt dstbuto fucto s a easoable fom to model seso data ad s a secod ode lea appomato [7]. hs lea appomato coespods to the use of a Gaussa (havg all hghe momets of eo). Secod, based o the cetal lmt theoem, the sum of a umbe of depedet vaables has a Gaussa dstbuto egadless of the dvdual dstbutos. he stadad devatos alog the thee aes of the dstbuto coespod to estmates of the ucetat the age obsevato alog these aes. hese stadad devatos ae a fucto of tsc seso paametes (such as camea les shape accuac) as well as etsc seso paametes (such as the dstace to the obseved pot o featue). hs model ca be theoetcall appomated as [0]: σ,, f ( etsc paametes, tsc paametes) () S,, d whee S s a tsc paamete ucetat costat,,, s a etsc paamete ucetat costat, d s the dstace to the featue/evomet pot, ad s a costat (tpcall ). Povded two obsevatos ae daw fom a omal dstbuto, the obsevatos ca be meged to a mpoved estmate b multplg the dstbutos. Sce the esult of multplg two Gaussa dstbutos s aothe Gaussa dstbuto, the opeato s smmetc, assocatve, ad ca be used to combe a umbe of dstbutos a ode. he caocal fom of the Gaussa dstbuto dmesos depeds o the stadad dstbutos, σ,,, a covaace mat (C) ad the mea ( ) [7]: σ σ σ () p( ) ep ( ) C ( ), whee C σ σ σ ( π ) C σ σ σ whee the epoet s called the Mahalaobs dstace. Fo u-coelated measued data ρ0. he fomulato Equato s the spatal coodate fame. Howeve, all measuemets ae made the camea (o seso) coodate fame. hs poblem s addessed though a tasfomato of paametes fom the obsevato fame to the spatal efeece fame as follows: Ctasfome d R( θ ) C R( θ ) (3) whee R(θ) s the otato mat betwee the two coodate fames. he agle of the esultg pcpal as ca be obtaed fom the meged covaace mat: C C meged C (4) C + C whee C s the covaace mat assocated wth the th measuemet. Addtoall, a taslato opeato s appled to the esult fom Equato, to bg the esult to the spatal efeece fame..4. Defto of the atg fucto (RF) A atg fucto s used to deteme the et pose of the camea fom whch to loo at the uow evomet. he am s to acque ew fomato of the evomet that would lead to a moe detal ad moe etesve evomet map. I selectg ths ew camea state the followg fou costats ae cosdeed: () Goal cofguato s collso fee fom the pobablstc geometc evomet model, (,,) locatos wth P,, < P empt 0.05 (σ) ae cosdeed as uoccuped. Such pots fom caddate cofguato space camea pose coodates. () Goal eached b a collso fee path ths s a fucto of the camea mapulato ematcs ad the ow evomet model. () Goal cofguato should ot be fa fom the cuet oe a Eucldea metc cofguato space, wth dvdual weghts α o each degee of feedom of the camea pose c, s used to defe the dstace moved b the camea: ( c c ) d α (5) whee c ad c ae vectos of the ew ad cuet camea poses espectvel. (v) Measuemet at the goal cofguato should mame fomato tae Specfcall, the ew fomato (NI) s equal to the epected fomato of the uow/patall ow ego vewed fom the camea pose ude cosdeato. hs s based o the ow obstacles fom the cuet evomet model, the feld of vew of the camea (see Fgue 5) ad a famewo fo etopc thesholdg of fomato. Shao showed that a defto of etop, smla fom to a coespodg defto statstcal mechacs, ca be used to measue the fomato gaed fom the selecto of a specfc evet amog a esemble of possble evets [6]. hs etop fucto, H, ca be epeseted as: H ( q, q,..., q ) q l q (6) whee q epesets the pobablt of occuece fo the th evet, ad uquel satsfes the followg thee codtos [6]: H(q, q,, q ) s a mamum fo q / fo. hs mples that a ufom pobablt dstbuto possesses the mamum etop. H(AB)H(A)+H A (B) whee A ad B ae two fte schemes. H(AB) epesets the total etop of schemes A ad B ad H A (B) s the codtoal etop of scheme B gve scheme A. H(q, q,, q,0) H(q, q,, q ) o a evet wth eo pobablt of occuece a scheme does ot chage the etop fucto. Shao s emphass was descbg the fomato cotet of -D sgals. I -D the ga level hstogam of a mage ca be used to defe a pobablt dstbuto: q f / N fo...n ga (7) whee f s the umbe of pels the mage wth ga level, N s the total umbe of pels the mage, ad N ga s the umbe of possble ga levels. Wth ths defto, the etop of a mage fo whch all the q ae

4 the same coespodg to a ufom ga level dstbuto o mamum cotast s a mamum. he less ufom the hstogam, the lowe the etop. Camea Feld of Vew Depth of Vew Kow ego (fom eale measuemets) Epected ew fomato (NI) Uow ego Obstacle Fgue 5: Evaluato of epected ew fomato It s possble to eted ths dea of etop to a 3-D sgal the evomet model. I such a stace the scee pobablt dstbuto fo etop (fomato) aalss s stll gve b Equato 7. Howeve, N s the mamum umbe of voels vsble b the vso sstem (lmted b the depth of feld ad the feld of vew), ad f s the umbe of voels the scee wth ga level. he possble ga values ae defed as follows. Fo a pevousl sampled spatal voel, a ga (pobablstc) occupac value betwee 0 ad s foud. Net the value, p(), s modfed as follows: p() < p() d voel stetchg : p () p() d p () scalg : p () p () voel p() 0.5 p() < 0.5 p() 0.5 (8a) whee d voel s the Eucldea dstace of the voel fom the camea coodate fame. hs pocess causes egos wth pobablt destes close to 0 o (egos of most cetat) to have a educed effect o the ew fomato epected. Regos that have a pobablt dest close to 0.5 (egos of least cetat of occupac) ae stetched out the scee pobablt dstbuto, thus ceasg the ew epected fomato assocated wth those egos. Addtoall, fo all uow/usampled voels a ga value betwee ad s defed: d voel p( ) + (8b) d ma whee d ma s the mamum dstace of a voel the camea feld of vew to the camea (equal to the depth of feld). A ufom dscetato of ths age of ga values ma be pefomed to defe N ga. Wth these deftos q (Equato 7) s evaluated ad the esults appled to Equato 6 esultg a metc fo ew fomato (NI). Note that b applg the thee codtos descbed above, ths defto fo NI does behave a tutvel coect fom. Fo eample, fo a gve camea pose, f the feld of vew s occluded the NI deceases. If eve pot the feld of vew s ow ad s empt the NI0. NI ceases as the umbe of uows the feld of vew ceases. Futhe, Equato 8a esults ceasg the ew fomato epected wth egos that ae ow wth meda pobablstc values.e. values that dcate wth least amout of cetat whethe a voel s occuped o ot. O the othe had, egos wth hgh pobablstc values fo occupac esult educed assocated fomato. o pla the moto cosstetl, costats () ad (v) ae meged to a uque atg fucto (RF): RF (NI - K. d ). ( P,, ) (9) whee K, ae scalg costats. Shote dstaces ehbt a hghe atg. hs atg fucto ca be evaluated ad optmed to fd the et most pomsg camea cofguato fom whch to mae futue measuemets of the evomet. Although ths choce of atg fucto s somewhat abta, good esults wee obtaed. Addtoal costats ca also be accommodated..5. Suspeso moto coecto A fal step s to detf the moto of the camea to allow fo data fuso. hs pocess elmates mapulato postog eos ad vehcle suspeso motos. A sgle spatal pot the base fame,, s elated to the mage pot (u, v ) b the 44 tasfomato mat g 0 (see Fgue 6). Camea base fame (u,v) (u,v,f) f Spatal pot g 0 aget fame Fgue 6: Relatoshp of camea ad taget fames Fo moto calbato we eed to detf g 0 : u [ ] v R (0) g0 f 0 whee R 0 s the otatoal mat, s the taslato vecto, f s the camea focal legth, ad s a scalg costat. Fo computatoal easos t s moe coveet to teat the 9 otatoal compoets of R 0 as depedet (athe tha a tascedetal elato of 3 depedet paametes). Each spatal pot gves 3 algebac equatos, but also toduces a ew vaable, multplcatve costat to eted the th mage pot vecto (u,v,f) to the th spatal pot the camea coodate fame. ma be foud fom the dspat pa of the steeo mages. Fo pots we have: u g 0 u v f u v f u v g 0 f () hs set of lea equatos ca be eadl solved usg covetoal techques. A least mea squae eo

5 soluto s gve b: ( ) g 0 u () he otato mat, R 0, ad the taslato vecto,, of the camea fame wth espect to the base fame ae etacted dectl fom ths soluto of g 0. Howeve, fo eal measued data ad assocated ucetat, a lage umbe of scee pots ae equed to moe coectl detf the geometc tasfomato mat, g 0. Gve the () st scee ad mage pot, fom Equato R ad ca be obtaed. A ecusve method ca be used to deteme the mea ad covaace of ad R 0 based o the pevous measuemets as follows: ˆ C ( ˆ + ) C + + [ ˆ ][ ˆ ] + ( ˆ ( l, ( l, R + R ) (3) ˆ ( l, R + R( l, ( l, [ ˆ ( l, ( l, ][ ˆ ( l, R( l, C + R R R R ] C + Fall, the ssue of obtag appopate spatal pots fo vehcle moto compesato s addessed. Spatal pots ae obtaed b matag a fte set of fducals that ae taced dug map buldg ad vsble b the cameas. As the camea moves, the fducals move elatve to the camea, evetuall movg out of the camea vew. hs eques methods to tac ad detf ew fducals. Fst, fo the puposes of ths stud fducals ae taced usg a computatoall fast ego gowg method. Secod, ew fducals ae selected fom the pobablstc evomet model based o the degee of cetat wth whch a sampled pot s ow. Specfcall, all local peas the pobablstc geometc evomet map (potetal fducals) ae detfed. Net, at each local pea a pocess called sphecal epaso s pefomed. I sphecal epaso, usg local gadet decet o eghbog voels, the lagest sphecal ego aoud a local pea, beod whch the voel values cease, s foud. Lastl, epaded sphees ae scoed based o the poduct of the ad ad magtude of local pea. hese scoes ae omaled based o the dstace to the cuet camea posto. Hghe scog peas fom bette fducals ad ae selected accodgl. Although, alteatve scog fuctos ma be emploed, ths smple oe poves hghl effectve. Note that, b owg the camea posto ad the camea am ematcs, the obot base posto ca be easl etapolated. 3. Smulato esults Results usg the atg fucto, to eploe a plaa evomet ad develop a pobablstc geometc evomet model, ae gve hee. Fgue 7 shows the esults obtaed of scag a plaa evomet of adom obstacles. wo vso sstems fuse 00 samples each to gve the pobablstc map see Fgue 7(b). B ceasg the umbe of scas tae, the ucetat ths pobablstc map deceases. (a) Smulated evomet (b) Pobablstc evomet map afte 400 scas Fgue 7: Mappg a smulated plaa evomet able : Compaso of eploed space afte 3 scas Seach method Fathest vsual pot fom stat Aveage adal dstace fom stat σ of vewed space Radom (m0) Radom (m50) Radom (m00) Radom (m00) Radom (m300) Ehaustve % of wold vewed Ehaustve seach Radom wal - m300 Radom wal - m00 Radom wal - m00 Radom wal - m50 Radom wal - m0 Raste sca mappg Numbe of camea postos Fgue 8: Pecetage of evomet vewed he atg fucto (RF) caot be optmed aaltcall. I pactce, fdg a optmum value fo RF eques ehaustve seachg though the ete ow cofguato space a pocess that taes 0() tme, whee s the umbe of dscete pots the cofguato space. Oe wa to educe the seach tme s

6 to emplo a fte adom selecto of goal cofguatos. Fo m possble cofguatos, ths pocess taes 0( tme m s a costat. hus, whle the best goal cofguato would be the oe mamg RF, a cofguato wth a hgh value fo RF should suffce. Such a cofguato ca be foud wth easoable effot. Fo compaso, esults fom adom sample selecto usg 0, 50, 00, 00, ad 300 pots ae peseted alog wth a ehaustve seach, Fgue 8 ad table. Note that as the umbe of seach pots the adom selecto ceases, the eploed/vewed space gows moe ufoml (measued as the stadad devato of the adus of eve pot the vewed evomet space). hs eaches a theshold as the seach becomes moe ehaustve atue. Fgue 8 shows the pecetage cease of the evomet vewed as a fucto of the umbe of scas. Fom ths t appeas that the effects of adom wal seaches poduce equvalet esults as a ehaustve seach. Addtoall, fo compaso Fgue 8 pesets the esults of modelg the evomet usg a covetoal aste sca (whee the et vewg posto s selected sequetall fom the avalable poses of the ow evomet). Cleal, thee s sgfcat decease pefomace effcec. he specfc umbes peseted hee ae a fucto of camea popetes (such as the FOV ad the DOF) ad the evomet obstacles, ad should be used to eflect the ted, ot the eact behavo. 4. Coclusos I feld evomets t s ofte ot possble to povde obotc teams wth detaled a po evomet ad tas models. I such ustuctued evomets, coopeatg obots wll eed to ceate a dmesoall accuate 3-D geometc model b pefomg appopate seso actos. Howeve, ucetates obot locatos ad sesg lmtatos/occlusos mae ths dffcult. A ew algothm based o teatve seso plag ad seso edudac s poposed to buld a geometcall cosstet dmesoal map of the evomet fo moble obots that have atculated sesos. hs algothm s uque that t uses a metc of the qualt of fomato pevousl obtaed b the sesos to fd ew vewg postos fo the cameas. Smulatos show pomsg esults. 5. Refeeces. Asada, M. Map buldg fo a moble obot fom seso data. IEEE asactos o Sstems, Ma, ad Cbeetcs. Vol. 37, o. 6, Novembe/Decembe Baumgate, E.., P. S. Schee, C. Lege, ad. L. Hutsbege. Seso-fused avgato ad mapulato fom a plaeta ove. Poceedgs SPIE Smposum o Seso Fuso ad Decetaled Cotol Robotc Sstems, Vol. 353, Bosto, MA, Nov Betge-Beet, S., Hebet, P., Chatla, R., ad Dev, M. Uceta map mag atual evomets. Poceedgs of the 996 IEEE Iteatoal Cofeece o Robotcs ad Automato, Meapols, Mesota, Apl, Buscha, D. Ebest, C. ad Robl, C. Vso based model geeato fo doo evomets. Poceedgs of the 997 IEEE Iteatoal Cofeece o Robotcs ad Automato, Albuqueque, New Meco, Apl, Cooll, C.I. he detemato of the et best vews. Poceedgs of the IEEE Iteatoal Cofeece o Robotcs ad Automato, pp , Cowa, G.K. ad Koves, P.D. Automatc seso placemet fom vso tas equemets. IEEE asactos o Patte Aalss ad Mache Itellgece, vol. 0, o. 3, pp , Ma Hutsbege,.L. Autoomous mult-ove sstem fo comple plaeta eteval opeatos. Poceedgs. SPIE Smposum o Seso Fuso ad Decetaled Cotol Autoomous Robotc Agets, Pttsbugh, PA, Oct 997, pp Jegs, C., Mua, D., ad Lttle, J. Coopeatve obot localato wth vso-based mappg. Poceedgs of the 999 IEEE Iteatoal Cofeece o Robotcs ad Automato, Detot, Mchga, Ma Kecec, F., oo, M., Nagel, H.H., ad Gegebach, V. Impovg vsuall sevoed dsassembl opeatos b automatc camea placemet. Poceedgs of the 998 IEEE Iteatoal Cofeece o Robotcs ad Automato, Leuve Belgum. Ma Kuse, E., Gutsche, R., ad Wahl, F.M. Effcet, teatve, seso based 3-D map buldg usg atg fuctos cofguato space. Poceedgs of the 996 IEEE Iteatoal Cofeece o Robotcs ad Automato, Meapols, Mesota, Apl, Lumels, V., Muhopadha, S. ad Su, K. Sesobased tea acqusto: the sghtsee stateg. Poceedgs of the 8 th Cofeece o Decso ad Cotol. ampa, Floda. Decembe Luo, R.C. ad M.G. Ka. Multseso tegato ad fuso tellget sstems. IEEE asactos o Sstems, Ma, ad Cbeetcs, Vol. 9, No. 5, Septembe, Relets, I., Dude, G., ad Mlos, E. Mult-obot collaboato fo obust eploato. Poceedgs of the 000 IEEE Iteatoal Cofeece o Robotcs ad Automato, Sa Facsco, CA. Apl, Repo,. ad Rog, J. Modelg stuctued evomets b a sgle movg camea. Poceedgs. Secod Iteatoal Cofeece o 3-D Dgtal Imagg ad Modelg, 999. O page(s): ,4-8 Oct Shaffe, G.; Stet, A. A obotc sstem fo udegoud coal mg. Poceedgs of the IEEE Iteatoal Cofeece o Robotcs ad Automato, 99. Pages(s): vol. 6. Shao, C. E. A mathematcal theo of commucato. he Bell Sstem echcal Joual, vol. 7, pp ad , Jul ad Octobe, Smth, R.C. ad Cheesema, P. O the epesetato ad estmato of spatal ucetat. Iteatoal Joual of Robotcs Reseach. 5(4): aabas, K.A., Alle, P.K. ad sa, R.Y. A suve of seso plag compute vso. IEEE asactos o Robotcs ad Automato, Vol. o., Pp Febua, hu, S., Bugad, W., ad Fo, D. A eal-tme algothm fo moble obot mappg wth applcatos to mult-obot ad 3D mappg. Poceedgs of the 000 IEEE Iteatoal Cofeece o Robotcs ad Automato. Sa Facsco, CA, Apl, Suja, V.A. Compesatg fo Ucetat the Cotol of Coopeatve Robots Feld Evomets. Ph.D. hess, Depatmet of Mechacal Egeeg, Massachusetts Isttute of echolog, Jue 00.