Hao Li, Fawzi Nashashibi

Transcription

1 A New Mehod for Occuancy Grid Mas Merging: Alicaion o Muli-vehicle Cooeraive Local Maing and Moving Objec Deecion in Oudoor Environmen Hao Li, Fawzi Nashashibi o cie his version: Hao Li, Fawzi Nashashibi. A New Mehod for Occuancy Grid Mas Merging: Alicaion o Muli-vehicle Cooeraive Local Maing and Moving Objec Deecion in Oudoor Environmen. ICARCV 0 - h Inernaional Conference on Conrol, Auomaion, Roboics and Vision, Dec 0, Guangzhou, China. 0. <hal > HAL Id: hal hs://hal.inria.fr/hal Submied on 8 Dec 0 HAL is a muli-discilinary oen access archive for he deosi and disseminaion of scienific research documens, wheher hey are ublished or no. he documens may come from eaching and research insiuions in France or abroad, or from ublic or rivae research ceners. L archive ouvere luridiscilinaire HAL, es desinée au déô e à la diffusion de documens scienifiques de niveau recherche, ubliés ou non, émanan des éablissemens d enseignemen e de recherche français ou érangers, des laboraoires ublics ou rivés.

2 A New Mehod for Occuancy Grid Mas Merging: Alicaion o Muli-vehicle Cooeraive Local Maing and Moving Objec Deecion in Oudoor Environmen Hao LI IMARA eam, INRIA Le Chesnay, France hao.li@inria.fr Fawzi NASHASHIBI IMARA eam, INRIA Le Chesnay, France fawzi.nashashibi@inria.fr Absrac Auonomous maing, esecially in he form of SLAM (Simulaneous Localizaion And Maing), has long since been used for many indoor roboic alicaions and is also useful in oudoor inelligen vehicle alicaions such as objec deecion. Mos exising research works on environmen maing and objec deecion in oudoor alicaions have been dedicaed o single vehicle sysem. On he oher hand, muli-vehicle cooeraive erceion based on iner-vehicle daa sharing can bring considerable benefis in many scenarios ha are challenging for a single vehicle sysem. In his aer, a new mehod for occuancy grid mas merging is roosed: an objecive funcion based on occuancy likelihood is inroduced o measure he consisency degree of mas alignmen; geneic algorihm imlemened in a dynamic scheme is adoed o oimize he objecive funcion. A scheme of muli-vehicle cooeraive local maing and moving objec deecion using he roosed occuancy grid mas merging mehod is also inroduced. Real-daa ess are given o demonsrae he effeciveness of he inroduced mehod. Keywords occuancy grid ma, SLAM, cooeraive erceion, moving objec deecion I. INRODUCION Auonomous maing has long since been a fundamenal ask for mobile robos oeraing in an unknown environmen []. Since he robo ose is no known a riori in many alicaions, he maing rocess is usually juxaosed wih he localizaion rocess, forming a rocess called Simulaneous Localizaion And Maing (SLAM) [] [3]. Originally, SLAM was rooed in indoor environmen alicaions, where he urose of SLAM is o esablish a consisen saial reresenaion for he global environmen and localize he robo in his global environmen reresenaion. For oudoor environmen alicaions where GPS (Global Posiioning Sysem) measuremens can be available, SLAM gradually loses is imorance on global maing and global localizaion as originally in indoor environmen alicaions. Neverheless, SLAM mehods can sill be emloyed o imrove odomeerbased local localizaion resul and build accurae and consisen local mas for objec deecion [4] [5]. Mos exising research works on environmen maing and objec deecion in oudoor environmen alicaions have been dedicaed o single vehicle sysem (he erm vehicle and robo are used inerchangeably in his aer). On he oher hand, muli-vehicle cooeraive erceion based on inervehicle daa sharing can bring considerable benefis in many scenarios ha are challenging for a single vehicle sysem. ake vehicle overaking scenario as an examle, see Fig.; his scenario is challenging and oenially dangerous, because he view of he overaking vehicle is occluded by he overaken vehicle. Wha migh haen o he overaking vehicle if a careless edesrian is rushing across he road in fron of he overaken vehicle? For safey reason, he overaking vehicle always wans o know wha exis in he occluded area; unforunaely, i can no have any inference on he occluded area. overaking vehicle overaken vehicle dangerous edesrian occluded Fig Poenially dangerous overaking scenario Wih he hel of iner-vehicle communicaion [6], he overaken vehicle can share is erceion resuls wih he overaking vehicle so ha he overaking vehicle can indirec erceive he occluded environmen. More secifically, he erm erceion here imlies cerain local ma reresenaion around he vehicle. hen, an essenial requiremen for realizing his idea of cooeraive erceion is o merge he local mas of he wo vehicles ino a consisen local ma.

3 If each vehicle is recisely localized in he same global reference, hen he local mas from differen vehicles can be relaed o each oher using he recise localizaion resuls and local mas merging can be effecively solved. However, a vehicle is usually no recisely localized in realiy; for a vehicle equied wih low-cos GPS, he global localizaion error can be as large as en meers in he osiion comonen. Local mas merging a he exisence of large vehicle localizaion error is no rivial. A yical racice for mas merging is based on esimaion of iner-vehicle relaive ose [7] [8] [9] [0], which is no easy o ackle in oudoor raffic environmen: firs, reliable vehicle deecion and recogniion are sill a challenging roblem ha deserves furher research works. Second, daa associaion is also a challenging roblem, esecially when vehicle localizaion accuracy is low. Secial aerns migh be designed o faciliae vehicle deecion as well as daa associaion. However, housands of vehicles exis in raffic environmen. he ask of designing roer aerns o disinguish such huge number of vehicle sysems is no rivial; besides, occlusions migh cause miss deecion and false deecion of hese aerns. Even if vehicle deecion and daa associaion are erformed correcly, he deecion resul usually corresonds o arial conour of he deeced vehicle (someimes of irregular shae), which makes i difficul o exrac accurae geomeric informaion of he deeced vehicle. Anoher racice for mas merging is o merge he mas direcly [], comleely ignoring he issue of iner-vehicle relaive ose esimaion. We focus on merging occuancy grid mas [] [3] insead of feaure-based mas [4], for he general environmen reresenaion caabiliy of occuancy grid mas. Moreover, as in [], we wan o avoid any reliminary rocedure of feaure exracion and focus on direcly idenifying he alignmen of he mas o-be-merged. In his aer, a new mehod for occuancy grid mas merging is roosed (his mehod has been used as a comonen in our revious works and has been briefly menioned in [7]; here he mehod is resened wih more deails): an objecive funcion based on occuancy likelihood is inroduced o measure he consisency degree of mas alignmen; geneic algorihm imlemened in a dynamic scheme is adoed o oimize he objecive funcion. hen a scheme of muli-vehicle cooeraive local maing and moving objec deecion is described, which uilizes he occuancy grid mas merging mehod. he aer is arranged as follows: single vehicle local SLAM based on occuancy grids and vehicle global localizaion based on GPS are briefly reviewed in Secion. he roosed occuancy grid mas merging mehod is inroduced in Secion 3. he scheme of muli-vehicle cooeraive moving objec deecion is resened in Secion 4. Real-daa exerimens are given in Secion 5, followed by a conclusion in Secion 6. II. SINGLE VEHICLE LOCALIZAION AND MAPPING A. Single Vehicle Local SLAM based on Occuancy Grid Occuancy grid based ma reresenaion is used for is abiliy o reresen general unsrucured oudoor environmen. he occuancy grid is a wo-dimensional laice of recangular cells and each cell is associaed wih a real value in he uni inerval [0, ]. he cell value reresens he degree of he cell being occuied or free. he cell value 0.5 reresens he cell being in unknown sae, neiher occuied nor free. For cell value larger han 0.5, he larger he cell value is, he more likely he cell is occuied. For cell value smaller han 0.5, he smaller he cell value is, he more likely he cell is free. Here, we ado he incremenal maximum likelihood SLAM mehod in [5], considering is comuaional efficiency and is insensiiveness o dynamic eniies; his mehod is briefly reviewed. Generally, le x denoes vehicle local ose in SLAM, M denoes udaed ma, u denoes odomeer daa, z denoes range daa. Le subscri denoes he ime index. he incremenal maximum likelihood SLAM is a reeaed rocess of execuing rocedures () and (): = arg max{ P( z x, Mˆ ). P( x xˆ, u )} () x ˆ x Mˆ = Mˆ {ˆ x, z } () he rocedure () is o search he oimal x which maximizes he marginal likelihood of he -h ose and erceion relaive o he (-)-h ose and ma; he grid-based maximum likelihood scan maching mehod in [5] is used for he searching. he rocedure () is o generae a new (-h) ma from he old ((-)-h) ma based on he esimaed -h ose and he -h erceive daa. Deailed imlemenaion is referred o [5]. An examle of wo local mas buil by differen vehicles is shown in he o wo sub-figures of Fig.. B. Single Vehicle Global Localizaion based on GPS GPS can rovide direc and error-bounded global osiion measuremen; he measuremen error level deends on he GPS qualiy as well as he environmen where he GPS oeraes. In comaraively oen area, a RK-GPS can achieve cenimeerlevel osiioning accuracy; in conras, he osiioning error of a low-cos GPS can be en meers. Normally, a GPS ouus measuremens a a low frequency and does no rovide direc measuremen on vehicle orienaion, a filering rocess is usually erformed o esimae full sae of vehicle ose (osiion and orienaion). In he resened works, EKF (Exended Kalman Filer) is used for he filering rocess, as follows: ) Global ose evoluion he evoluion of vehicle ose can be modeled according o kinemaic bicycle model (denoed generally as funcion F): = F, u ) (3α) ( u ufu = F F + F (3β) he denoes vehicle global ose (differen from he vehicle local ose x); u denoes vehicle moion variables, which can be odomeer daa. In order o reduce odomeer error, he local SLAM described in he revious sub-secion is used o correc odomeer daa and he correced odomeer daa are used as u

4 in (3a). he F and F u in (3b) resecively denoe he Jacobian marices of he funcion F wih resec o and u. ) Global ose udae Le he GPS measuremen be denoed as Z =(x,y ). he measuremen model can be described as: Z = H + E where H =[I x 0 x ]; he measuremen error E is assumed o follow he Gaussian disribuion N(0, ). he global ose is udaed wih he GPS measuremen: K = III. H = + K( Z = ( I KH ( H H ) H ) + ) OCCUPANCY GRID MAPS MERGING A. An objecive funcion based on occuancy likelihood We follow he comounding noaion in [4]: x x y y x x y y x = x x = x cos y sin sin + y cos + cos y sin sin + y cos + x + y + x + y (4α) (4β) x xcos ysin inv( = y ) xsin ycos (4χ) Le M A and M B be wo occuancy grid mas o-be-merged. he rocess of occuancy grid mas merging can be generalized as he following oimizaion roblem: Firs, design an objecive funcion F c in erms of wo arbirary occuancy grid mas M and M, i.e. F c (M, M ), which is used o measure heir consisency degree. Second, search he oimal relaive ose BA ha maximizes he consisency measure beween M A and BA M B, i.e. ˆ arg max F ( M, M ) (5) BA = c BA In [], he objecive funcion F c consiss of a similariy erm and a lock erm: he similariy erm which is based on a disance-ma reresens he overall disances beween he mas o-be-merged; he lock erm is a ar heurisically added o counerac he over-fiing effec. his objecive funcion in [] has wo major disadvanages: firs, he arameer c lock in he heurisically added lock erm has o be uned emirically according o concree scenarios. A BA B Second, his objecive funcion is sensiive o mas inheren inconsisency i.e. mas inconsisency ha sill exiss even if he mas o-be-merged are aligned correcly. Mas inheren inconsisency can be caused by dynamic eniies which are common in oudoor environmen. Mas inheren inconsisency can also be caused by he inconsisency of erceion oses a differen vehicles; for examle, he same environmen migh aear noiceably differen if i is scanned by laser scanners a differen heighs. For he objecive funcion in [], mas inheren inconsisency would cause drasic value change in he disance-ma based similariy erm and false couning of agreemen and disagreemen in he lock erm. Here, we use an objecive funcion based on occuancy likelihood, similar o he idea of he occuancy grid based scan maching as inroduced in [5]. Le he occuied cells wih local maximum occuancy sae (referred o as local maximum occuied cells) in M B be denoed as a se of wo-dimensional oins {o B(), o B(),, o B(nb) }. Le he occuancy sae of a oin in an occuancy-grid ma M be denoed as M(); hen he objecive funcion F c is defined as in (6): nb F c ( MA, BA MB) = Occ i ( ){ A ( BA B( i) )} BA o M o B( ) MA i= he objecive funcion (6) comues he occuancy likelihood sum of he local maximum occuied cells of M B in M A. he Occ means he se of occuied cells, which are seleced by a hreshold. Here, he Occ hreshold is no inended o deermine wheher a grid cell is ruly occuied or no in realiy; i is only used o selec grid cells ha end o be occuied or be closer o ruly occuied cells. So here is fair flexibiliy in seing his hreshold. For examle, we can se he Occ hreshold o be 0.6. his objecive funcion only akes ino accoun he consisen ar of he mas o-be-merged; hus i is insensiive o mas inheren inconsisency. For local mas of enough size, sable and consisen objecs (buildings, infrasrucures ec) are usually he dominaing facors, which always conribue o successful local mas merging. B. Oimizaion using geneic algorihm he iniial value of BA can be comued wih GPS based vehicle global localizaion resuls, ye his iniial value migh be far away from he oimal mas alignmen. For inelligen vehicle sysems wih low-accuracy GPS, he iniial osiion error of BA can be weny meers; iniial orienaion error of BA can also be large. Besides, he value sace of he objecive funcion (6) is normally mulimodal and of irregular shae on he whole. herefore, local oimizaion searching echniques such as gradien based analyical echniques end o fail when facing such large iniial esimae error. he sraegy of evoluionary geneic algorihm [5] is adoed o solve he oimizaion roblem (5). One imoran moivaion for using geneic algorihm is ha i is indeenden of he objecive funcion value sace and i is ready o solve mulimodal, non-differeniable, or non-coninuous roblems. (6)

5 Geneic algorihm is raher a mehodology insead of being a lis of concree execuion rocedures. As an analogy o secies evoluion under he influence of naural selecion, he fundamenal siri of geneic algorihm is o evaluae he finess values of a grou of enaive soluion individuals, vary hem wih biologically insired oeraions such as crossover and muaion, and kee hose beer individuals. he concree rocedures o u his siri ino racice are roblem oriened and can be secially designed and modified. he concree rocedures in our imlemenaion are as follows:. Iniializaion: randomly generae an iniial oulaion of BA : (-a) Comue he iniial value of BA(ini) wih GPS based global localizaion resuls of he wo vehicles. (-b) In a cerain error range around BA(ini), randomly generae an iniial oulaion of BA i.e. { BA(k) k=,,,n}. Wih an inenion o examine he robusness of he mehod, we deliberaely exaggerae his iniial error range o be +30 meers in osiion and +30 degrees in orienaion.. Evoluion: ieraively erform he following sub-ses as follows: (-a) Comue he likelihood value (or finess value in radiional geneic algorihm erms) of each individual in he oulaion, according o (6). (-b) Comue mean likelihood value of he oulaion. For an individual, if is likelihood value is above he mean likelihood value, assign he individual o he elie grou; oherwise, assign i o he inferior grou. (-c) Muae he individuals in he elie grou. For an individual, if is muaion has higher likelihood value han is own, hen relace his individual wih is muaion; oherwise, jus kee his individual originally in he elie grou. FOR IF F ( c END FOR { BA(elie) * = muae( *) > F ( c } ) ) HEN = Among he elie grou, he bes individual is an exceion, which ges more imes (for examle, 00 imes) of muaion. If no muaion is beer, hen jus kee he bes individual unchanged; oherwise, kee he bes muaion o relace he original bes individual. (-d) Relace he inferior grou wih new individuals; more secifically, relace each individual in he inferior grou wih a new individual ha is generaed from old individuals by alying he following geneic oeraions wih secified robabiliies: (-d-i) Coy he bes individual (only erformed once). * (-d-ii) Randomly selec an individual from he elie grou and muae i o be he new individual. (-d-iii) Randomly selec wo individuals from he elie grou, creae a new individual by execuing crossover on hem and muaing he crossover resul. wo sors of crossover are designed: Crossover I: Mix he osiion ars and orienaion ars of he wo individuals. Le he wo elie individuals be denoed as BA(e) =[x BA(e), y BA(e), BA(e) ] and BA(e) =[x BA(e), y BA(e), BA(e) ] ; he new individual is generaed as follows: = BA(new) [ x BA(e), yba(e), BA(e) ] or [ xba(e), yba(e), BA(e) ] Crossover II: Make a random linear combinaion of he wo individuals (he is a randomly generaed real value in [0, ]: BA(new) = BA(e) + ) ( BA(e) (-d-iv) Re-iniializaion: Creae he new individual according o GPS based vehicle global localizaion resuls and he error range, as in he iniializaion rocess. his reiniializaion racice is o kee he diversiy of he oulaion. When wo vehicles mee or re-mee, he iniializaion se is erformed once and he sub-ses in evoluion are reeaedly erformed. A dynamic scheme of he geneic algorihm is used: he generaion of BA individuals from las eriod is roagaed o he curren eriod, according o he change of local ma coordinaes sysems. As long as he vehicles are in he neighborhood and in cooeraion, he evoluion se can be erformed unceasingly. As a resul, we only need o assign few imes of evoluion for each eriod (for examle, once), which largely reduces comuaional burden a one eriod; moreover, as he evoluion coninuous unceasingly, he dynamic scheme of geneic algorihm will finally converge o he oimum. In our ess, he geneic algorihm usually converges o he oimum in only few eriods (no more han one second). IV. MULI-VEHICLE COOPERAIVE LOCAL MAPPING AND MOVING OBJEC DEECION he urose of his secion is no o roose cerain moving objec deecion mehod, bu o demonsrae a scheme of mulivehicle cooeraive local maing and moving objec deecion, where he occuancy grid mas merging mehod can be alied o merge he moving objec deecion resuls of differen vehicles. Here, we ado he consisency based aroach and he moion objec ma based aroach [4] [5] for single vehicle moving objec deecion. Consisency-based deecion: given a new scan of range measuremens and reviously consruced occuancy grid mas, he idea is o find he inconsisen ar beween range measuremens and free sace in he local occuancy grid ma. If a range oin is deeced on a locaion of reviously free sace, hen i is regarded as a moving oin. he range daa are clusered ino segmens; for a segmen, if he number of moving oins is larger han a half of he oal oins, hen he segmen is idenified as oenial moving objec.

6 Moving objec ma based deecion: a local moving objec ma is creaed o sore informaion abou reviously deeced moving objecs; each cell in he moving objec ma sores a value indicaing he number of observaions ha a moving objec has been observed a ha cell locaion. If he cell value is above cerain hreshold, he range oin associaed wih his cell is regarded as a moving oin. During muli-vehicle cooeraion, a vehicle (referred o as ego vehicle) will merge he local occuancy grid ma of anoher vehicle ino is own occuancy grid ma, using he mehod inroduced in Secion 3. he deeced moving objecs of anoher vehicle can also be ransformed ino he ego vehicle reference and fused wih he deeced moving objecs of he ego vehicle: if a deeced moving objec of anoher vehicle and a deeced moving objec of he ego vehicle have a leas arial overla, hen he wo objecs are regarded as he same objec and fused ino one objec. V. EPERIMEN wo CyCab vehicle laforms (develoed by IMARA eam, INRIA) [6] are used for real daa exerimens which are carried ou in INRIA camus: each vehicle is equied wih a RK-GPS, odomeer sensor, and an IBEO laser scanner. A RK-GPS can achieve cenimeer-level osiioning accuracy; however, he RK-GPS ouus are inenionally degraded wih error noise in order o simulae vehicle sysems wih lowaccuracy GPS. Le he GPS ouu of one vehicle be degraded wih an error bias comonen of (8m, 6m) and a noise comonen of mean 0 and sandard deviaion 7m; le he GPS ouu of he oher vehicle be degraded wih an error bias comonen of (-9m, 6m) and a noise comonen of mean 0 and sandard deviaion 8m. he degraded RK-GPS ouus are used in he ess; he ime of he wo vehicle sysems are relaed o he GPS universal ime. Each vehicle erforms occuancy grid based local SLAM using he mehod in Secion.; he local SLAM ouus are used o correc odomeer daa. he degraded GPS measuremens are fused wih correced odomeer daa o erform global localizaion, using he mehod in Secion.. When he wo vehicles are in cooeraion mode service deecion for iniiaing cooeraion is based on vehicle global localizaion resul cooeraive local maing and moving objec deecion are erformed using he mehod inroduced in Secion 3 and Secion 4. Some examle resuls are demonsraed in Fig.-4. In Fig., he o wo sub-figures are he local occuancy grid mas buil by he wo vehicles. he boom-lef sub-figure shows he merging effec using he low-accuracy GPS based localizaion resuls; here is large alignmen inconsisency beween he wo local mas. he boom-righ sub-figure shows he occuancy grid mas merging effec using he mehod inroduced in Secion 3; he wo local mas are aligned correcly. Anoher examle of occuancy grid mas merging is demonsraed in Fig.3, he o wo sub-figures are wo local occuancy grid mas. he boom-lef sub-figure shows he merging effec of ma occuied cells; he boom-righ subfigure shows he merged occuancy grid ma. As we can see, here is considerable mas inheren inconsisency beween he wo local mas; however, he roosed occuancy grid mas merging mehod is insensiive o he mas inheren inconsisency and merges he wo local mas correcly. Fig (o) local mas of wo vehicles; (boom-lef) local mas merging using low-accuracy GPS localizaion resuls; (boom-righ) consisen local mas merging Fig 3 (o) local mas of wo vehicles; (boom-lef) merged mas occuied cells; (boom-righ) merged occuancy grid ma Cooeraive moving objec deecion is demonsraed in Fig.4, each of he lef wo sub-figures shows he local ma and moving objec deecion resul of one single vehicle; he

7 deeced moving objecs are marked by blue boxes. he merged occuancy grid ma and moving objec deecion resul are shown in boom-righ sub-figure. Comared wih he boom-lef sub-figure, he boom-righ sub-figure shows a more comlee view for he vehicle. Fig 4 (lef) local mas and single vehicle moving objec deecion; (o-righ) local mas merging; (boom-righ) cooeraive moving objec deecion VI. CONCLUSION his aer rooses a new mehod for occuancy grid mas merging, which uses an objecive funcion based on occuancy likelihood and uses geneic algorihm imlemened in a dynamic scheme o oimize he objecive funcion. he occuancy grid mas merging mehod is used for muli-vehicle cooeraive local maing and moving objec deecion. he inroduced mehods are esed on real-daa exerimens and several erformance examles are given o demonsrae he effeciveness of he mehods. Cooeraive moving objec deecion can be valuable for many scenarios such as overaking scenarios ha are challenging for single vehicle sysem. In fuure, more advanced moving objec deecion mehods can be incororaed ino he scheme of muli-vehicle cooeraive local maing and moving objec deecion. In he resened alicaion of cooeraive moving objec deecion, moving objecs are deeced based on local ma of each single vehicle firs and hen merged. As merged local ma can rovide more comlee view han he local ma of each single vehicle, moving objec deecion based on merged local ma migh yield beer deecion resul. his can also be a direcion of fuure works. REFERENCE [] S. hrun, Roboic maing: A survey, echnical Reor CMU-CS-0-, School of Comuer Science, Carnegie Mellon Universiy, 00 [] H. Durran-Whye,. Bailey, Simulaneous localizaion and maing: ar I, IEEE Roboics & Auomaion Magazine, 3(), 006,.99-0 [3]. Bailey, H. Durran-Whye, Simulaneous localizaion and maing (SLAM): ar II, IEEE Roboics & Auomaion Magazine, 3(3), 006,.08-7 [4] C.C. Wang, Simulaneous Localizaion, Maing and Moving Objec racking, PhD hesis, Roboics Insiue, Carnegie Mellon Universiy, Pisburgh PA, 004 [5].D. Vu, Vehicle erceion: Localizaion, maing wih deecion, classificaion and racking of moving objecs, PhD hesis, Insiu Naional Polyechnique de Grenoble, 009 [6] Y. Khaled, M. sukada, J. Sana, J. Choi,. Erns, A usage oriened analysis of vehicular neworks: from echnologies o alicaions, Journal of Communicaions, 4(5), 009, [7] R. Madhavan, K. Fregene, L.E. Parker, Disribued cooeraive oudoor mulirobo localizaion and maing, Auonomous Robos 7, 004,.3-39 [8] A. Howard, L.E. Parker, G.S. Sukhame, he SDR exerience: Exerimens wih a large-scale heerogeneous mobile robo eam, Exerimenal Roboics I, SAR, Sringer-Verlag Berlin Heidelberg, 006,.-30 [9] A. Howard, Muli-robo simulaneous localizaion and maing using aricle filers, Inernaional Journal of Roboics Research, 5(), 006, [0] L. Carlone, M.K. Ng, J. Du, B. Bona, M. Indri, Simulaneous localizaion and maing using rao-blackwellized aricle filers in muli robo sysems, Journal of Inelligen and Roboic Sysems, 63(), 0, [] A. Birk, S. Carin, Merging occuancy grids from mulile robos, Proceedings of he IEEE, 94(7), 006, [] A. Elfes, Occuancy grids: a robabilisic framework for robo erceion and navigaion, PhD hesis, Carnegie Mellon Universiy, 989 [3] S. hrun, Learning occuancy grids wih forward sensor models, Auonomous Robos 5, 003,.-7 [4] G. Dedeoglu, G. Sukhame, Landmark-based maching algorihm for cooeraive maing by auonomous robos, Inernaional Symosium on Disribued Auonomous Roboics Sysems, 000,.5-60 [5] K.F. Man, K.S. ang, S. Kwong, Geneic algorihms, New York: Sringer-Verlag, 999 [6] h:// [7] H. Li, F. Nashashibi, Muli-vehicle cooeraive localizaion using indirec vehicle-o-vehicle relaive ose esimaion, IEEE Inernaional Conference on Vehicular Elecronics and Safey, 0,.67-7 ACKNOWLEDGMEN his research work is suored by he French naional rojec ABV (Auomaisaion Basse Viesse).