Simultaneous Localization and Mapping with Stereo Vision

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1 Simulaneous Localizaion and Mapping wih Sereo Vision Mahew N. Dailey Compuer Science and Informaion Managemen Asian Insiue of Technology Pahumhani, Thailand Manukid Parnichkun Mecharonics Asian Insiue of Technology Pahumhani, Thailand Absrac In he simulaneous localizaion and mapping (SLAM) problem, a mobile robo mus build a map of is environmen while simulaneously deermining is locaion wihin ha map. We propose a new algorihm, for visual SLAM (VSLAM), in which he robo s only sensory informaion is video imagery. Our approach combines sereo vision wih a popular sequenial Mone Carlo (SMC) algorihm, he Rao-Blackwellised paricle filer, o simulaneously explore muliple hypoheses abou he robo s six degree-of-freedom rajecory hrough space and mainain a disinc sochasic map for each of hose candidae rajecories. We demonsrae he algorihm s effeciveness in mapping a large oudoor virual realiy environmen in he presence of odomery error. Keywords Localizaion, mapping, sereo vision, Rao- Blackwellised paricle filer, visual landmarks I. INTRODUCTION Simulaneous Localizaion and Mapping (SLAM) is he problem of a mobile robo consrucing a meric map from noisy sensor readings while simulaneously esimaing is locaion from he parial map and noisy odomery measuremens. SLAM is one of he fundamenal challenges for mobile roboics research. Alough recen years have seen grea advances in 2D mapping wih laser range finders, exclusively vision-based SLAM (VSLAM) is sill limied o relaively small scale, highly srucured indoor environmens. We are ineresed in aking VSLAM beyond he ypical office building environmen ino larger, bu sill srucured, environmens such as college campuses, office parks, and shopping malls. Poenial applicaion areas include securiy, inspecion, landscape mainenance, agriculure, and personal service. Achieving his goal wihou giving he robo an a-priori map requires new echnology. The majoriy of vision-based SLAM research o dae has focused on auomaic consrucion of occupancy grids or opological maps (see [8] for a survey), boh of which are inappropriae for large-scale meric mapping. The ideal approach would consruc a sparse 3D represenaion of he environmen. Early VSLAM sysems did use sparse feaures, bu hey ypically compressed he map o 2D. For example, Kriegman, Triendl, and Binford s sysem [11] uses a sereo sensor o exrac verical lines from he environmen. Observed lines are used o reduce odomeric uncerainy using an exended Kalman filer (EKF), hen he observaions are in urn used o updae an environmen map conaining 2D poin feaures represening he observed verical lines. Yagi, Nishizawa, and Yachida s sysem [21] ook a similar approach bu used a single omnidireciona vision sensor and accumulaion of measuremens over ime, raher han sereo, o deermine he posiions of verical line landmarks. These sysems and ohers have amply demonsraed he efficacy of VSLAM based on line landmarks in consrained indoor environmens wih smooh floors. Faugeras and colleagues [1], [22] were he firs o develop a VSLAM sysem soring a sparse 3D map. Their sysem firs consrucs a local 3D line segmen map of he curren scene using rinocular sereo. I explicily represens he uncerainy abou each feaure s robo-relaive pose in he form of a covariance marix. The new local map is regisered agains he curren global map and used o updae an esimae of he robo s posiion using an EKF. Finally, assuming he robo s posiion, he global map is be updaed wih he freshly observed feaures, again using EKFs. Se, Lowe, and Lile [16] demonsrae he use of SIFT (scale invarian feaure ransform) poin feaures as landmarks for he VSLAM problem. Their sysem also uses a rinocular sereo camera rig and models he posiional uncerainy of he landmarks wih Kalman filers. Sim and Dudek [17] ake a differen approach; raher han prespecifying he feaures (lines, poins, corners, and so on) ha should be used for map building and localizaion, heir sysem learns generaive models for he appearance of salien feaures during exploraion. Unil quie recenly, mos VSLAM sysems limied hemselves by separaing he moion esimaion and map esimaion problems. Typically, a each sep, he robo s locaion would be esimaed via Bayesian inference or some oher esimaion echnique, hen ha posiion would be assumed for he map updae. While his approach leads o fas algorihms, no considering alernaive robo poses when esimaing landmark posiions is subopimal. Oher researchers in he roboics communiy ook a formal probabilisic approach and explored he possibiliy of represening, a each poin in ime, he full join poserior disribuion over robo rajecories and landmark /06/$20.00 c 2006 IEEE ICARCV 2006

2 posiions. Smih, Self, and Cheeseman [19] inroduced he sochasic map, which represens no only he posiions of landmarks in he world wih heir associaed uncerainies, bu also he uncerainy of he robo s posiion, he covariance beween each pair of landmarks, and he covariance beween he robo s posiion and each landmark. This seminal heoreical work inspired many successful SLAM sysems, e.g. [2], [7], [12]. In a paricularly impressive demonsraion of he power of he sochasic map approach, Davison and colleagues [5], [6] have solved he VSLAM problem wih poin landmarks exraced from a single camera wihou odomery. Their sysem runs in real ime a 30 Hz. While he sochasic map very accuraely represens all of he available informaion abou landmark and robo posiions (wihin he limis of he Gaussian approximaion), he mehod unforunaely canno scale o he housands of landmarks needed for large-scale environmens, due o he size of he full covariance marix. Murphy [13], however, recognized ha in SLAM, map elemens are condiionally independen given he robo s rajecory hrough ime. He used his insigh in he design of he Rao-Blackwellised paricle filer (RBPF), in which he join poserior over robo rajecories and maps is represened by a se of samples or paricles, each paricle conaining one possible robo rajecory and he corresponding sochasic map. The fac ha he robo s rajecory is fixed for a given paricle has an imporan consequence: all of he covariances beween differen map elemens in he sochasic map become 0. For a landmark map, his means he covariance marix for each individual landmark is sufficien o represen all of he available knowledge of he environmen. Murphy only demonsraed he RBPF on a oy problem, bu more recen work has applied he echnique o he real world wih immense success. Monemerlo, Thrun, and colleagues [20] use he RBPF and 2D poin landmarks measured by a laser scanner o consruc large-scale 2D maps. In heir sysem, each paricle represens a possible robo rajecory, se of daa associaions, and landmark map. The maps are sored in a ree srucure ha allows sharing subrees beween paricles, allowing a real-ime implemenaion ha scales o housands of landmarks. Eliazar and Parr [9] also use he RBPF and a laser scanner for SLAM, bu build a 2D occupancy grid raher han a landmark daabase. Their algorihm also requires a sophisicaed daa srucure ha allows sharing maps beween paricles. Even more recenly, researchers have begun o apply he RBPF o he VSLAM problem. Sim e al. [18] exrac SIFT poin feaures from sereo daa and combine he observaions wih visual odomery o build 3D landmark maps. According o he auhors, his sae-of-he ar sysem has consruced he larges and mos deailed VSLAM map ever, in a large indoor laboraory environmen. In our work, we ake a similar approach, combining he RBPF wih vision sensors, excep ha we use 3D line segmens for localizaion and map building, raher han he more commonly used poin feaures [18], [20]. Line parameers can be esimaed more accuraely han poins, since he esimae incorporaes more observed daa. This means i may be possible o obain more accurae robo localizaion from line landmarks han poin landmarks, depending on he characerisics of he robo s workspace. Lines also provide more informaion abou he environmen s geomery han do poins, allowing more sophisicaed inference abou he srucure of he world. However, lines also have an imporan disadvanage wih respec o poins: hey are less disincive, making i more difficul o find correc correspondences beween a se of observed lines and he lines in a sored model. We overcome his difficuly by sampling many possible poses from he robo s moion model, obaining a differen possible observaion-model correspondence given each robo pose, and allowing he fies correspondences o survive in he paricle filer. Our algorihm is called VL-SLAM (Visual Line-based SLAM). Here we describe VL-SLAM and demonsrae is effeciveness in a series of experimens. The main conribuions of his paper are 1) an effecive sensor model for line landmarks obained from a sereo camera rig, 2) a new proposal disribuion for he RBPF ha overcomes he limiaions imposed by highly uncerain correspondences, and 3) experimenal evidence of he feasibiliy of VL-SLAM using realisic, albei synheic, daa. II. VL-SLAM VL-SLAM is based on he FasSLAM family of algorihms proposed by Monemerlo, Thrun and colleagues [20]. A each poin 1... T, he robo performs an acion u aking i from posiion s 1 o s and uses is sensors o obain an observaion z. We seek a recursive esimae of p(s 0:, Θ u 1:, z 1: ) (1) where Θ is a map conaining he posiions of each of a se of poin landmarks. Raher han esimae he disribuion (1) analyically, we approximae he poserior wih a discree se of M samples (someimes called paricles) { < s [m] 0:, Θ[m] 0: >, where each index m 1... M }. (2) Here s [m] 0: is he specific robo rajecory from ime 0 o ime associaed wih paricle m, and Θ [m] 0: is he sochasic landmark map associaed wih paricle m (he map is derived from s [m] 0:, z 1:, and u 1: ). FasSLAM (and VL-SLAM) use he sequenial Mone Carlo echniques of sequenial imporance sampling and imporance resampling. Firs, for each paricle, we sample from some proposal disribuion π(s 0:, Θ 0: z 1:, u 1: ) (3) o obain a emporary se of paricles for ime, hen evaluae he imporance weigh w [m] for each emporary paricle, where w(s 0:, Θ 0: ) = p(s 0:, Θ 0: u 1:, z 1: ) π(s 0:, Θ 0: u 1:, z 1, ). (4) The imporance weighs are normalized o sum o 1, hen we sample M paricles, wih replacemen, from he emporary paricle se according o he normalized weighs.

3 VL-SLAM exends FasSLAM wih a new sensor model for 3D line segmens and a new proposal disribuion π( ) appropriae for environmens wih highly ambiguous observaionmodel correspondences. We firs describe he 3D line segmen sensor model hen VL-SLAM proposal disribuion. A. VL-SLAM 3D Line Segmen Sensor Model Afer each robo moion u, a se of rinocular sereo images is capured, and a se z of landmark measuremens (line segmens) is exraced from hose images. These line segmen measuremens, along wih he measured moion u, are used o updae each paricle s map and posiion esimae. Our sysem assumes a calibraed sereo camera rig wih hree pinhole cameras. I can handle general fundamenal marices (he images need no be perfecly recified), bu we do assume ha one camera is roughly horizonally displaced and a second camera is roughly verically displaced from a hird (reference) camera. The basic 2D feaure in our sysem is he line segmen. We exrac line segmens using Canny s mehod [4] following he implemenaion in VISTA [14]. The edge deecor firs performs nonmaxima suppression, links he edge pixels ino chains, and reains he srong edges wih hyseresis. Once edge chains are exraced from he image, we approximae each chain by a sequence of line segmens. Shor line segmens, indicaing edges wih high curvaure, are simply discarded in he curren sysem. We use a sraighforward sereo maching algorihm similar o he approach of [22]. For each line segmen in he reference image, we compue he segmen s midpoin, hen consider each segmen inersecing ha midpoin s epipolar line in he horizonally displaced image. Segmens no meeing line orienaion and dispariy consrains are discarded. Each of hese poenial maches deermines he locaion and orienaion of a segmen in he hird image. If such a consisen segmen is indeed found in he hird image, he poenial mach is reained; oherwise i is discarded. If a he end of his process, we have one and only one consisen mach, we assume i correc; oherwise, he reference image line segmen is simply ignored. Now our goal is o esimae a hree-dimensional line from he hree observed wo-dimensional lines. Infinie lines have four insrinsic parameers, so i would make sense o use a four-dimensional represenaion of a lines. However, since VL-SLAM uses a Kalman filer o combine landmark observaions, we require a linear parameerizaion of landmarks, and no linear four-dimensional represenaion of lines exiss [1]. Insead we represen lines wih six componens: a 3D poin represening he midpoin of he observed line segmen and a 3D vecor whose direcion represens he direcion of he line and whose lengh represens he disance from he line segmen s midpoin o one of is endpoins. This 6D represenaion behaves well under linear combinaion, so long as he direcion vecors are flipped o have a posiive do produc. Firs we obain a maximum likelihood esimae of he infinie 3D line s parameers assuming Gaussian measuremen error in he image using Levenberg-Marquard minimizaion [15]. As an iniial esimae of he line s parameers, we use he 3D line (uniquely) deermined by wo of he 2D line segmen measuremens. Once he infinie line has been esimaed, we find he segmen s exrema and midpoin using he observed daa. Through each sep of he 3D line esimaion process, we mainain explici Gaussian error esimaes. We begin by assuming spherical Gaussian measuremen error in he image wih a sandard deviaion of one pixel. Arranging he n (x, y) coordinaes of he pixels in a line as a column vecor x, he covariance of x is simply Σ x = I 2n 2n. Since he vecor of parameers l describing he 2D line bes fiing x is a nonlinear funcion l = f(x), he covariance of l is Σ l = JΣ x J T, where J is he Jacobian marix f x evaluaed a x. The maximum likelihood esimae of he 3D line obained from he hree 2D line segmens l = (l 1, l 2, l 3 ) is clearly no a simple funcion, since i is compued by an ieraive opimizaion procedure. However, if l = f(l) is he funcion mapping from he parameer space o he measuremen space, i urns ou ha, o firs order, ˆL is a random variable wih covariance marix (J T Σ l J) 1, where J is he Jacobian marix l L [10]. The rank of he resuling covariance marix is only four, however, so o consrain he remaining wo degrees of freedom, we add o he rank-deficien covariance marix a covariance marix describing he expeced error in our esimae of he segmen s midpoin and anoher covariance marix describing he expeced error in our esimae of he segmen s lengh. This gives us a full-rank covariance marix ha resrics maching line segmens o no only be similar in erms of heir supporing infinie line, bu also o overlap and have similar lengh. Once he six-dimensional represenaion of an observed 3D line is esimaed from a rinocular line correspondence, i is necessary o ransform ha line from camera coordinaes ino robo coordinaes, since he reference camera is in general ranslaed and roaed relaive o he robo iself. I is also necessary o ransform landmarks from robo coordinaes ino world coordinaes, when he robo s posiion is deermined, for insance, and from world coordinaes back o robo coordinaes, when a landmark in he map is considered as a possible mach for an observed (robo coordinae) landmark. In each of hese cases, he ransformed line L = (L) is compued as a nonlinear funcion of he original line, and he ransformed line s covariance is propagaed by Σ L = JΣ L J T, where J is he Jacobian marix L evaluaed a L. B. VL-SLAM Proposal Disribuion The proposal disribuion π( ) (3) can be any disribuion ha is sraighforward o sample from. However, i is bes if π( ) closely approximaes he full join poserior (1), in which case he imporance weighs will be nearly uniform, and mos paricles will survive he resampling sep. In FasSLAM 1.0 [20], he proposal disribuion is simply p(s s 1, u ), i.e. he moion model predicing s given a previous posiion s 1 and acion u. The auhors observe ha his proposal disribuion,

4 Fig. 1. (a) (b) (c) Sample rinocular image se capured in simulaion. (a) Reference image. (b) Horizonally aligned image. (c) Verically aligned image. while simple o sample from, does no ake ino accoun he curren observaion z. This leads o FasSLAM 2.0, in which he proposal disribuion is p(s s [m] 0: 1, Θ[m] 0: 1, u 1:, z 1: ). This disribuion akes no only he previous robo pose s 1 and curren acion u ino accoun, bu also considers he curren map Θ 0: 1 and new observaion z. In he general case, his disribuion could be quie difficul o sample from, bu he auhors find ha by linearizing he sensor model and applying he Markov assumpion, he proposal disribuion can be approximaed o firs order by a Gaussian disribuion whose mean and covariance can be calculaed from known quaniies, if he correspondence beween he observaion z and he curren map Θ 0: 1 is known. When he correspondences are unknown (he usual case in SLAM), FasSLAM 2.0 assumes he maximum likelihood correspondence or draws a sample from a probabiliy disribuion over all possible correspondences. When he observaions and landmarks are sparse, as is he case in he FasSLAM environmen, his is sraighforward, and FasSLAM 2.0 is much more successful han FasSLAM 1.0, since i uses he available se of paricles wisely [20]. In VL-SLAM, however, each observaion consiss of on he order of 100 individual 3D line segmens, and ypically he landmark daabase conains several poenial maches for each observed line. This means ha i is impossible o consider even a small fracion of he possible correspondences for each paricle. In pracice, o limi he compuaional complexiy, we mus draw a single correspondence from he se of all possible correspondences wihou considering oo many alernaives. Bu how can we choose a likely correspondence for a given observaion? In VL-SLAM, when propagaing a paricle forward from ime 1 o ime, we firs fraw a sample s from he robo s moion model o esablish a correspondence beween he observed line segmens and he curren map (resembling FasSLAM 1.0), hen from ha inermediae sample poin, assuming he esablished correspondence, sample again, from he FasSLAM 2.0 proposal disribuion. As in FasSLAM 2.0, he proposal disribuion is closer o he full join poserior disribuion, concenraing more of he emporary paricles in regions of high probabiliy according o he full join poserior. To calculae he imporance weighs for he he VL-SLAM proposal disribuion, we firs inroduce random variables n indicaing he correspondence beween he line segmens observed a ime and he map. In VL-SLAM, he mh paricle s map Θ [m] 0: is a deerminisic funcion of he sampled rajecory s [m] 0:, he sampled correspondences n[m] 1:, and he observaions z 1:, so we rewrie he desired full join poserior as p(s 0:, n 1: u 1:, z 1: ). (5) Now, assuming we have a good esimae of he full join poserior a ime 1, he VL-SLAM proposal disribuion can be wrien as he produc n [m] p(n [m], s [m], s [m] 0: 1, n[m] 0: 1, z 1:, u 1: ) s [m] s [m] 0: 1, n[m] 1: 1, z 1: 1, u 1: ) p(s [m] s [m] 0: 1, n[m] 1: 1, z 1: 1, u 1: ) 0: 1, n[m] 0: 1 u 1: 1, z 1: ), (6) where s represens he inermediae sample drawn from he moion model. For he mh paricle, he imporance weigh is he raio of he expressions in (5) and (6), which, wih several applicaions of Bayes rule and he Markov assumpion, can be closely approximaed as (deails ommied): w [m] = s [m] 1, u )p(z s [m] 0:, n[m] 1:, z 1: 1) z, s [m], n [m] 1:, s[m] 0: 1, z 1: 1, u 1: )p(s [m] s [m] 1, u ) (7) Following [20], we linearize he sensor model and moion model, which leads o sraighforward Gaussian approximaions for each of he erms in (7). Excep for he sensor model and proposal disribuion jus described, VL-SLAM is similar o FasSLAM (see [20] for deails). Once correspondences and he sampled pose are deermined for an individual paricle, each observed landmark is combined wih is corresponding map landmark using an exended Kalman filer, or iniialized as a new landmark in he map. To achieve fas search for landmarks corresponding o a given observaion, each paricle s map is sored in a binary k- D ree whose leaves are he 3D line segmens wih associaed Gaussian uncerainies. However, o minimize oal memory requiremens and o enable consan-ime copying of maps

5 during he resampling sage, he paricles are allowed o share subrees. As we shall see in he nex secion, he diversiy of possible correspondences inroduced by he firs sampling sep (as in FasSLAM 1.0), combined wih he use of he curren observaion z in he proposal disribuion (as in FasSLAM 2.0), allows VL-SLAM o ouperform boh FasSLAM 1.0 and FasSLAM 2.0 on a challenging synheic esbed. III. EXPERIMENTAL RESULTS To enable rigorous esing of VL-SLAM in an environmen wih a precisely known ground ruh, we implemened a virual realiy simulaion allowing a virual robo o move hrough a virual world rendered wih OpenGL from a VRML model. We chose as an environmen a publically-available 3D model of Housesead s for, a Roman garrison from he 3rd cenury A.D. on Hadrian s Wall in Briain [3]. A sample view from our virual rinocular sereo rig is shown in Figure 1. We eleoperaed our virual robo hrough his virual world in a long loop of abou 300m. A approximaely 1m inervals, he virual camera rig was insruced o capure a se of sills from is hree cameras. The virual camera models a real 10cm baseline, 70 field of view rinocular rig we recenly buil in our lab. To make he daase somewha challenging, we simulaed he effecs of a raveling on an imperfec oudoor surface, so ha he robo s verical (Z) posiion varied approximaely ±0.04m from 0, is pich and roll varied ±2.5 degrees from 0, and is yaw varied ±3 degrees from is expeced course. This environmen is an ineresing esbed for VL-SLAM because, on he one hand, i generaes many long, srong, sraigh edges ha should be useful for localizaion. On he oher hand, i is highly exured, creaing a large number of edges, and he exures are highly repeiive in many places, leading o many ambiguiies for correspondence algorihms. I is also large enough o preclude fine-grained grid-based echniques and noisy enough o preclude he use of fla-earh or hree-degree-of-freedom assumpions. We compared VL-SLAM wih our own implemenaions of FasSLAM 1.0 and 2.0. As previously discussed, FasSLAM 2.0 was no designed o handle large observaions wih highly uncerain correspondences. In our implemenaion, we simply obain he maximum likelihood correspondence assuming he robo is a he posiion obained by propagaing s [m] 1 forward in ime according o odomery o obain ŝ [m]. Wih his cavea abou he FasSLAM 2.0 resuls, Figure 2 shows one measure of each algorihm s performance: he log-likelihood of he observaion daa given he bes paricle s robo rajecory sample and map; Figure 3 shows he final map according o he bes VL-SLAM paricle. All of he localizaion algorihms do much beer han he baseline (odomery-only) algorihm. Due o is commimen o robo posiion ŝ [m] when deermining correspondences in our implemenaion, FasSLAM 2.0 fares raher poorly. Since FasSLAM 1.0 samples from he moion model before obaining a correspondence, i performs much beer, bu VL-SLAM, which combines he bes feaures of boh algorihms, ouperforms hem boh. IV. CONCLUSION In his paper, we have demonsraed he feasibiliy of VL- SLAM on a challenging synheic daa se. The VL-SLAM proposal disribuion improves on FasSLAM in environmens wih large numbers of ambiguous observaions. However, Figure 2 shows ha here is sill improvemen o be made: he log-likelihood of he observaions given perfec localizaion is sill much beer han he log-likelihood of he observaions under VL-SLAM s model. This means here is sill informaion abou he robo s posiion o be exploied in he observed daa. This is also evidenced in Figure 3, which compares he VL- SLAM map o he map consruced wih perfec knowledge of he robo s locaion. Alhough he map is locally fairly accurae, global drif occurs hroughou he run, prevening he algorihm from closing he loop when he robo reurns o is saring posiion. This is mos likely due o an impoverished se of paricles. In fuure work, we plan o improve VL-SLAM s loop closing behavior and evaluae he algorihm on a variey of indoor and oudoor real-world daa ses. ACKNOWLEDGMENTS This research was suppored by Thailand Research Fund gran MRG o MND. REFERENCES [1] N. Ayache and D. Faugeras. Mainaining represenaions of he environmen of a mobile robo. IEEE Transacions on Roboics and Auomaion, 5(6): , [2] S. Borhwick and H. Durran-Whye. Simulaneous localisaion and map building for auonomous guided vehicles. In Proceedings of he IEEE/RSJ/GI Inernaional Conference on Inelligen Robos and Sysems (IROS), pages , [3] Briish Broadcasing Corporaion. Housesead s For (3D model), hp:// hisory/3d/housead.shml. [4] J. Canny. A compuaional approach o edge deecion. IEEE Transacions on Paern Analysis and Machine Inelligence, 8(6), [5] A. Davison. Real-ime simulaneous localisaion and mapping wih a single camera. 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