SLAM in Large Indoor Environments with Low-Cost, Noisy, and Sparse Sonars

Transcription

1 SLAM in Large Indoor Environmens wih Low-Cos, Noisy, and Sparse Sonars Teddy N. Yap, Jr. and Chrisian R. Shelon Deparmen of Compuer Science and Engineering Universiy of California, Riverside, CA 92521, USA {yap, Absrac Simulaneous localizaion and mapping (SLAM) is a well-sudied problem in mobile roboics. However, he majoriy of he proposed echniques for SLAM rely on he use of accurae and dense measuremens provided by laser rangefinders o correcly localize he robo and produce accurae and deailed maps of complex environmens. Lile work has been done on he use of low-cos bu noisy and sparse sonar sensors for SLAM in large indoor environmens involving large loops. In his paper, we presen our approach o SLAM wih sonar sensors by applying paricle filering and a line-segmen-based map represenaion wih an orhogonaliy assumpion o map indoor environmens much larger and more challenging han hose previously considered wih sonar sensors. Resuls from roboic experimens demonsrae ha i is possible o produce good maps of large indoor environmens wih large loops despie he inheren limiaions of sonar sensors. I. INTRODUCTION Since i was firs inroduced by Smih and Cheeseman [1], he simulaneous localizaion and mapping (SLAM) problem has become one of he mainsream research areas in mobile roboics. The SLAM problem involves esimaing he posiion and orienaion of he robo while building a map of he environmen in parallel. In order o accomplish SLAM, he robo is usually equipped wih sensors (e.g. wheel encoders, range sensors, cameras) ha allow i o observe (hough only parially and inexacly) he sae of he world including iself. The SLAM problem is inherenly difficul and complex alhough he specific sensor used also conribues o he hardness of SLAM. SLAM is a well-sudied problem in mobile roboics and a number of echniques have been proposed. However, he majoriy of he proposed echniques for SLAM rely on he use of accurae and dense measuremens provided by laser rangefinders o correcly localize he robo and produce accurae and deailed maps of complex environmens (see e.g. [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]). Relaively lile work has been done on he use of low-cos bu noisy and sparse sonar sensors for SLAM in large indoor environmens involving large loops. Obviously, he SLAM problem is much more difficul and challenging in he case of sonar sensors han laser rangefinders (which have become he de faco range sensors for SLAM). Despie he difficuly, we believe ha i is ineresing o invesigae he exen o which sonar sensors can be used for SLAM especially in mapping large indoor environmens wih large loops. Alhough sonar sensors are no as accurae and do no provide as dense observaions as laser rangefinders, hey are sill an aracive alernaive o laser rangefinders when i comes o cos, power consumpion, size and weigh, and compuaional requiremens. Compared o laser rangefinders, sonars cos several orders of magniude less, consume less power, are small and lighweigh, and impose minimal compuaional requiremens. As such, sonar sensors are well-suied for use in inexpensive consumer-oriened and minimally-equipped robos ha are ypically limied in boh power and compuaional capabiliy. In his paper, we presen our approach o SLAM wih sonar sensors by applying paricle filering and an orhogonal linesegmen-based map represenaion o map indoor environmens much larger and more challenging han hose previously considered wih sonar sensors. Raher han employing a grid-based represenaion for he map, we use a feaurebased represenaion where he feaures are represened as line segmens. Line segmens are suiable for compacly describing mos srucured indoor environmens ha are usually composed of walls, doors, glass windows, ec. ha are eiher parallel or perpendicular o each oher. Similar o [11], we also make use of he orhogonaliy assumpion abou he shape of he environmen in order o reduce he complexiy, mapping only lines ha are eiher parallel or perpendicular o each oher. A major difficully in using line segmens as an environmen s represenaion is exracing hem from noisy and sparse sensors such as sonars (in our case, an array of 16 sonar ransducers) compared o a single dense scan of a 180 laser rangefinder. Thus, in his work, we adop he muliscan approach [12] o group consecuive sparse scans so ha measuremens from muliple ime frames can be used o exrac line segmens, alhough our work differs on how he sparse scans are colleced and he frequency a which he feaure exracion is performed. The conribuions of his paper can be summarized as follows. We show hrough exensive experimens ha i is possible o produce good qualiy maps of large indoor environmens wih large loops even wih noisy and sparse sonar sensors. To our knowledge, he environmens we consider in our experimens are much larger and more challenging han hose previously repored in he lieraure for SLAM wih sonars. The resuls provide significan supporive evidence

2 for he poenial viabiliy of sonars for large-scale indoor SLAM. Our mehod employs a paricle filering echnique where each paricle carries a single map raher han a disribuion over possible maps. Moreover, we apply he orhogonaliy assumpion o reduce he complexiy. Finally, we discuss how we exrac line segmens from sonar daa and we inroduce a simple sensor model for compuing he likelihood of he observaions. II. PRIOR WORK While much of he work on SLAM wih proximiy sensors has focused on laser scanners (see e.g. [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]), some researchers have used sonars. In his secion, we briefly describe some of he echniques proposed for carrying ou SLAM wih sonars. There are wo main crieria ha can be used o caegorize exising sonarbased SLAM echniques: he represenaion used o model he environmen and he echnique used o esimae he sae belief disribuion. Zunino and Chrisensen [13] described an algorihm for SLAM based on he exended Kalman filer (EKF). The EKF approach was used o build and mainain he map of he environmen. Their mehod used poin feaures as landmarks (represening corners, edges, and hin poles deecable by sandard sonar sensors hrough a riangulaion echnique). They also presened a mehod for deecing he failures of he EKF approach and recovering from such failures. Experimens were performed using a Nomadic SuperScou mobile robo in a living room of size 5m 9m. Tardós e al. [14] described a echnique for he creaion of feaure-based sochasic maps using sandard Polaroid sonar sensors. In heir work, hey used he Hough ransform [15] for deecing poin feaures (represening corners and edges) and line segmen feaures (represening walls) from sonar daa acquired from muliple uncerain vanage poins. Insead of building one global map from he sar, hey generaed a sequence of local maps of limied size, and hen joined hem ogeher, o obain he global map. Techniques for joining and combining several sochasic maps were presened. The locaions of geomeric feaures in he environmen and he posiion of he robo were joinly esimaed in a sochasic framework via he EKF. Experimens were carried ou using a B21 mobile robo equipped wih a ring of 24 Polaroid sensors in a 12m 12m environmen. A similar approach o ha of Tardós was proposed by Leonard e al. [16] excep ha hey incorporaed pas robo posiions o he sae vecor and explicily mainained he esimaes of he correlaions beween curren and previous robo saes. By doing so, i became possible o consisenly iniialize new map feaures by combining daa from muliple vanage poins. Experimens were conduced in a esing ank of size 10m 3m 1m for underwaer sonar-based SLAM, a simple box environmen made of plywood, and along a 25m long corridor. A much earlier work along he same lines of feaurebased sochasic mapping using he EKF was given by Rencken [17] alhough experimens were only performed in a simulaion of a 5m 5m room. Insead of joinly esimaing he robo sae and he locaions of line segmen feaures via he EKF, Lorenzo e al. [18] used he EKF o esimae only he robo sae. The environmen was described by a global segmen-based map ha was buil using local sonar-based occupaion maps o idenify obsacle boundaries. The Hough ransform was used o exrac he segmens ha represen he obsacle boundaries. The segmens were hen incorporaed o he global segmenbased map. The Hough-based approach provided a correcion of he esimaed robo pose which was inegraed wih odomeric informaion via he EKF. The approach was esed wih a Nomad 200 mobile robo equipped wih a ring of 16 sonar sensors raversing a corridor environmen. More recenly, Schröer, Böhme, and Gross [19] presened a combinaion of map-maching wih a Rao-Blackwellized paricle filer (RBPF) [20] which enabled hem o solve he SLAM problem wih low-resoluion sonar range sensors. They inroduced a simple and fas bu very efficien shared represenaion of gridmaps which reduced he memory cos overhead caused by inheren redundancy beween he paricles. Experimenal resuls were presened wih a SCITOS A5 robo plaform navigaing in a home sore environmen. Oher noable recen relaed work on SLAM wih sparse sensors include he work of Beevers and Huang [12] on SLAM wih sparse sensing using he muliscan approach and RBPF, Abrae, Bona, and Indri [21] on experimenal EKFbased SLAM for mini-rovers wih IR sensors only, and Choi, Lee, and Oh [22] on a line based SLAM wih infrared sensors using geomeric consrains and acive exploraion. The focus of our work repored in his paper is on SLAM in large srucured indoor environmens involving large loops using sonar sensors. The larges environmen we consider has an approximae area of 70.0m 53.7m conaining wo major loops and is made up of various ypes of obsacles (e.g. brick walls, iled walls, glass windows and doors, and cable railings). Our work differs from [19] in ha we use a line-segmen-based insead of a grid-based represenaion for he map. By adoping a line-segmenbased map represenaion, we can avoid he usual problems associaed wih a grid-based represenaion such as daa smearing [14], he srong independence assumpion beween he grid cells, and he considerable amoun of memory required for sorage. However, a major difficuly wih line segmens is exracing hem from sparse and noisy sonars. To overcome he sparseness, we apply he muliscan approach [12] o group consecuive sparse scans. In order o reduce he complexiy of SLAM, similar o [11], we make use of he orhogonaliy assumpion abou he shape of he environmen by mapping only lines ha are parallel or perpendicular o each oher. Unlike [14], [16], [17], [18], we use paricle filers o sample he disribuion over he mos recen robo poses. Each paricle in our paricle filer is associaed wih a single map raher han a disribuion over possible maps.

3 III. OUR LOCALIZATION APPROACH The basis of our approach is a paricle filer, where each paricle is an esimae of he recen m robo poses. Thus, he paricles collecively sample he space of he recen m robo poses. Here we assume ha he robo moves in a planar environmen so ha is pose a ime can be represened as x = (x, y, θ ) T, where (x, y ) T is is Caresian coordinaes and θ is is heading or orienaion wih respec o some global reference frame. Each paricle carries an esimaed map of he environmen ha is represened as a se of line segmens. Because of he orhogonaliy assumpion abou he shape of he environmen, he map will conain only wo ypes of lines: horizonal and verical. Horizonal (verical) lines are assigned o be parallel o he x-axis (y-axis) of he global reference frame. Exraced line segmens ha are no close o being eiher horizonal or verical are simply discarded and no placed in he map. A. Moion Model Le he ih paricle a ime be p [i] = (x [i] m+1:, M[i] ), where x [i] m+1: is he sequence of he recen m robo poses x [i] m+1,x[i] m+2,...,x[i] according o paricle i and is he se of line segmens represening he map of M [i] paricle i a ime. The paricles move according o he probabilisic moion model p(x x 1,c ), where c is he conrol command execued by he robo during he ime inerval [ 1, ), o accoun for he inheren uncerainy in robo moion. The conrol command c is given by he pair (d, r ) T, where d is he disance raveled and r is he roaion made by he robo, according o he wheel encoders. Due o he probabilisic naure of he moion model, he paricles spread and generae differen possible robo rajecories. Here we use he moion model in [23]: x = x 1 + ˆd cos(θ 1 + ˆr ) y = y 1 + ˆd sin(θ 1 + ˆr ) θ = (θ 1 + ˆr ) mod 2π, where ˆd and ˆr denoe he robo s rue ranslaion and roaion, respecively. The rue ranslaion and roaion boh differ from he ranslaion and roaion measured by he robo due o sysemaic and random errors. Specifically, ˆd = d + δ rans d + ǫ rans ˆr = r + δ ro d + ǫ ro, where δ rans and δ ro describe he sysemaic error and ǫ rans N(0, σrans 2 ) and ǫ ro N(0, σro 2 ) are he addiive random variables represening he random errors. In our experimens, δ rans = , δ ro = , σ rans = 2mm, and σ ro = 2. B. Sensor Model When using paricle filering for sae esimaion, paricles are usually assigned weighs based on heir curren esimaes and he curren measuremens or observaions obained abou he sysem. The weighs are assigned in such a way ha likely (good) paricles receive higher weighs han unlikely (bad) paricles. The weighs are used during he resampling sage of he paricle filer such ha paricles wih higher weighs are resampled wih higher probabiliy han paricles wih lower weighs. Through resampling, i is hoped ha good paricles (hose ha can explain he daa well) are reained while bad paricles are eliminaed. Typically, he sensor model (usually expressed in probabilisic form) is uilized in compuing he appropriae weighs for he paricles. For SLAM, he weigh assigned o paricle i is commonly direcly proporional o he likelihood of he observaions p(s x [i], M [i] ) where s = {s 1, s 2,..., s K } is he se of sensor measuremens aken by he K available sensors a ime. From he preceeding discussion, i is eviden ha using an accurae and robus sensor model is herefore crucial o he success of he paricle filer and oher sae esimaion echniques in general. However, deriving an accurae and robus model for sensors is generally a difficul problem. In his paper, we propose a heurisic bu simple way o calculae he weighs of he paricles which is inspired by he work of Schröer, Böhme, and Gross [19] on map maching. In [19], hey need o mach a local map o a global one. They calculae he weigh of paricle i as [i] = e m f, (1) where f is a free parameer ha influences he spread of he paricle weighs and m [i] is a measure of he qualiy of he mach. [19] employs a grid-based map, so we replace heir definiion of m [i] wih our own. For each sonar range measuremen s k obained by sensor k a ime, we perform ray racing along he facing direcion of sensor k wice: a) using he curren map M [i] and b) using he curren map bu wih he line segmens exended by a cerain lengh of L ex (e.g. 200mm) a boh ends. 1 For each ray racing operaion for sensor k a ime, we calculae he rue (expeced) range measuremen 2 s k for sensor k a ime. If he absolue difference beween he acual and expeced range measuremens is less han or equal o he sandard deviaion of he sonar measuremens σ d (50mm) (i.e. s k s k σ d ), we coun i as +1. Oherwise, we coun i as 1. We hen ake he average of he couns obained from he wo ray racing operaions for sensor k and use ha as he sensor s conribuion. We sum hese conribuions o obain m [i]. Fig. 1 illusraes how he mach value is compued. In his way, a paricle whose map can explain he curren measuremens well will be assigned a higher weigh han one ha canno. We should poin ou ha he above procedure o compue he mach value is jus a simple heurisic ha is found o work well in our experimens. We believe ha beer scheme for compuing he paricle weighs would produce beer paricle filer performance. 1 We exclude hose measuremens s k ha are equal o he maximum sonar range s max (e.g. 5000mm) since hey provide us wih lile informaion as o he locaion of objecs or obsacles. 2 The rue (expeced) range measuremen s k is inended o be he disance o he neares obsacle in he map along he facing direcion of he sensor. If he ray doesn inersec wih any obsacle in he map, s k = +.

4 Fig. 1. Compuaion of he mach value. (Lef) Resul of he firs ray racing operaion using he esimaed line segmens. Coun values are shown in parenhesis beside heir corresponding sonar measuremens. Missing sonar measuremens are equal o s max and are no considered in compuing he mach value. (Middle) Resul of he second ray racing operaion using he exended line segmens. (Righ) Average coun value for each sonar measuremen. The mach value m = 2 for his example. C. Paricle Filering I is well-known ha he resampling sage of he paricle filer can eliminae he correc paricle. This is called he paricle depleion problem [7]. In order o reduce he risk of paricle depleion, we also adop he selecive resampling approach repored in [7] by compuing he effecive number 1 of paricles N eff = P N (where = P w[i] i=1 (w[i] ) 2 Ni=1 ) and resampling only when N eff < N/2, where N is he sample size of he paricle filer. The following summarizes our sonar SLAM approach: For ime = 1, 2,..., T : 1) For each paricle p [i] 1, i = 1, 2,..., N: a) Updae he posiion of paricle p [i] 1 by sampling from he moion model p(x x [i] 1,c ) o ge he new posiion x [i] and hus p [i]. b) Updae he weigh of paricle p [i] according o: [i] e m f 1 2) Compue he effecive number of samples N eff. 3) If N eff < N/2, resample from he se of weighed paricles {(p [i], )} N i=1 wih replacemen wih each paricle having he probabily of being seleced proporional o he normalized weigh and se weighs o 1. 4) For each paricle p [i], i = 1, 2,..., N: a) Exrac line segmen feaures from recen m sonar scans s m+1: and recen m poses x [i] m+1:. b) Incorporae exraced line segmens o map M [i] c) Adjus map M [i]. In he nex secion, we discuss how we exrac line segmen feaures from he group of recen m (e.g. 15) sonar scans s m+1: and how he line segmens are incorporaed ino he map as well as how he map is mainained. IV. OUR MAP BUILDING APPROACH A. Line Segmen Exracion For exracing line segmens from he group of recen m sonar scans, we use he randomized Hough ransform (RHT) [24] echnique proposed by Kulanen, Xu, and Oja. Before line segmens can be exraced, we firs plo each sonar measuremen as a poin (in he global reference frame) ha represens he nominal posiion of he sonar reurn, compued. along he cenral axis (facing direcion) of he ransducer, wih respec o he robo pose where he measuremen was aken. Le P be he se of such poins. We hen use he RHT o find groups of (almos) collinear poins in P and exrac he parameers of he lines ha fi hose groups of poins. The Hough ransform [15] is a echnique used in digial image processing for exracing feaures such as lines and curves in binary edge images. I is a voing scheme where each poin (pixel) in he image voes for a se of feaures (lines, curves) ha pass hrough i. Voing is performed in a discreized parameric space, called he Hough space, represening all possible feaure locaions. The mos voed cells in he Hough space should correspond o he feaures acually presen in he image. The RHT is an improvemen on he original Hough ransform by reducing he compuaion ime and memory usage. The basis of he mehod lies on he fac ha a single parameer space poin can be deermined uniquely wih a pair, riple, or generally n-uple of poins from he image. Such an n-uple of poins can be chosen randomly from he image and hence he name. Unlike in he original Hough ransform where each poin in he image voes for a se of cells in he Hough space, a group of n randomly chosen poins from he image voes for only one parameer space poin in he RHT. The presence of a specific feaure in he image is quickly revealed by he accumulaion of a small number of parameer space poins. Raher han having a fixed-size array srucure for implemening he Hough space (also called he accumulaor space) as in he original Hough ransform (hus imposing some predefined accuracy in parameer poin locaion), in RHT, i is possible o use a dynamic ree srucure o sore he accumulaor cells wih non-zero voes in he parameer space. This way, one can achieve as high an accuracy as required while a he same ime bringing memory usage o near minimal. To use he RHT for line segmen exracion, we use he polar coordinae paramerizaion (ρ, θ) for lines, where ρ is he lengh of he normal from he origin o he line and θ is he angle ha he normal makes wih he posiive x-axis. Using his paramerizaion, he equaion of he line can be wrien as ρ = x cosθ + y sin θ. (2)

5 To ensure unique paramerizaion of lines, we impose ha 0 ρ ρ max and 180 θ < 180. In our implemenaion, we discreize he Hough space using he resoluions ρ = 50mm and θ = 1. Le A be he fixed-size accumulaor array for implemening he discreized Hough space. A poin (ρ, θ) in he Hough space corresponds o he accumulaor cell A ij wih i = ρ/ ρ and j = (θ θ min )/ θ. The following oulines he RHT o exrac line segmens from he se P : While P conains a leas N 0 poins and he maximum number of rials has no been reached: 1) Rese he accumulaor cells A ij o 0. 2) While he accumulaor array A does no have a global maximum ha exceeds a hreshold τ (e.g. 100) a) Pick wo poins p a and p b randomly from P. b) Solve he line parameers (ρ, θ) from he line equaion wih poins p a and p b. c) Incremen he accumulaor cell A ij corresponding o (ρ, θ) by 1. 3) Le (ˆρ, ˆθ) be he line deermined by he locaion of he maximum in A. 4) Le Q be he se of poins in P ha are close o he line (ˆρ, ˆθ). 5) If Q conains a leas N 0 poins, use Q and (ˆρ, ˆθ) o exrac line segmens. 6) Remove from P poins in Q used o generae segmens. Prior o exracing line segmens in Sep 5 above, we apply he orhogonaliy assumpion and proceed wih he line segmen exracion only if he line (ˆρ, ˆθ) is close o being horizonal or verical. This is done by esing wheher ˆθ is wihin a cerain hreshold ǫ θ = 5 from 90 or 90 for horizonal line and 180, 0, or 180 for verical line. If so, we hen se ˆθ o be one of { 180, 90, 0, 90 } accordingly and updae ˆρ so as o bes fi he poins in Q in he leas-square sense. We denoe he line resuling from applying he orhogonaliy assumpion as (ˆρ, ˆθ ). Given (ˆρ, ˆθ ), we projec he poins in Q ono he line (ˆρ, ˆθ ). Le R = {p 1, p 2,...} be he se of projeced poins arranged sequenially saring from one of he exreme endpoins. We hen sequenially pariion R ino subses S h, h = 1, 2,..., wih each S h represening he se of poins belonging o a line segmen. We break he line ino segmens if here is a gap greaher han a hreshold L sep = 500mm. Afer pariioning R ino subses S h, h = 1, 2,..., he line segmens are easily obained as hose ha connec he exreme endpoins in each S h. To increase he reliabiliy of he line segmen exracion phase, only hose line segmens ha are made up of a leas N 0 = 8 poins and wih lengh a leas L min = 200mm are incorporaed ino he map. B. Line Merging and Map Managemen When incorporaing a line segmen ino he map, we firs es wheher i can be merged wih he line segmens of he same ype already in he map. Two line segmens can be merged if hey overlap and he perpendicular disance beween hem is less han or equal o L dis (300mm); or Overlapping and Non overlapping Lines disance of separaion perpendicular disance perpendicular disance Fig. 2. The perpendicular disance and disance of separaion beween overlapping and non-overlapping horizonal lines. hey do no overlap bu he perpendicular disance beween hem is less han or equal o L dis and heir disance of separaion is less han or equal o L sep. Fig. 2 illusraes he perpendicular disance and disance of separaion beween overlapping and non-overlapping horizonal lines. A similar inerpreaion exiss for verical lines. To merge wo line segmens, we firs compue he posiion (i.e. he ρ-value) of he resuling line segmen. The posiion of he resuling line segmen is he sum of he posiions of he given line segmens, weighed by heir respecive number of poins. We hen projec he endpoins of he given line segmens ono he resuling line and he wo projecions ha are farhes apar define he endpoins of he resuling line segmen. The number of poins of he resuling line segmen is jus he sum of he number of poins of he given line segmens. If a line segmen canno be merged wih he line segmens already in he map, i is simply added o he map. Afer incorporaing he line segmens ino he map, we coninue o merge segmens ha mee our crieria unil no furher mergings are possible. This sep can have he desirable effec of inegraing wo disinc line segmens represening he same environmenal feaure ino one (e.g. a long srech of wall occassionally occluded by dynamic obsacles or relaively small and insignifican objecs). V. EXPERIMENTAL RESULTS We have implemened our SLAM approach for sonars and esed i on he AcivMedia roboics P3-DX mobile robo plaform. The robo is equipped wih a fron sonar array wih eigh sensors, one on each side and six facing forward a 20 inervals. I also has a rear sonar array wih eigh sensors, one on each side and six facing backward a 20 inervals. Therefore, a single sonar scan yields a oal of 16 sonar measuremens. Of he 16 sonar measuremens in a single scan, only a small fracion acually corresponds o correc measuremens while he res are unreliable due o angular uncerainy (20 o 30 for sonars), specular and muliple reflecions, crossalk, ec. This is in sark conras o ypical laser rangefinders ha produce accurae (wih a saisical error of 5mm in range measuremen and angular beam widh of 1 for each beam) and dense measuremens (e.g. 180 or 360 measuremens in each scan) and are no affeced by problems such as specular reflecions and crossalk. As such, SLAM wih sonars is much more difficul and challenging han SLAM wih laser rangefinders. Despie he shorcomings of sonars, our experimenal resuls show ha i is possible o produce good qualiy maps of large indoor environmens wih large loops using sonars.

6 In our experimens, he robo is conrolled by an IBM ThinkPad X32 noebook compuer and navigaed around differen environmens by visiing predefined waypoins while collecing conrol and sensor daa along he way. We considered hree es environmens of increasing sizes and complexiies. The firs es environmen is a makeshif environmen ha represens a scaled-down version of a ypical office environmen. The associaed map of he environmen has an approximae size of 6.7m 6.7m. I is mosly made up of smooh cardboard walls. The second es environmen is a porion of he faculy suie on he hird floor of our Engineering Building II. I is bigger han he firs wih an approximae map size of 38.6m 12.7m and conains wo major loops. Finally, he hird es environmen is he enire hallway of he hird floor of our Engineering Building II, including he wo bridges connecing o he old engineering building. I is he bigges environmen in our experimens wih a map size of approximaely 70.0m 53.7m and conains wo major loops. The hird es environmen is made up of various ypes of obsacles such as brick walls, iled walls, cable railing, glass windows, rash bins, ec. Unlike he firs wo es environmens, he hird es environmen is dynamic wih people walking along he corridors during he experimens. Fig. 3 (cols. 1 and 2) shows he hree es environmens and heir associaed maps while Table I provides summary informaion abou our experimens. To show he effeciveness of our SLAM approach using sonars o compensae for odomeric errors, we show in Fig. 3 (col. 2) he rajecory from he raw encoder readings (broken lines) agains he desired pah of he robo (solid lines) for all hree es environmens. I is eviden from Fig. 3 (col. 2) ha he robo s odomery suffers from drif ha ges more pronounced in larger environmens. Therefore, relying only on he robo s odomery for performing SLAM is no sufficien and sonar measuremens aken mus be used for correcing he robo s pose. Fig. 3 (col. 3) shows he resuling maps and robo rajecories wih our approach for he hree es environmens. Alhough he generaed maps are no exacly he same as he rue maps, hey do capure he main srucure of he environmens. Addiionally, our approach managed o close he loops properly in all es environmens which is generally considered a difficul problem in SLAM. Lines in our maps correspond o acual major obsacles such as walls, glass windows, doors, cable railings, as well as o some minor ones such as rash bins and poss. Because of he Hough ransform, our line exracion procedure is quie robus o noise caused by specular and muliple reflecions and phanom readings. Also, since we only consider horizonal and verical lines, our line exracion procedure is effecive a filering ou dynamic objecs paricularly for he hird es environmen. We also performed experimens wihou using he orhogonaliy assumpion and he final maps and robo rajecories are shown in Fig. 3 (col. 4). Wihou he orhogonaliy assumpion, he resuling maps and robo rajecories are no properly esimaed and correced. Finally, we also implemened a RBPF using gridmaps for SLAM based on map maching [19] and he resuling maps for all hree es environmens are also shown in Fig. 3 (col. 5). Noe ha we used he same se of parameer values for generaing he resuls for all hree es environmens wih our approach (excep for he number of paricles N) while we had o use differen ses of parameer values o generae he resuling gridmaps shown in Fig. 3 (col. 5) using RBPF wih map maching. We can easily see he effec of daa smearing when using a cell-based approach o SLAM; measuremens are ofen blurred ono a region of he map o accoun for angular and disance uncerainy. VI. CONCLUSIONS SLAM has received considerable aenion in he mobile roboics communiy for he las wo decades. However, much of he research effor for SLAM has focused on he use of highly accurae and dense measuremens provided by laser rangefinders o correcly localize he robo and produce accurae and deailed maps of complex environmens. In his paper, we presened an approach o SLAM for a mobile robo equipped wih low-cos bu noisy and sparse sonar sensors navigaing in large indoor environmens involving large loops. The proposed approach applies paricle filering where each paricle is an esimae of he recen robo poses and carries a map of he environmen represened as a se of line segmens. To overcome he sparseness of sonars and o allow for he reliable exracion of line segmen feaures from he environmen, we used he muliscan approach and grouped consecuive sparse scans ino muliscans. To reduce he complexiy of SLAM paricularly when sonars are used, we applied he orhogonaliy assumpion abou he shape of he environmen by mapping only lines ha are parallel or perpendicular o each oher. The orhogonaliy assumpion is reasonable especially for mos man-made indoor environmens where major srucures such as walls, windows, and doors are eiher parallel or perpendicular o each oher. The randomized Hough ransform was used o exrac line segmens from muliscans and was quie robus o noise caused by specular and muliple reflecions and phanom readings, problems usually associaed wih sonars. Despie he inheren limiaions of sonars, resuls of empirical validaion, carried ou using a real mobile robo plaform navigaing in differen environmens of increasing sizes and complexiies, provide supporive evidence for he poenial viabiliy of sonars for complex large-scale indoor SLAM. REFERENCES [1] R. C. Smih and P. Cheeseman, On he represenaion and esimaion of spaial uncerainy, IJRR, vol. 5, no. 4, pp , [2] E. Brunskill and N. Roy, SLAM using incremenal probabilisic PCA and dimensionaliy reducion, in Proc. IEEE ICRA 05, Apr. 2005, pp [3] A. Eliazar and R. 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7 TABLE I E XPERIMENTS SUMMARY Map Size Daa Collecion Time Disance Traveled Toal Time Seps T Number of Sonar Measuremens (excluding smax ) Average Number of Sonar Measuremens per Time Sep (excluding smax ) Number of Paricles Used N Tes Environmen 1 6.7m 6.7m 5 minues 26.7m 545 5, Tes Environmen m 12.7m 9 minues 85.7m 727 7, Tes Environmen m 53.7m 30 minues 283.5m 1, , Fig. 3. The hree es environmens (col. 1) and heir associaed maps (col. 2). Col. 2 also shows he pahs of he robo (solid lines) and he rajecory esimaes based from encoder readings (broken lines). The esimaed maps and robo rajecories wih our approach (col. 3). Maps and robo rajecories esimaed wihou using he orhogonaliy assumpion (col. 4). Maps and robo rajecories esimaed using a RBPF using grid maps (col. 5). For he grid maps, dark regions indicae high level of occupancy, whie regions indicae low level of occupancy, and gray regions represen unexplored areas. [6] A. Garulli, A. Giannirapani, A. Rossi, and A. Vicino, Mobile robo SLAM for line-based environmen represenaion, in Proc. 44h IEEE CDC-ECC 05, Dec. 2005, pp [7] G. Grisei, C. Sachniss, and W. Burgard, Improving grid-based SLAM wih Rao-Blackwellised paricle filers by adapive proposals and selecive resampling, in Proc. IEEE ICRA 05, Apr. 2005, pp [8] D. Ha hnel, W. Burgard, D. Fox, and S. Thrun, An efficien FasSLAM algorihm for generaing maps of large-scale cyclic environmens from raw laser range measuremens, in Proc. IEEE/RSJ IROS 03, Oc. 2003, pp [9] M. Monemerlo, S. Thrun, D. Koller, and B. Wegbrei, FasSLAM: A facored soluion o he simulaneous localizaion and mapping problem, in Proc. 18h AAAI 02, July Aug. 2002, pp [10] M. Monemerlo and S. Thrun, Simulaneous localizaion and mapping wih unknown daa associaion using FasSLAM, in Proc. IEEE ICRA 03, vol. 2, Sep. 2003, pp [11] V. Nguyen, A. Harai, A. Marinelli, R. Siegwar, and N. Tomais, Orhogonal SLAM: a sep oward lighweigh indoor auonomous navigaion, in Proc. IEEE/RSJ IROS 06, Oc [12] K. R. Beevers and W. H. Huang, SLAM wih sparse sensing, in Proc. IEEE ICRA 06, May 2006, pp [13] G. Zunino and H. I. Chrisensen, Navigaion in realisic environmens, in Proc. 9h SIRS 01, July 2001, pp [14] J. D. Tardo s, J. Neira, P. M. Newman, and J. J. Leonard, Robus mapping and localizaion in indoor environmens using sonar daa, IJRR, vol. 21, no. 4, pp , Apr [15] R. O. Duda and P. E. Har, Use of he Hough ransformaion o deec [16] [17] [18] [19] [20] [21] [22] [23] [24] lines and curves in picures, Comm. ACM, vol. 15, no. 1, pp , Jan J. J. Leonard, R. J. Rikoski, P. M. Newman, and M. Bosse, Mapping parially observable feaures from muliple uncerain vanage poins, IJRR, vol. 21, no , pp , Oc. Nov W. D. Rencken, Concurren localisaion and map building for mobile robos using ulrasonic sensors, in Proc. IEEE/RSJ IROS 93, July 1993, pp J. M. P. Lorenzo, R. Va zquez-marı n, P. Nu n ez, E. J. Pe rez, and F. Sandoval, A Hough-based mehod for concurren mapping and localizaion in indoor environmens, in Proc. IEEE RAM 04, Dec. 2004, pp C. Schro er, H.-J. Bo hme, and H.-M. Gross, Memory-efficien gridmaps in Rao-Blackwellized paricle filers for SLAM using sonar range sensors, in Proc. 3rd ECMR 07, Sep K. P. Murphy, Bayesian map learning in dynamic environmens, in NIPS 12, 2000, pp F. Abrae, B. Bona, and M. Indri, Experimenal EKF-based SLAM for mini-rovers wih IR sensors only, in Proc. 3rd ECMR 07, Sep Y.-H. Choi, T.-K. Lee, and S.-Y. Oh, A line feaure based SLAM wih low grade range sensors using geomeric consrains and acive exploraion for mobile robo, Auon. Robo., vol. 24, no. 1, pp , N. Roy and S. Thrun, Online self-calibraion for mobile robos, in Proc. IEEE ICRA 99, May 1999, pp P. Kulanen, L. Xu, and E. Oja, Randomized Hough ransform (RHT), in Proc. 10h ICPR 90, vol. 1, June 1990, pp