Exploration with Active Loop-Closing for FastSLAM

Transcription

1 Exploraion wih Acive Loop-Closing for FasSLAM Cyrill Sachniss Dirk Hähnel Wolfram Burgard Universiy of Freiburg Deparmen of Compuer Science D Freiburg, Germany Absrac Acquiring models of he environmen belongs o he fundamenal asks of mobile robos. In he las few years several researchers have focused on he problem of simulaneous localizaion and mapping (SLAM). Classic SLAM approaches are passive in he sense ha hey only process he perceived sensor daa and do no influence he moion of he mobile robo. In his paper we presen a novel and inegraed approach ha combines auonomous exploraion wih simulaneous localizaion and mapping. Our mehod uses a grid-based version of he FasSLAM algorihm and a each poin in ime considers acions o acively close loops during exploraion. By re-enering already visied areas he robo reduces is localizaion error and his way learns more accurae maps. Experimenal resuls presened in his paper illusrae he advanage of our mehod over pervious approaches lacking he abiliy o acively close loops. I. INTRODUCTION In general, he ask of acquiring models of unknown environmens requires soluions o hree sub-asks, which are mapping, localizaion and conrol. Mapping is he problem of inegraing he informaion gahered wih he robo s sensors ino a given represenaion. Localizaion is he problem of esimaing he posiion of he robo. Finally, he conrol problem involves he quesion of how o seer a vehicle in order o efficienly guide i o a desired locaion. A naive approach o realize an inegraed echnique, which solves all hree asks simulaneously, could be o combine a SLAM algorihm wih an exploraion procedure. Since exploraion sraegies ry o explore unknown errain as fas as possible, hey focus on reducing he amoun of unseen area and hus avoid repeaedly raveling hrough known areas. This sraegy, however, is subopimal in he conex of he SLAM problem, because he robo ypically needs o re-visi places o localize iself again. A good pose esimaion is necessary o make he correc daa associaion, i.e., o deermine if he curren measuremens fi ino he map buil so far. If he robo uses an exploraion sraegy ha avoids muliple visis of he same place, he probabiliy of making he correc associaions is reduced. This indicaes ha combinaions of exploraion sraegies and SLAM algorihms should consider wheher i is worh re-enering already covered spaces or o explore new errain. I can be expeced ha a sysem which akes his decision ino accoun can improve he qualiy of he resuling map. Figure 1 gives an example ha illusraes why an inegraed approach doing acive place re-visiing provides beer resuls han approaches ha do no consider re-enering known errain during he exploraion phase. In he siuaion sar sar Fig. 1. This figure shows wo maps obained by a real world experimen performed a Sieg Hall, Universiy of Washingon. The op image depics an experimen in which he robo drove around he loop once and hen enered he long corridor. As can be seen robo was unable o localize iself correcly before enering he corridor. This leaded o a big error in he orienaion of he horizonal corridor. If he robo did acive loopclosing and re-visied he loop i ypically performed much beer (boom image). shown in he upper image he robo raversed he loop jus once. The robo was no able o correcly deermine he angle beween he loop and he sraigh corridor, because i did no collec enough daa o accuraely localize iself. The second map shown in he lower image has been obained wih he approach described in his paper afer he robo raveled wice around he loop before enering he corridor. As can be seen from he figure, his reduces he orienaion error from approximaely 7 degrees (op image) o 1 degree (boom image). This example illusraes ha he capabiliy o acively close loops during exploraion allows he robo o reduce is pose uncerainy during exploraion and hus o learn more accurae maps. The conribuion of his paper is an inegraed algorihm for generaing rajecories o acively close loops during SLAM. Our algorihm uses a grid-based version of he FasSLAM algorihm and expliciely akes ino accoun he uncerainy abou he pose of he robo during he exploraion ask. Addiionally i avoids ha he robo becomes overly confiden in is pose when acively closing loops which is a ypical problem of paricle filers in his conex. As a resul we obain more accurae maps compared o combinaions of SLAM wih greedy exploraion. This paper is organized as follows. Afer he discussion of relaed work in he following secion, we explain he idea of grid-based FasSLAM, he SLAM algorihm used hroughou his work. In Secion IV we presen our inegraed exploraion echnique. We furhermore describe

2 how o ake ino accoun he pose uncerainy and how o acively close loops. Secion V hen presens experimens carried ou on real robos as well as in simulaion. II. RELATED WORK This paper presens an inegraed echnique o simulaneous localizaion, mapping, and exploraion. Several previous approaches o SLAM and mobile robo exploraion are relevan. In he conex of exploraion, mos of he echniques presened so far focus on generaing moion commands ha minimize he ime needed o cover he whole errain [1], [9], [17], [18]. Oher mehods seek o opimize he view-poins of he robo o maximize he expeced informaion gain and o minimize he uncerainy of he robo abou grid cells [6], [14]. Mos of hese echniques, however, assume ha he locaion of he robo is known during exploraion. In he area of SLAM he vas majoriy of papers focuses on he aspec of sae esimaion as well as belief represenaion and updae [2], [3], [4], [7], [8], [11], [12], [15]. These echniques, however, are passive and only consume incoming sensor daa wihou expliciely generaing conrols. Recenly, some echniques have been proposed which acively conrol he robo during simulaneous mapping and localizaion. For example, Makarenko e al. [10] exrac landmarks ou of laser range scans and use an Exended Kalman Filer o solve he SLAM problem. They furhermore inroduce a uiliy funcion which rades-off he cos of reaching froniers wih he uiliy of seleced posiions wih respec o a poenial reducion of he pose uncerainy. This approach is similar o he work done by Feder e al. [5] who consider local decisions o improve he pose esimae during mapping. Boh echniques, however, rely on he fac ha he environmen conains landmarks ha can be uniquely deermined during mapping. In conras o his, he approach presened in his paper makes no assumpions abou disinguishable landmarks in he environmen. I uses raw laser range scans o compue accurae grid maps. I considers he uiliy of re-enering known pars of he environmen and following an encounered loop o reduce he uncerainy of he robo in is pose. This way he resuling maps become highly accurae. III. GRID-BASED FASTSLAM To esimae he map of he environmen we use a highly efficien varian of he FasSLAM algorihm [11] which iself is an exension of he Rao-Blackwellized paricle filer for simulaneous localizaion and mapping proposed by Murphy e al. [3]. The key idea of he Rao-Blackwellized paricle filer for SLAM is o esimae a poserior p(x 1: z 1:, u 0: 1 ) abou poenial rajecories x 1: of he robo given is observaions z 1: and is odomery measuremens u 0: 1 and o use his poserior o compue a poserior over maps and rajecories: p(x 1:, m z 1:, u 0: 1 ) = p(m x 1:, z 1: )p(x 1: z 1:, u 0: 1 ). (1) This can be done efficienly, since he quaniy p(m x 1:, z 1:, u 0: 1 ) can be compued analyically once x 1: and z 1: are known. To esimae he poserior p(x 1: z 1:, u 0: 1 ) over he poenial rajecories FasSLAM uses a paricle filer in which an individual map is associaed o every sample. Each map is consruced given he observaions z 1: and he rajecory x 1: represened by he corresponding paricle. During resampling, he weigh ω of each paricle is proporional o he likelihood p(z m, x ) of he mos recen observaion given he map m associaed o his paricle and he pose x of he corresponding rajecory. The FasSLAM algorihm used hroughou his paper compues grid maps. I applies a scan-maching procedure o compue highly accurae odomery daa and uses his correced odomery in he predicion sep of he paricle filer [8]. This way he number of paricles can be reduced so ha maps of even large environmens can be consruced online. In he following secion we describe how he FasSLAM algorihm for grid maps can be exended o acively close loops during exploraion. IV. EXPLORATION WITH ACTIVE LOOP-CLOSING FOR FASTSLAM During FasSLAM, whenever he robo explores new errain, all samples have more or less he same imporance weigh, since he mos recen measuremen is ypically consisen wih he par of he map consruced from he immediaely preceding observaions. As a resul, he uncerainy of he paricle filer increases. As soon as i reeners known errain, however, he maps of some paricles are consisen wih he curren measuremen and some are no. Accordingly he weighs of he samples differ largely. Due o he resampling sep he uncerainy abou he pose of he robo usually decreases. Noe ha his effec is much smaller if he robo jus moves backward a few meers o re-visi previously scanned areas. This is because each map associaed o a paricle is generally locally consisen. Inconsisencies mosly arise when he robo re-eners areas explored some ime ago. Therefore, visiing places seen furher back in he hisory has a sronger effec on he differences beween he imporance weighs and ypically also on he reducion of uncerainy compared o places recenly observed. The key idea of our approach is o idenify opporuniies for closing loops during errain acquisiion. Here closing a loop means acively re-enering he known errain and following a previously raversed pah. To deermine, wheher here exiss a possibiliy o close a loop we consider wo differen represenaions of he environmen. In our curren sysem we associae o each paricle s an occupancy grid map m [s] and a opological map G [s] which boh are updaed while he robo is performing he exploraion ask. In he opological map G [s] he verices represen posiions visied by he robo. The edges represen he rajecory corresponding o he paricle s. To consruc he opological map we iniialize i wih one node corresponding o he saring locaion of he robo. Le x [s] be he pose of paricle

3 x [s] I(s) x [s] x [s] Fig. 2. The red dos and lines in hese hree image represen he nodes and edges of G [s]. In he lef image I(s) conained wo nodes and in he middle image he robo closed he loop unil he pose uncerainy is reduced. Afer his i coninued wih he acquisiion of unknown errain (righ image). s a he curren ime sep. We add a new node a x [s] o G [s] if he disance beween x [s] and all oher nodes in G [s] exceeds a hreshold of c = 2.5m or if none of he oher nodes in G [s] is visible from x [s] : [ n nodes(g [s] ) : dis m [s](x [s], n) > c no visible m [s](x [s], n) ]. (2) Whenever a new node is added, we also add an edge from his node o he mos recenly visied node. To deermine wheher or no a node is visible from anoher node we perform a ray-casing operaion in he occupancy grid m [s]. Figure 2 depics such a graph for one paricular paricle during differen phases of an exploraion ask. In each image, he opological map G [s] is prined on op of meric map m [s]. To moivae he idea of our approach we would like o refer he reader o he lef image of his figure. Here he robo was almos closing a loop. This can be deeced by he fac ha he lengh of he shores pah beween he curren pose of he robo and previously visied locaions in he opological map G [s] was large, where as i was small in he grid-map m [s]. Thus, o deermine wheher or no a loop can be closed we compue for each sample s he se I(s) of posiions of ineres, which conains all nodes ha are close o curren pose x [s] of paricle s based on he grid map m [s] bu are far away given he opological map G [s] of s: I(s) = {x [s] nodes(g[s] ) dis m [s](x [s], x[s] ) < c 1 dis G [s](x [s], x[s] ) > c 2 }.(3) Here dis M (x 1, x 2 ) is he lengh of he shores pah from x 1 o x 2 given he represenaion M. The disance beween wo nodes in G [s] is given by he lengh of he shores pah beween boh nodes, whereas he lengh of a pah is compued by he sum over he lenghs of he raversed edges. The erms c 1 and c 2 are consans ha mus saisfy he consrain c 1 < c 2. In our curren implemenaion he values of hese consans are c 1 = 6m and c 2 = 20m. If I(s) here exis so-called shorcus from x [s] o he posiions in I(s). These shorcus represen edges ha would close a loop in he opological map G [s]. The lef image of Figure 2 illusraes a siuaion in which a robo encouners he opporuniy o close a loop since I(s) conains wo nodes. The key idea of our approach is o use such shorcus whenever he uncerainy of he robo in is Fig. 3. The paricle depleion problem: a robo raveled hrough he inner loop several imes (lef image). Afer his he diversiy of hypoheses abou he rajecory ouside he inner loop had decreased oo much (middle image) and he robo is unable o close he ouer loop correcly (righ image). pose becomes oo large. The robo hen re-visis porions of he previously explored area and his way reduces he uncerainy in is posiion. To deermine he mos likely movemen allowing he robo o follow a previous pah of a loop, one in principle has o inegrae over all paricles and consider all poenial oucomes of ha paricular acion. Since his would be oo ime consuming for online-processing we consider only he paricle s wih he highes accumulaed imporance weigh: s = argmax s i=1 log ω [s] i. (4) Here ω [s] i is he weigh of sample s a ime sep i. If I(s ) we choose he node x e from I(s ) which is closes o x [s ] : x e = argmin dis m [s ](x [s ], x). (5) x I(s ) In he sequel x e is denoed as he enry poin a which he robo has he possibiliy o close a loop. e corresponds o he las ime he robo was a he node x e. To deermine wheher or no he robo should acivae he loop-closing behavior our sysem consanly moniors he uncerainy H() abou he robo s pose a he curren ime sep. The necessary condiion for saring he loopclosing process is he exisence of an enry poin x e and ha H() exceeds a given hreshold. Once he loop-closing process has been acivaed, he robo approaches x e and hen follows he pah aken afer arriving previously a x e. During his process he uncerainy in he pose of he vehicle ypically decreases, because he robo is able o localize iself in he map buil so far and unlikely paricles vanish. We furhermore have o define a crierion for deciding when he robo acually has o sop following a loop. A firs aemp could be o inroduce a hreshold and o simply sop he rajecory following behavior as soon as he uncerainy becomes smaller han a given hreshold. This crierion, however, can be problemaic especially in he case of nesed loops. Suppose he robo encouners he opporuniy o close a loop ha is nesed wihin an ouer and so far unclosed loop. If i eliminaes all of is uncerainy by repeaedly raversing he inner loop, paricles necessary o close he ouer loop may vanish. As a resul, he filer diverges and he robo fails o build

4 Algorihm 1 The loop-closing algorihm Compue I(s ) if I(s ) hen begin H H( e ) pah x [s ] shores pah G [s ](x e, x [s ] ) while H() > H H() > hreshold do robo follow(pah) end a correc map (see Figure 3). To remedy his so-called paricle depleion problem [16] we inroduce a consrain on he uncerainy of he robo. Le H( e ) denoe he uncerainy of he poserior when he robo visied he enry poin las ime. Then he new consrain allows he robo o re-raverse he loop only as long as is curren uncerainy H() exceeds H( e ). If he consrain is violaed he robo resumes is fronier-based exploraion process. The idea of his consrain is o avoid he depleion of relevan paricles during he loop-closing process. To beer illusrae he imporance of his consrain consider he following example: a robo moves from place A o place B and hen repeaedly observes B. While i is mapping B i does no ge any furher informaion abou A. Since each paricle represens a whole rajecory of he robo also hypoheses represening ambiguiies abou A will vanish when reducing poenial uncerainies abou B. Our consrain avoids he depleion of paricles represening ambiguiies abou A by aboring he loop-closing behavior a B as soon as he uncerainy drops below he uncerainy semming from A. Finally we have o describe how we acually measure he uncerainy in he posiion esimae. The ypical way of measuring he uncerainy of a poserior is o calculae he enropy. In he case of muli-modal disribuions, however, he enropy does no consider he disance beween he differen modes. In our experimens we figured ou ha we obain beer resuls if we use he volume expanded by he samples insead of he enropy of he poserior. We herefore calculae he pose uncerainy by deermining he volume of he oriened bounding box around he paricle cloud. A good approximaion of he minimal oriened bounding box can be obained efficienly by a principal componen analysis. As long as he robo is localized well enough or no loop can be closed, we use a fronier-based exploraion sraegy [1] o choose arge poins for he robo. In our curren sysem we deermine froniers based on he map of he mos likely paricle s. Here a fronier is any known cell ha is an immediae neighbor of an unknown, unexplored cell [18]. A precise formulaion of he loop-closing sraegy is given by Algorihm 1. In our implemenaion his algorihm runs as a background process ha is able inerrup he fronier-based exploraion procedure. An applicaion of his algorihm in a simulaion run is illusraed in Figure 2. A. Handling Muliple Nesed Loops Noe ha our loop-closing echnique can also handle muliple nesed loops. During he loop-closing process he sar Fig. 4. Acive loop-closing of muliple nesed loops. robo follows is previously aken rajecory o re-localize. I does no leave his rajecory unil he erminaion crierion, described in previous secion, is fulfilled. Therefore i never sars a new loop-closing process before he curren one is compleed. A ypical example wih muliple nesed loops is shown in Figure 4. In he siuaion depiced in he lef image he robo sars wih he loop-closing process for he inner loop. Afer compleing his loop i moves o he second inner one and again sars he loop-closing process. Since our algorihm considers he uncerainy a he enry poin i keeps enough variance in he filer o close he ouer loop. In general, he qualiy of he soluion and wheher or no he overall process succeeds depends on he number of paricles used. Since deermining his quaniy is an open research problem he number of paricles has o be defined by he user in our curren sysem. V. EXPERIMENTS Our approach has been implemened and evaluaed in a series of real world and simulaion experimens. For he real world experimens we used an irobo B21r robo and an AcivMedia Pioneer II robo. Boh are equipped wih a SICK laser range finder. For he simulaion experimens we used he real-ime simulaor of he Carnegie Mellon Robo Navigaion Toolki [13]. This simulaor generaes realisic noise in he odomery and laser range sensor daa. The experimens described in his secion are designed o illusrae ha our approach can be used o acively learn accurae maps of large indoor environmens. Furhermore, hey demonsrae ha our inegraed approach yields beer resuls han an approach wihou acive loop-closing. Addiionally, we analyze how he acive erminaion of he loop-closure influences he resul of he mapping process. A. Real World Exploraion The firs experimen was carried ou o illusrae ha our curren sysem can effecively conrol a mobile robo o acively close loops during exploraion. To perform his experimen we used a Pioneer II robo o explore he main lobby of he Deparmen for Compuer Science a he Universiy of Freiburg. The size of his environmen is 51m imes 18m. Figure 5 depics he final resul obained by a compleely auonomous exploraion run using our acive loop-closing echnique. I also depics he rajecory of he robo, which has an overall lengh of 280m. The robo decided four imes o re-ener a previously visied loop in order o reduce he uncerainy in is pose. Figure 5 also shows he corresponding enry poins as well as he posiions where he robo lef he loops ( exi poins ). In his experimen he FasSLAM rouine used 250 paricles. As can be seen he resuling map is quie accurae.

5 Fig. 5. This image shows he resuling map of an exploraion experimen carried ou using a Pioneer II robo equipped wih a laser range scanner in he enrance hall of he Deparmen for Compuer Science a he Universiy of Freiburg. Also shown is he pah of he robo as well as enry and exi poins where he robo sared and sopped he acive loopclosing process. Fig. 6. This figure depics an environmen wih wo large loops. The ouer loop has a lengh of over 220m. The lef image show he resuling map of a rajecory in which he robo drove hrough he loops only once. In he second run he robo visied every loop wice and obained a highly accurae map (see righ image). B. Acive Loop-Closing vs. Fronier-Based Exploraion The second experimen was carried ou o compare our algorihm wih a sandard exploraion sraegy ha does no consider loop closing acions. The lower image of Figure 1 shows he map obained wih a B21r robo in he Sieg Hall a he Universiy of Washingon using our algorihm. To eliminae he influence of measuremen noise and differen movemens of he robo we removed he daa corresponding o he second loop raversal from he recorded daa file and used his daa as inpu o our FasSLAM algorihm. This way we simulaed he behavior of a greedy exploraion sraegy which forces he robo o direcly ener he corridor afer reurning o he saring locaion in he loop. As can be seen from he upper image of Figure 1, an approach ha does no acively re-ener he loop fails o correcly esimae he angle beween he loop and he corridor which should be oriened horizonally in ha figure. Whereas he angular error is 7 degrees wih he sandard approach i is only 1 degree wih our mehod. Boh maps correspond o he paricle wih he highes accumulaed imporance facor. A furher experimen ha illusraes he advanage of place re-visiing is shown in Figure 6. The environmen used in his simulaion run is 80m imes 80m and conains wo large nesed loops wih nearly feaureless corridors. The lef image shows he resul of he fronier-based approach which raversed each loop only once. Since he robo is no able o correc he accumulaed pose error, he resuling map conains large inconsisencies and wo of he corridors are mapped ono each oher. Our approach, avg. error in posiion [m] loop-closing froniers Fig. 7. This figure compares our loop-closing sraegy wih a pure fronier-based exploraion echnique. The lef bar in his graph plos he average error in he pose of he robo obained wih our loop-closing sraegy. The righ one shows he average error if a fronier-based approach was used. As can be seen our echnique significanly reduces he disances beween he esimaed posiions and he ground ruh (confidence inervals do no overlap). in conras, firs revisis he ouer loop before enering he inner one (see righ image). Accordingly, he resuling map is quie accurae. C. A Quaniaive Analysis To quaniaively evaluae he advanage of he loopclosing behavior we performed a series of simulaion experimens in an environmen similar o he Sieg Hall. We performed 20 experimens, 10 wih acive loop-closing and 10 wihou. Afer compleing he exploraion ask we measured he average error in he relaive disances beween posiions lying on he resuling esimaed rajecory and he ground ruh provided by he simulaor. The resuls are depiced in Figure 7. As can be seen he acive loop-closing behavior significanly reduces he error in he posiion of he robo. D. Imporance of he Terminaion Crierion In his final experimen we analyze he imporance of he consrain ha erminaes he acive loop-closing behavior as soon as he curren uncerainy H() of he belief drops under he uncerainy H( e ) of he poserior when he robo was a he enry poin las ime. In his simulaed experimen he robo had o explore an environmen conaining wo nesed loops (see Figure 8 (d)). In one case we simply used a consan hreshold o deermine wheher or no he loop-closing behavior should be sopped. In he second case we applied he addiional consrain ha he uncerainy should no become smaller han H( e ). Figure 3 shows he map of he paricle wih he highes accumulaed imporance weigh obained wih our algorihm using a consan hreshold insead of considering H( e ). In his case he robo repeaedly raversed he inner loop (lef image) unil is uncerainy was reduced below a hreshold. Afer hree and a half rounds i decided o again explore unknown errain, bu he diversiy of hypoheses had decreased oo much (middle image). Accordingly he robo was unable o accuraely close he ouer loop (righ image). We repeaed his experimen several imes and in no case he robo was able o correcly map he environmen. In conras o ha, our approach using he addiional consrain always generaed an accurae map. One example run is shown in Figure 8. Here he robo

6 (a) (b) wihou a complee re-run of he whole algorihm. Such issues are subjec of fuure research. ACKNOWLEDGMENT This work has parly been suppored by he German Science Foundaion (DFG) under conrac number SFB/TR- 8 (A3) and by he EC under conrac number IST The auhors would like o hank all people who are involved in he developmen of CARMEN, especially Nicholas Roy. Furhermore we would like o hank Luis Monesano for he fruiful discussions and help during he real world experimens. (c) Fig. 8. These images depic snapshos of our loop-closing sraegy. The robo explored he errain and deeced an opporuniy o close a loop in order o reduce is uncerainy (a). I hen raversed pars of he inner loop unil is uncerainy H() did no exceed he uncerainy H( e) of he poserior when he robo a he enry poin anymore. I hen urned back and lef he loop o explore new errain (b). Afer his, enough hypoheses are lef o correcly close he ouer loop (c) and (d). In conras o ha, a sysem considering only a consan hreshold crierion fails o map he environmen correcly as depiced in Figure 3. sopped he loop-closing afer raversing half of he inner loop. In boh cases we used 80 paricles. As his experimen illusraes, he erminaion of he loop-closing is imporan for he convergence of he filer and o obain accurae maps in environmens wih several (nesed) loops. Noe ha similar resuls in principle can also be obained wihou his erminaion consrain if he number of paricles is dramaically increased. Since exploraion is an online problem and since every paricle carries is own map i is of umos imporance o keep he number of paricles as small as possible. Therefore our approach also can be regarded as a conribuion o limi he number of paricles during FasSLAM. (d) VI. CONCLUSION In his paper we presened a novel approach for acive loop-closing during auonomous exploraion. We combined a Rao-Blackwellized paricle filer for localizaion and mapping wih a fronier-based exploraion echnique exended by he abiliy o acively close loops. Our algorihm forces he robo o raverse previously visied loops again and his way reduces he uncerainy in he pose esimaion. As a resul, we obain more accurae maps compared o sandard combinaions of SLAM algorihms wih exploraion echniques. One general problem of FasSLAM is ha he number of paricles needed o build an accurae map is no known in advance. Even our echnique does no provide ools o esimae his quaniy bu i produces beer maps wih a given number of paricles compared o a naive combinaion of fronier-based exploraion wih FasSLAM. The major resricions of our algorihm are similar o hose of Fas- SLAM, e.g, here are no means o recover from divergence REFERENCES [1] W. Burgard, M. Moors, D. Fox, R. Simmons, and S. Thrun. Collaboraive muli-robo exploraion. In Proc. of he IEEE In. Conf. on Roboics & Auomaion (ICRA), [2] G. Dissanayake, H. 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