Pose Uncertainty in Occupancy Grids through Monte Carlo Integration

Transcription

1 Pose Uncerainy in Occupancy Grids hrough Mone Carlo Inegraion Daniek Jouber Elecronic Sysems Lab Elecrical and Elecronic Engineering Sellenbosch Universiy, Souh Africa Willie Brink Applied Mahemaics Deparmen of Mahemaical Sciences Sellenbosch Universiy, Souh Africa Ben Herbs Applied Mahemaics Deparmen of Mahemaical Sciences Sellenbosch Universiy, Souh Africa Absrac We consider he dense mapping problem where a mobile robo mus combine range measuremens ino a consisen world-cenric map. If he range sensor is mouned on he robo, as is usually he case, some form of SLAM mus be implemened in order o esimae he robo s pose (posiion and orienaion) a every ime sep. Such esimaes are ypically characerized by uncerainy, and for safe navigaion i can be imporan for he map o reflec he exen of hose uncerainies. We presen a simple and compuaionally racable means of incorporaing he pose disribuion reurned by SLAM direcly ino an occupancy grid map. We also indicae how our mechanism for handling pose uncerainy fis naurally ino an exising adapive grid mapping algorihm, which is more memory efficien, and offer some improvemens o ha algorihm. We demonsrae he effeciveness and benefis of our approach using simulaed as well as real-world daa. I. INTRODUCTION Dense and consisen mapping of a mobile robo s environmen is vial for collision-free pah planning and safe navigaion. Measuremens obained from a range sensor mouned on he robo provide informaion on he srucure of he visible environmen, bu are relaive o he robo s unknown pose (locaion and orienaion). In order o combine hese range measuremens ino a world-cenric map, some form of simulaneous localizaion and mapping (SLAM) ha esimaes he robo s pose a every ime sep is necessary. However, since landmark measuremens and robo moion are inherenly noisy, he pose esimaes are ypically characerized by uncerainy. When building a map i is essenial o deal wih he uncerainies in pose esimaes and range measuremens in a principled manner o avoid overconfidence in he map. Occupancy grids are well-suied for he ask of mainaining uncerainy in he map as new measuremens become available over ime and his makes hem enormously popular [1]. However, occupancy grids are usually employed o solve he mapping wih known poses problem where an exac pose is available a every ime sep. In pracice, where a SLAM sysem provides he pose disribuion, he sandard approach for he dense mapping sage seems o be o ake he mos likely pose from ha disribuion [2] and discard any furher informaion on he uncerainy in such an esimae. We address his issue and propose a compuaionally racable means of incorporaing pose uncerainy ino occupancy grid maps. Effors have been made o improve pose esimaion prior o mapping, by decreasing he associaed uncerainy [3]. However, he problem of direcly incorporaing pose uncerainy ino he occupancy grid mapping process has received lile aenion. A noable excepion is he work of O Callaghan e al. [4], [5]. Gaussian processes are used o incorporae he effecs of pose uncerainy, leading o a coninuous funcional represenaion of map properies (such as occupancy) from which a grid map can be exraced. Our work differs from heirs in he sense ha we reain he simpliciy of he radiional occupancy grid paradigm and aler only he way in which cell occupancy probabiliies are updaed. Merali and Barfoo [6] also deal wih uncerainy in occupancy grid maps, by relaxing he assumpions of independence beween grid cells and independence beween measuremens aken over ime, bu hey do no specifically focus on he issue of pose uncerainy. For he purposes of his paper we shall assume ha a SLAM sysem is in place and oupus a every ime sep a disribuion describing he robo s esimaed pose. In Secion II we ouline he SLAM problem and menion wo commonly used soluions. These illusrae wo fundamenal ways of describing pose uncerainy: wih parameers of a closed-form probabiliy densiy funcion or wih a se of weighed paricles. The idea hen is o combine dense range measuremens aken over ime ino a consisen map. An esimae of he robo s pose is available, so hose measuremens can be ransformed o global map coordinaes. An occupancy grid is used o represen he map, and a brief descripion of he radiional algorihm is given in Secion III. We consider a way of modelling range measuremen uncerainy in Secion IV and address he issue of pose uncerainy in Secion V, where he occupancy grid updae equaion is alered o include weighed samples from he pose disribuion. An issue in occupancy grids ha is becoming increasingly relevan, paricularly wih he developmen of more affordable real-ime 3D scanning echnologies and he need for larger maps, is ha of high memory usage. In Secion VI we consider he adapive grid mapping mehod of Einhorn e al. [7], which selecs and updaes local resoluion based on he measuremens, and argue how i inegraes easily wih our handling of pose uncerainy.

2 We es our mehods, boh in simulaion and wih real daa, and repor on resuls in Secion VII. We find ha our inclusion of pose uncerainy does no reduce accuracy, compared o oupu from he radiional algorihm, bu raher increases informaion in he map. II. POSE UNCERTAINTY FROM SLAM Online SLAM uses conrol inpus and sensor readings o esimae a every ime sep he join poserior probabiliy of he robo s pose x and a map m. The map consruced by SLAM is ypically sparse, in he form of posiion coordinaes of salien landmarks, and no paricularly suiable for pah planning or obsacle avoidance. Dense mapping can be performed wih measuremens from addiional sensors such as laser range finders or sereo cameras. These sensors are usually mouned on he robo and, in order o combine such measuremens coherenly ino a world-cenric map, he dense mapping process mus rely on he localizaion oupu from some ype of SLAM sysem. In our mapping algorihm we incorporae he pose esimaes from SLAM and, imporanly, also consider he issue of uncerainy in hese esimaes. We proceed by firs providing a brief descripion of wo fundamenally differen forms in which SLAM may reurn his informaion. Thrun e al. [2] and Durran-Whye and Bailey [8] give more in-deph descripions of he SLAM problem in general, and he wo sysems menioned here. A. Pose uncerainy from EKF-SLAM I is quie common o assume ha he noise in boh landmark measuremens and robo moion is Gaussian, in order o employ he exended Kalman filer (EKF) for esimaing robo pose and landmark locaions. A mean sae vecor and associaed covariance marix are updaed a every ime sep and ogeher define he join poserior over he robo s pose variables (posiion and orienaion) and landmark posiions. In order o exrac he pose esimae from his join disribuion one simply marginalizes ou he landmark variables. The resuling disribuion remains Gaussian [9]. We noe ha his is an example of he case where he pose uncerainy is represened as parameers of a known closedform disribuion. B. Pose uncerainy from FasSLAM In order o circumven he someimes resricive assumpion of Gaussian noise, he FasSLAM algorihm of Monemerlo e al. [1] uilizes a Rao-Blackwellized paricle filer for is esimaion. In his formulaion he robo pose variables are represened by paricles, and herefore need no assume any paricular disribuion, while landmarks are esimaed by separae low-dimensional EKFs. A every ime sep he se of paricles (eiher before or afer he cusomary resampling sep in he paricle filer), along wih heir imporance weighs, serve as an approximaion o he pose disribuion. Such a se of weighed paricles ha approximaes a disribuion is he second fundamenal form in which he pose uncerainy can be represened. III. TRADITIONAL OCCUPANCY GRID MAPPING The occupancy grid mapping algorihm, firs inroduced by Moravec and Elfes [11], discreizes he area o be mapped ino a regular grid of cells (squares in 2D or cubes in 3D). Ulimaely, every cell mus be labelled as eiher free or occupied. However, since measuremens of he environmen can be noisy and he exac pose of he robo on which he sensor is mouned can be uncerain, a hard labelling is risky. Insead i seems more appropriae o mainain probabiliies of cells being occupied, and herein lies he power of occupancy grids. If m i is he even ha cell i is occupied, he aim is o deermine he join poserior probabiliy p(m 1:N z 1:, x 1: ). Here m 1:N denoes he inersecion of m 1, m 2,..., m N, wih N he number of cells, and z 1: and x 1: are all he range measuremens and robo poses up o ime. Compuing his join probabiliy is inracable, and a sandard remedy is o assume condiional independence beween cells [2] so ha p(m 1:N z 1:, x 1: ) = N p(m i z 1:, x 1: ). (1) i=1 Once he measuremens relaive o he robo have been ransformed o global map coordinaes we can omi he pose iself from he esimaion. Furhermore, by applying Bayes rule and assuming condiional independence beween measuremens a differen imes, we have p(m i z 1: ) = p(m i z ) p(z ) p(m i z 1: 1 ), (2) p(m i ) p(z z 1: 1 ) and, in erms of log odds raios, log p(m i z 1: ) p(m c i z 1:) = log p(m i z ) p(m c i z ) + log p(m i z 1: 1 ) p(m c i z 1: 1) log p(m i) p(m c (3) i ), where m c i denoes he complemen of m i. This expression is he sandard occupancy grid updae equaion. The log odds raio of a paricular cell a ime is found simply by adding he log odds raio arising from he new measuremen z o he log odds raio obained a he previous ime sep and subracing a prior. This prior log odds raio is se o, i.e. p(m i ) = 1 2, if no prior informaion abou he environmen is available. The firs wo erms on he righ-hand side of (3) require probabiliies of he form p(m i z). This is called he inverse sensor model, and we provide deails of ours in he nex secion. IV. MEASUREMENT UNCERTAINTY The occupancy grid algorihm assigns and mainains a probabiliy for every cell, based on measuremens capured a discree ime seps. A range measuremen consiss of one or muliple rays emanaing from he sensor, each associaed wih a disance o he firs observed obsacle along ha ray. All cells inerseced by a ray mus be updaed according o some funcion of ha measured disance, and he rules specifying

3 1.5 l r g(r) 1.5 p(m i z = 2) Fig. 1. The ideal sensor model (op lef) is convolved wih a Gaussian noise model, wih σ =.3, o produce our Gaussian inverse sensor model (righ). This model corresponds o a range measuremen of z = 2. hese updaes are known as sensor models. For he derivaion of our inverse sensor model we focus on sensors wih fairly narrow beams, so ha he uncerainy in angle is negligible compared o he uncerainy in range. If he sensor reurns perfec noise-free measuremens we can employ an ideal sensor model such as he one shown in Fig. 1 (op lef). This example corresponds o a range measuremen of z = 2. Cells closer han 2 unis from he sensor are updaed wih a probabiliy value of (corresponding o free), cells ha are around 2 unis far wih a value of 1 (occupied), and hose furher han 2 unis away are updaed wih a probabiliy value of 1 2 which corresponds o unknown. The widh of he peak (l in Fig. 1) indicaes he range of cell disances ha are deemed occupied by he curren measuremen and can be se o he diagonal of a grid cell. If we wan o assume ha he measuremen is corruped by addiive Gaussian noise, say cenred around he recorded disance, we need o convolve he ideal sensor model wih a Gaussian funcion. If z is he measured disance and he noise variance is σ 2 (which can be a funcion of z), our Gaussian inverse sensor model is given explicily as, r (, z l 2 ), g(r) = 1 2 A B, r [z l 2, z + l 2 ), (4) 1 4 A B 1 4 C, r [z + l 2, ), where A = erf ( z/( 2σ) ), B = erf ( (r 2z + l 2 )/( 2σ) ) and C = erf ( (r 2z l 2 )/( 2σ) ). The funcion g is obained by convolving he ideal sensor model and a zero-mean Gaussian wih variance σ 2. As menioned, he variance of he Gaussian noise model can depend on he measured disance, and his dependence in urn is dicaed by he ype of sensor used. The uncerainy in range measuremens reurned by a sereo camera sensor, for example, grows quadraically wih disance and σ is ofen chosen as z 2 /(bf) where b is he baseline and f he focal lengh [12]. The res of he discussion is no dependen on a specific choice of inverse sensor model. In our experimens, however, we employ he Gaussian model in (4). r V. POSE UNCERTAINTY Occupancy grid mapping ypically funcions under he assumpion ha he pose of he robo is known exacly, a every ime sep, so ha measuremens relaive o he sensor are easily ransformed o global coordinaes before being incorporaed ino he map. The problem wih his assumpion is ha, if he robo s pose has large uncerainy, he resuling map will no reflec i. We deal wih his problem by sampling from he pose disribuion (reurned by he SLAM sysem), ransforming he measuremen o map coordinaes using every sample individually and, finally, updaing he map by summing over he samples. A. Sampling from he pose disribuion We consider wo basic forms in which a ypical SLAM sysem migh reurn he pose disribuion, namely closed-form (such as he mulivariae Gaussian reurned by EKF-SLAM) and a sample-based approximaion (such as he weighed paricles reurned by FasSLAM). If he pose disribuion is known in closed form we can sample direcly from i using he inverse ransform mehod [13]. In some cases, paricularly when he disribuion is Gaussian, he number of samples can be calculaed from a required level of represenaiveness [14]. If he pose disribuion is already approximaed by a se of weighed samples, as is he case when a paricle filer is employed for SLAM, here is no need for furher sampling and we can proceed. B. Inegraing he samples Le us now assume ha he pose disribuion a ime is described by a se of samples { } x = x [1], x [2],..., x [M] (5) and corresponding weighs (summing o 1) { } w = w [1], w [2],..., w [M]. (6) Using each pose sample we ransform he measuremen a ime o global coordinaes, o obain a se of M measuremens { } z = z [1],..., z [M]. (7), z [2] The log odds raio wih which o updae cell i is now approximaed using he se of ransformed measuremens z and weighs w. If y is a random variable defined as is expeced value can be esimaed as M E[y] = p(y)y dy y = log p(m i z ) p(m c i z ), (8) j=1 w [j] log p(m i z [j] ) p(m c i z[j] ). (9) This Mone Carlo approximaion replaces he firs erm on he righ-hand side of (3). We noe ha i will converge o he rue expeced value as M (according o he srong law of large numbers).

4 Fig. 2. An example o illusrae he effec of incorporaing pose uncerainy: a simulaed 2D environmen and field of view (lef); he occupancy grid resuling from using he exac pose and an ideal sensor model (middle); and he occupancy grid afer he incorporaion of uncerainy in robo posiion and orienaion (righ). We updae a paricular cell s value by compuing a log odds raio for every sample using he inverse sensor model, muliplying ha raio by he sample weigh, aking he sum over all samples, and hen adding he resul o he cell s currenly sored value (and subracing he prior, if applicable). We illusrae he effec of his sraegy by means of a simulaed example in Fig. 2. The robo is placed in a simple 2D environmen and a range measuremen is capured. Uncerainy in pose is modelled wih a 3-dimensional Gaussian disribuion (for posiion and orienaion), wih a randomly generaed covariance marix. Samples are drawn from his disribuion and a map is consruced. In order o depic occupancy probabiliies we use grey levels ranging from whie (free space) o black (occupied space). VI. ADAPTIVE OCCUPANCY GRID MAPPING An imporan consideraion in he design of an occupancy grid is ha of cell size. The map mus be able o represen a cerain level of deail, necessiaing a fine resoluion, bu memory and compuaional limiaions ofen hamper such a requiremen. The use of an adapive grid, ha changes is resoluion locally based on he measuremens received, can be hugely effecive a alleviaing his conflic. In his secion we explain how our mechanism for handling pose uncerainy is exended o adapive grids. An adapive grid map consiss of an array of squares or cubes wih differen side lenghs. A sandard way of represening such maps is by means of region rees quadrees for 2D maps and ocrees for 3D maps. By allowing nodes on differen levels of he ree o be acive, a map of varying resoluion is obained. The ree is ypically iniialized a some level. As measuremens are received over ime, cells are checked and, if deemed necessary, recursively spli for higher resoluion in a local region or merged for lower resoluion. We focus on he spliing and merging rules of Einhorn e al. [7], as our incorporaion of pose uncerainy fis naurally ino heir mehod, and offer some improvemens. A. Spliing a cell A cell should be spli if is curren resoluion is inadequae o model he environmen as observed by he sensor. Tha is, we need o spli a cell if i receives conflicing informaion regarding is occupancy. Einhorn e al. [7] keep rack of he number of his (measuremen rays indicaing an obsacle wihin he cell boundaries) and misses (rays ha pass hrough he cell before hiing an obsacle). The disribuion of his and misses is compared o an expeced disribuion, ha accouns for sensor noise, by means of a χ 2 -es. If he es fails, he cell is believed o be parially occupied and subjeced o a spli. The process is coninued recursively unil no more splis are performed or unil a predefined fines resoluion is reached. Once a cell is spli, he newly creaed children inheri heir paren s occupancy probabiliy from he previous ime sep. We noe ha his es alone may give rise o errors in he map. Consider he example in Fig. 3. The dashed lines in (a) represen a grid cell for which only misses are recorded (hose rays ha hi an obsacle before reaching he cell are ignored) so ha he cell is believed o be enirely free of obsacles (b). However, his curren measuremen indicaes ha only par of he cell is free and he res unknown, as shown in (c), necessiaing a spli. I is herefore clear ha rays hiing obsacles before reaching he cell in quesion mus be aken ino consideraion. We adap he algorihm of Einhorn e al. by couning no only his and misses bu also unknowns (rays ha hi obsacles before reaching a paricular cell). The disribuion of hese hree observables is hen compared o expeced disribuions, using a χ 2 -es wih one exra degree of freedom, and if any significan deviaion is found he cell is spli. Boh he hi and miss couns are carried over o he nex ime sep, while he number of unknowns is discarded as i need no influence a cell ha becomes visible in a laer view. This echnique for increasing local resoluion is easily exended o incorporae our handling of pose uncerainy. As explained in Secion V, we have a every ime sep a se of measuremens wih accompanying weighs. For every cell we coun his, misses and unknowns for every individual measuremen in his se, muliply hose couns by he corresponding sample weigh and sum over he samples. grid cell B (a) ray A passes hrough a grid cell, while B sops before reaching i A (b) cell is believed o be enirely free and should no be spli (c) cell is in fac measured as parially free and mus be spli Fig. 3. In adapive occupancy grids we coun his and misses for every cell. This example shows ha hese couns alone can lead o errors. No his are recorded for he grid cell in (a), and i is herefore believed o be enirely unoccupied (b). However, by aking ino consideraion hose rays ha hi obsacles before reaching he cell, we realize ha he measuremen indicaes he sae o be only parially unoccupied, and oherwise unknown, so he cell mus be spli (c).

5 B. Merging cells Once all necessary splis have been done and every acive node s probabiliy value has been updaed, we check o see if any cells can be merged (or pruned from he ree). Following he work of Einhorn e al. [7], children wih a common paren are merged if hey saisfy any of he following crieria: he sandard deviaion of heir probabiliy values is less han some predefined hreshold and heir mean is wihin a hreshold disance of (cerainly free) or 1 (cerainly occupied); all probabiliy values are greaer han a predefined value; all probabiliy values are less han a predefined value. Merging is performed recursively as long as he crieria are me. Afer a merge, he newly acivaed cell mus receive a probabiliy value. For his we assign he mean of he merged cells log odds raios. In doing so lile informaion is los since we merge siblings only when hey have similar values or are almos cerainly occupied or free. VII. EXPERIMENTAL RESULTS In his secion we presen some resuls using simulaed as well as real-world daa. Since our mapping algorihm requires a pose disribuion a every ime sep, we mus have a SLAM sysem running in he background. I is imporan o noe ha we canno measure he performance of he occupancy grid mapping algorihm and ha of he SLAM sysem separaely, as boh influence he map. However, for he purposes of our experimens, we shall assume ha he SLAM sysem does model he pose disribuions realisically. A. Simulaed daa We make use of he simulaion environmen of Brink e al. [15] ha was developed originally as a esing plaform for FasSLAM wih sereo vision. A 2D environmen consising of sraigh-edge obsacles is creaed and landmarks are defined. A simulaed robo moves hrough his environmen by following se waypoins and gahers measuremens (sereo image coordinaes) of he landmarks. Noise is added o hese measuremens and also o he conrol commands. A every ime sep he SLAM sysem akes hese inpus and generaes a pose disribuion. Furhermore, we equip he robo wih a simulaed laser scanner ha capures range measuremens for our occupancy grid mapping. Every cell in an obained occupancy grid can be classified as eiher occupied or free, by imposing some hreshold, for comparison o he rue environmen. We can hen measure false posiive and rue posiive raes, and by varying he hreshold we generae a receiver operaing characerisic (ROC) curve. In Fig. 4 (a) we compare he ROC curve obained from our inclusion of pose uncerainy ( wih pose unc. ) o he ROC curve of a map generaed from only he mos likely pose a every ime sep ( w/o pose unc. ). The performance of our algorihm is comparable o radiional occupancy grid mapping, which implies ha by incorporaing pose uncerainy o he map lile (if any) accuracy is los while informaion regarding ha uncerainy is gained. rue posiive rae xxxxxxxxx w/o pose unc. wih pose unc false posiive rae (a) rue posiive rae xxxxxxxxx w/o unknowns wih unknowns false posiive rae Fig. 4. ROC curves depicing (a) he performance of radiional occupancy grid mapping and our inclusion of pose uncerainy, measured agains he rue map; and (b) he performance of adapive mapping wih and wihou couning unknowns, measured agains a fine regular grid. Nex we consider he performance of our adapaion o he adapive occupancy grid mapping algorihm of Einhorn e al. [7]. The aim of an adapive grid is o replicae is regular (fine resoluion) counerpar, using fewer cells. We herefore measure false posiives and rue posiives agains a regular grid map, raher han he rue environmen, and obain he ROC curves shown in Fig. 4 (b). We see ha our adapaion ( wih unknowns ) does indeed ouperform he exising algorihm ( w/o unknowns ), as expeced. B. Real-world daa In order o es our mehod on real-world daa we make use of he Bicocca indoor se from he Rawseeds Projec [16]. A wheeled robo equipped wih various sensors is driven hrough fairly narrow corridors wih office doors on heir sides. Recorded odomery daa and racked sereo image feaures provide inpu for our FasSLAM sysem, which we base on an implemenaion by Brink e al. [15], ha generaes pose disribuions. Noe ha, in he absence of loop closure and since no absolue locaion informaion is rerievable from racked sereo image feaures, he uncerainy in pose is expeced o increase over ime. A every ime sep we ake he esimaed pose disribuion, which is given as a se of paricles and associaed imporance weighs, and range daa from he robo s forward facing laser scanner o consruc a 2D occupancy grid map. In Fig. 5 we compare resuls from he radiional occupancy grid algorihm, ha simply akes a maximum likelihood sample from he pose disribuion as inpu, wih our algorihm ha incorporaes informaion from all he paricles a every ime sep (in hese depicions he robo moves upwards). We show close-ups of he maps o beer demonsrae he behaviour of he wo algorihms. Our incorporaion of pose uncerainy leads o a map wih an overall smooher appearance and, more imporanly, i seems ha he effecs of inaccuraely esimaed poses are lessened. The resul in Fig. 5 (a) illuminaes a problem ofen encounered when a maximum likelihood pose is drawn from a se of paricles, for use in mapping. As he imporance weighs of paricles are updaed over ime, based on he (b)

6 grid algorihm significanly improves he abiliy of he adapive grid o mimic is regular (fine resoluion) counerpar. For fuure work we hope o invesigae he possibiliy of incorporaing a Gaussian pose disribuion by blurring he grid map wih an appropriae kernel. This idea is no ha sraighforward o implemen in pracice, however, due o difficulies wih he dimensions of he kernel ha correspond o he robo s bearing. We se ou o validae he heoreical argumens behind our approach, bu here is sill room for improving he implemenaion. In fac, he new updae equaion can lead o an implemenaion srucure slighly differen from he radiional occupancy grid algorihm. For every cell a single assignmen can be made from all he measuremen beams ha inersec he cell across all pose samples. This srucure would lend iself o effecive parallelizaion for real-ime applicaions. (a) wihou pose uncerainy (b) wih pose uncerainy Fig. 5. Close-ups of occupancy grids generaed by (a) he radiional algorihm and (b) our algorihm ha incorporaes pose uncerainy. The pose disribuion a every ime sep, in he form of paricles esimaed by FasSLAM, is shown as a collecion of blue dos. The circled areas emphasize how he incorporaion of pose uncerainy can miigae inaccuracies in he map. observaions, he index associaed wih maximum weigh may jump around and cause a rack of he mos likely paricles o appear erraic. While a weighed average of he paricles a every ime sep migh produce a smooher rack, and herefore seem more appropriae, is likelihood can be low (given he pose disribuion). VIII. CONCLUSION We considered he problem of dense mapping wih range measuremens capured over ime by a mobile robo. We presened a means of incorporaing he uncerainy associaed wih he robo s pose, as esimaed by a SLAM sysem, ino occupancy grid maps. Our soluion requires samples from he pose disribuion. If a paricle filer is used for esimaion, as is he case in FasSLAM, his disribuion is already approximaed by samples. Alernaively, if he pose disribuion is given in closed-form as is he case when EKF-SLAM is employed, we generae samples from i. The occupancy grid updae equaion is hen alered o include hese samples hrough Mone Carlo inegraion. We also showed how he efficien adapive grid mapping algorihm of Einhorn e al. [7] exends easily o include our handling of pose uncerainy. We idenified a poenial shorcoming in how cells are seleced for spliing, o increase resoluion locally, and offered a remedy. For every cell we coun no only his and misses bu also unknowns (rays hiing obsacles before reaching he paricular cell). In doing so a cell ha is only parially observed by he curren measuremen can be recognized and spli if necessary. Simulaions sugges ha our incorporaion of pose uncerainy is effecive, giving a more informaive map, wihou leading o a loss in accuracy. Our adjusmen o he adapive ACKNOWLEDGMENTS The auhors hank he Harry Crossley Foundaion and TATA Africa for funding his work. REFERENCES [1] S. Thrun, Roboic mapping: a survey, Exploring Arificial Inelligence in he New Millennium, G. Lakemeyer and B. Nebel (ediors), Morgan Kaufmann, 22. [2] S. Thrun, W. Burgard and D. Fox, Probabilisic Roboics, MIT Press, 25. [3] E. Ivanjko and I. Perović, Exended Kalman filer based mobile robo pose racking using occupancy grid maps, IEEE Medierranean Elecroechnical Conference, pp , 24. [4] S. O Callaghan, F. Ramos and H. Durrand-Whye, Conexual occupancy maps incorporaing sensor and locaion uncerainy, IEEE Inernaional Conference on Roboics and Auomaion, , 21. [5] S. O Callaghan and F. Ramos, Gaussian process occupancy maps, Inernaional Journal of Roboics Research, vol. 31, no. 1, pp , 212. [6] R. Merali and T. Barfoo, Pach map: a benchmark for occupancy grid algorihm evaluaion, IEEE/RSJ Inernaional Conference on Inelligen Robos and Sysems, pp , 212. 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