Gas Source Localisaion by Consrucing Concenraion Gridmaps wih a Mobile Robo Achim Lilienhal 1, Tom Ducke 2 1 W.-Schickard-Ins. of Comp. Science, Universiy of Tübingen, D-72076 Tübingen, Germany lilien@informaik.uni-uebingen.de 2 Deparmen of Technology, AASS, Örebro Universiy, S-70182 Örebro, Sweden d@ech.oru.se Absrac. This paper addresses he problem of mapping he feaures of a gas disribuion by creaing concenraion gridmaps wih a mobile robo equipped wih a gas-sensiive sysem ( mobile nose ). By conras o meric gridmaps exraced from sonar or laser range scans, a gas sensor measuremen provides informaion abou a comparaively small area. To overcome his problem, a mapping echnique is inroduced ha uses a Gaussian densiy funcion o model he decreasing likelihood ha a paricular reading represens he rue concenraion wih respec o he disance from he poin of measuremen. The srucure of he mapped feaures is discussed wih respec o he parameers of he applied densiy funcion, he evoluion of he gas disribuion over ime, and he capabiliy o locae a gas source. 1 Inroducion This paper addresses he problem of modelling gas disribuion in indoor environmens by a mobile robo equipped wih an elecronic nose, comprising an on-board array of gas sensors. A new algorihm is presened for creaing concenraion gridmaps, by combining he recorded gas sensor readings of he robo wih locaion esimaes, provided by anoher sensor sysem. Inended applicaions of his sysem include deecion and localisaion of a disan gas source (e.g., as an elecronic wachman for deecing hazardous subsances [1]), especially in environmens where i is impracical or uneconomical o insall a fixed array of gas sensors. The mehod does no require arificial venilaion of he environmen, e.g., by imposing a srong, unidirecional airflow as in previous approaches for gas source localisaion [2, 3]. Gridmaps were originally inroduced o mobile roboics in he early 1980s as a means of creaing maps using wide-angle measuremens from sonar sensors [4]. The basic idea is o represen he robo s surroundings by a grid of small cells. In a convenional gridmap, each cell conains a cerainy value represening he robo s belief ha he corresponding area is occupied by any objec. In our approach, he cells in he gridmap correspond o he robo s esimae of he relaive concenraion of a deeced gas in ha paricular area of he environmen. There are several problems in creaing such a represenaion ha are specific o robos equipped wih gas sensors, discussed as follows. In conras o range-finder sensors such as sonar or laser, a single measuremen from an elecronic gas sensor provides informaion abou a very small area. This problem is furher complicaed by he fac ha he meal-oxide sensors ypically used for his purpose do no provide an insananeous measuremen of he gas concenraion. Raher, hese sensors are affeced by a long response ime and an even longer recovery ime. The ime consans of rise and decay of he mobile nose used were esimaed as τ r 1.8 s and τ d 11.1 s [5]. Thus, considerable inegraion of successive measuremens is carried ou by he sensors hemselves. Furhermore, he disribuion of gas molecules in an unconrolled environmen ends o be dominaed by urbulence raher han diffusion, ypically resuling in a jagged paern of emporally flucuaing eddies [6, 7]. To overcome hese problems, a mapping echnique is inroduced ha permis inegraion of many gas measuremens over an exended period of ime. Spaial inegraion of he poin measuremens is carried ou by using a Gaussian densiy funcion o exrapolae on he measuremens, by assuming a descreasing likelihood ha a given measuremen represens he rue concenraion wih respec o he disance from he poin of measuremen. By inegraing many measuremens, he underlying srucure of he gas disribuion can be separaed from he ransien variaions due o urbulence. The effecs of he long response and recovery imes are also reduced by incorporaing measuremens aken as he robo ravelled in many differen direcions. The locaion esimaes required for map building were obained by he exernal, vision-based absolue posiioning sysem W-CAPS [8], which is briefly described in Secion 3.2. However, he resuls are expeced o apply o any mobile
robo equipped wih a suiably accurae on-board posiioning sysem, e.g., by carrying ou simulaneous localisaion and mapping wih oher sensor sysems [9]. 2 Building Concenraion Gridmaps Gridmaps exraced from a sequence of measuremens are able o represen ime-consan feaures of he measured quaniy. Therefore, a properly consruced gas concenraion gridmap is expeced o show ime-averaged srucures ha migh indicae he locaion of an odour source. In rooms wih a consan unidirecional airflow hese srucures should be plume-like ones [10]. This paper, however, presens invesigaions performed in an unvenilaed laboraory room a Örebro Universiy. Recen experimens in unvenilaed rooms (including his one) showed concenraion profiles ha are also relaively sable over ime [1, 11]. These plume-like srucures are likely o be caused by consan air sreams ha occur as a consequence of spaial emperaure differences. In order o creae reasonable gridmaps, he cells have o be updaed muliple imes. This is no a problem wih gridmaps buil from laser or sonar scans, where each measuremen provides informaion abou an area ha overlaps considerably wih ha of previous scans. By conras, he gas sensor readings are very local measuremens represening he concenraion of he analye a he sensors surface ( 1cm 2 ). Neverheless hese readings conain informaion abou a larger area, for wo reasons. Firs, alhough urbulence ends o creae eddies in he gas disribuion [6, 7], i is reasonable o assume ha he gas concenraion in he viciniy of he poin of measuremen does no change drasically because of he smoohness of he ime-consan srucures. Second, he meal-oxide gas sensors perform emporal inegraion of successive readings implicily due o heir slow response and recovery. Thus spaial informaion is inegraed along he pah driven by he robo. As a firs approximaion, he sensor readings were assumed o represen he real concenraion a he curren locaion. The readings r were convolved using he wo dimensional normalised Gaussian f (x)= 1 x2 e 2σ 2πσ2 2. (1) Thus a weighing funcion is applied which indicaes he likelihood ha he measuremen represens he concenraion a a given disance from he poin of measuremen. In deail he following seps are performed. Firs, for each grid cell i wihin he cuoff radius R co, around he poin x where he measuremen was aken a ime, he displacemen δ (i) o he grid cell s cenre x (i) is calculaed as δ (i) = x (i) x. (2) Now he weighing for all he grid cells i is deermined by { w (i) f (δ (i) ) if δ (i) R = co 0 if δ (i) (3) > R co Then wo emporary values mainained per grid cell are updaed wih his weighing w (i) : he oal sum of he weighs and he oal sum of weighed readings W (i) WR (i) = w (i), (4) = r w (i). (5) For he laer calculaion, he normalised readings r were used, obained from he raw readings R as r = R R min, (6) R max R min using he minimum and maximum (R min, R max ) value of a given sensor. Finally, if he oal sum of he weighs W (i) exceeds he hreshold value W min, he value of he grid cell is se o c (i) = WR (i) /W (i) if W (i) W min. (7) Fig. 1 shows he sum of he weighing funcions for a sequence of seps along a sraigh line (wih a sep widh of 2σ). The figure shows he las five seps and he curren one indicaed by an arrow. One can see ha he readings recorded a posiions x 1 -x 5 are spread by he mapping process along he driven pah. While he spreading perpendicular o he pah is deermined mainly by he chosen parameer σ, he spreading along he pah is approximaely independen of his variable.
Fig. 1. Sum of he likelihood funcion for a sequence of seps along a sraigh line. 3 Experimenal Seup 3.1 Robo and Gas Sensors The experimens were performed wih a Koala mobile robo (see Fig. 2) equipped wih he Mark III mobile nose [5], comprising 6 in oxide sensors manufacured by Figaro Engineering Inc. This ype of chemical sensor shows a decreasing resisance in he presence of combusible volaile chemicals in he surrounding air. The sensors were placed in ses of hree (of ype TGS 2600, TGS 2610 and TGS 2620) inside wo separae ubes conaining a sucion fan each. Due o heir differen seleciviies, discriminaion of differen analyes is possible. For he invesigaions presened in his paper, however, he sensor arrays were used only o increase he robusness of he measured signal. Paps Fans (405F) were used o generae an airflow of 8 m 3 /h. The disance beween he wo ses of sensors was 40 cm. Fig. 2. (a) Koala robo wih he Örebro Mark III mobile nose. The picure shows he odour source, he gas sensors inside he wo sucion ubes mouned a he rear of he robo and he coloured ha used for deermining he absolue posiion of he robo. (b) Floor plan of he laboraory room a Örebro Universiy where he experimens were performed. 3.2 Absolue Posiioning Sysem To record he posiion of he robo he vision-based absolue posiioning sysem W-CAPS [8] was applied, which racks a disincly coloured objec mouned on op of he robo. The posiioning sysem uses four Philips PCVC 740K web-cameras wih a resoluion of 320 240 pixels o riangulae he (x,y) posiion of he cenre of he colour blob. By combining up o 6 single posiion esimaes, i provides cenimeer level accuracy. Fig. 2(b) shows he camera posiions and he respecive fields of view. The graded shadings indicae he number of cameras ha can sense each par of he environmen. 3.3 Environmen and Odour Source All experimens were performed in a recangular laboraory room a Örebro universiy (size 10.6 m 4.5 m). The robo s movemen was resriced such ha is cenre was always locaed inside he cenral region, which is also indicaed in Fig. 2(b), where precise and reliable posiion informaion is available. The air condiioning sysem in he room was deacivaed o provide an unvenilaed environmen.
To simulae a ypical ask for an elecronic wachman, an odour source was chosen o imiae a leaking ank. This was realised by placing a paper cup filled wih ehanol on a suppor in a bowl wih a perimeer of 12 cm (see Fig. 2). The ehanol dripped hrough a hole in he cup ino he bowl a a rae of approximaely 50 ml/h. Ehanol was used because i is non-oxic and easily deecable by he in oxide sensors. 3.4 Daa Acquisiion Sraegy Two differen sraegies were esed o collec concenraion daa. In one se of experimens, he robo was driven along a predefined pah, namely a recangular spiral around he locaion of he odour source. The minimal disance o he cenre of he source was 1 m, 0.75 m, 0.5 m, 0.35 m on he subsequen windings of he pah. Along he sraigh lines a consan speed was applied because his was found o enhance he localisaion capabiliy [1, 12]. Furhermore he robo was roaed slowly (10 /s) a he corners in order o minimise addiional urbulence. A complee cycle including an inward and an ouward phase lased abou 25 minues. These cycles were repeaed wih a randomly chosen saring corner and direcion a he sar of each rial. For a second se of experimens, wo differen reacive searching sraegies were applied in he manner of a Braienberg vehicle [13]. Based on he sereo archiecure of he mobile nose, a direc sensor-moor coupling was implemened. Uncrossed as well as crossed inhibiory connecions were used. In his way maximum wheel speed resuls if he sensed concenraion is low, which in urn implemens a simple sor of exploraion behaviour. Wih uncrossed connecions he robo urns oward higher concenraions (a behaviour ha Braienberg called permanen love) while he robo urns away from hem wih crossed connecions (exploring love). While he reacive sraegies proved o be useful in moving he robo owards he general direcion of he source on average, hey are no reliable enough o enable localisaion of he gas source wih high cerainy. Moreover, i is generally no possible o declare ha he gas source was found by deermining an insananeous global concenraion maximum. This is why he gas concenraion mapping echnique inroduced in his paper should be useful for smelling robos. Furher deails and especially he gas source localisaion performance of his smelling Braienberg vehicle are discussed in [6]. 4 Resuls 4.1 Widh of he Likelihood Funcion To build a gridmap wih he new algorihm (eqn. 1-7), a number of parameers mus firs be deermined: he cell size, he widh of he gaussian σ, he cuoff radius R co and he hreshold W min. For all experimens presened here, grid cells of size 2.5 2.5 cm 2 were used. The exac magniude of R co and W min does no have a srong influence, bu he parameer σ has a criical effec on he resuling gridmaps. Fig. 3 compares four gridmaps ha resul from differen values of σ, using consan values of R co = 3σ and W min = 1.0 (he number of sensors). All of he gridmaps were creaed from he same sensor daa colleced wih all 6 sensors over a period of 100 minues by a robo ha was driven along a sequence of recangular spirals. (One of hese spirals is ploed in Fig. 3 wih a hin broken line.) Concenraion values are indicaed by shadings of grey (dark low, ligh high) while he values higher han 90% of he maximum are indicaed wih a second range of dark-o-ligh shadings (of red). For small values of σ he resuling gridmaps are Fig. 3. Comparison of concenraion gridmaps from he same daa se wih gaussians of differen widh σ (eq. 1). dominaed by local variaions (see lef par of Fig. 3). Increasing σ causes hese maxima o be combined, and hus larger srucures of he gas disribuion appear as coniguous spos. A value of σ =15 cm seems o provide a reasonable radeoff beween hese wo effecs. All of he subsequen gridmaps presened were creaed using his parameer value.
4.2 Evoluion of he Gas Disribuion over Time Due o he local characer of he concenraion measuremens, i akes some ime o build a concenraion map. In addiion o spaial coverage, a cerain amoun of emporal averaging is also necessary unil he ime-consan srucure of he gas disribuion is represened in he map. The evoluion of he ime-consan srucures can be seen in Fig. 4, which shows wo sequences of gridmaps creaed from daa colleced up o he specified ime. The gridmaps were Fig. 4. Evoluion of concenraion gridmaps over ime. The upper row shows a sequence of gridmaps creaed from he daa ha were colleced along a predefined recangular spiral up ill he specified ime. In he same way he lower row depics gridmaps based on daa colleced in anoher experimen wih a Braienberg-vehicle wih uncrossed inhibiory connecions. creaed wih he parameers σ = 15 cm, R co = 3σ, W min = 6.0 using all six sensors. Grid cells ha have no ye been inspeced (wih W (i) W min ) are indicaed wih a differen colour (green). In he experimens where he robo moved along a predefined pah (secion 3.4), i ook approximaely 30 minues for he mapped srucures o sabilise. This can also be seen in Fig. 5(a), which shows he disance beween he cenre of he grid cell wih he maximum value and he cenre of he gas source. Afer abou 1500 s, his disance converges eiher o a relaively sable value, or i alernaes beween wo oherwise sable values. Slighly differen resuls were obained if he robo was conrolled reacively as a Braienberg vehicle, as explained in secion 3.4 (see lower row in Fig. 4 and Fig. 5(b)). Due o he fac ha areas wih high concenraion were acively explored, sable srucures could be deermined much more quickly, even hough he average speed was lower (approx. 4 cm/s compared o 5 cm/s). On he oher hand, he deeced global maximum changed more ofen because he robo has a endency o ge suck in local concenraion maxima. 4.3 Localisaion of a Gas Source In he case of a gas disribuion conrolled purely by diffusion, he locaion of he gas source would correspond o he maximum in he concenraion map. As menioned, his assumpion is no fulfilled under realisic condiions due o he relaively slow diffusion velociy of gases compared o spreading by urbulence. Neverheless, he posiion of he concenraion maximum can be used o esimae he approximae locaion of he source in some cases, as can be seen in Fig. 5. Here, he disance beween such an esimae and he cenre of he real posiion of he gas source is ploed agains ime, boh for daa colleced by driving along he predefined pah (a) and wih a Braienberg-ype sraegy (b). The velociy gain in he case of he reacively seered robo was 5 cm/s and he gas source was placed in he middle of he inspeced area. Three experimens were performed wih uncrossed sensor-moor connecions and anoher one wih crossed connecions, indicaed by he solid (red) line. An exac agreemen wih he posiion of he gas source (which
Fig. 5. Disance beween he cell wih he highes concenraion and he cenre of he gas source. The gas sensor readings were colleced (a) along a predefined pah and (b) applying a Braienberg-ype search sraegy. is shaded area in Fig. 5) was observed only emporarily. On he oher hand he error a he end of he experimen was < 75 cm in 6 ou of 7 and < 50 cm in 5 ou of 7 experimens. I is no guaraneed, however, o ge a good esimae of he source locaion wih his mehod. This can be seen in Fig. 5(a) bu was also observed in furher experimens wih reacive sraegies. 5 Oulook This paper presened a new echnique for modelling gas disribuions by consrucing concenraion gridmaps wih a mobile robo. Preliminary experimenal resuls for wo differen exploraion sraegies were presened. A presen, only ime-consan srucures in he gas disribuion were modelled by using emporal averaging. I would also be possible o model changing gas disribuions by aging he measuremens insead of averaging, so ha older measuremens gradually lose heir weigh. Oher possible developmens would include experimenal comparisons of differen exploraion sraegies for map building. Sraegies based on he sae of he map, e.g., by moving owards areas of high uncerainy, could also be considered. Fuure work will include developmen of an acual source-finding sraegy based on hese self-acquired maps. References 1. Achim Lilienhal, Michael R. Wandel, Udo Weimar, and Andreas Zell. Experiences Using Gas Sensors on an Auonomous Mobile Robo. In Proceedings of EUROBOT 2001, 4h European Workshop on Advanced Mobile Robos, pages 1 8. IEEE Compuer Press, 2001. 2. Hiroshi Ishida, K. Suesugu, Takamichi Nakamoo, and Toyosaka Moriizumi. Sudy of Auonomous Mobile Sensing Sysem for Localizaion of Odor Source Using Gas Sensors and Anemomeric Sensors. Sensors and Acuaors A, 45:153 157, 1994. 3. R. Andrew Russell, David Thiel, Reimundo Deveza, and Alan Mackay-Sim. A Roboic Sysem o Locae Hazardous Chemical Leaks. In IEEE In Conf. Roboics and Auomaion (ICRA 1995), pages 556 561, 1995. 4. Marin C. Marin and Hans P. Moravec. Robo evidence grids. Technical Repor CMU-RI-TR-96-06, The Roboics Insiue, Carnegie Mellon Universiy, 1996. 5. Achim Lilienhal and Tom Ducke. A Sereo Elecronic Nose for a Mobile Inspecion Robo. In Proceedings of he IEEE Inernaional Workshop on Roboic Sensing (ROSE 2003), Örebro, Sweden, 2003. 6. Achim Lilienhal and Tom Ducke. Experimenal Analysis of Smelling Braienberg Vehicles. In Proceedings of he IEEE Inernaional Conference on Advanced Roboics (ICAR 2003), Coimbra, Porugal, 2003. 7. R. Andrew Russell. Odour Sensing for Mobile Robos. World Scienific, 1999. 8. Achim Lilienhal and Tom Ducke. An Absolue Posiioning Sysem for 100 Euros. In Proceedings of he IEEE Inernaional Workshop on Roboic Sensing (ROSE 2003), Örebro, Sweden, 2003. 9. T. Ducke. A geneic algorihm for simulaneous localizaion and mapping. In Proceedings of he IEEE Inernaional Conference on Roboics and Auomaion (ICRA 2003), Taipei, Taiwan, 2003. 10. J. O. Hinze. Turbulence. McGraw-Hill, New York, 1975. 11. Michael R. Wandel, Achim Lilienhal, Tom Ducke, Udo Weimar, and Andreas Zell. Gas Disribuion in Unvenilaed Indoor Environmens Inspeced by a Mobile Robo. In Proceedings of he IEEE Inernaional Conference on Advanced Roboics (ICAR 2003), Coimbra, Porugal, 2003. 12. Ahmed Mohamod Farah and Tom Ducke. Reacive Localisaion of an Odour Source by a Learning Mobile Robo. In Proceedings of he Second Swedish Workshop on Auonomous Roboics, pages 29 38, Sockholm, Sweden, Ocober 10-11 2002. 13. Valenino Braienberg. Vehicles: Experimens in Synheic Psychology. MIT Press/Bradford Books, 1984.