Particle Filter-based State Estimation in a Competitive and Uncertain Environment

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1 Paricle Filer-based Sae Esimaion in a Compeiive and Uncerain Environmen Tim Laue Thomas Röfer Universiä Bremen DFKI-Labor Bremen Fachbereich 3 Mahemaik / Informaik Sichere Kogniive Sseme Enrique-Schmid-Sraße 5 Enrique-Schmid-Sraße 5 Bremen, German Bremen, German Tel.: +49 / (421) Tel.: +49 / (421) Fax: +49 / (421) Fax: +49 / (421) imlaue@informaik.uni-bremen.de Thomas.Roefer@dfki.de Acknowledgemens The auhors would like o hank he Deusche Forschungsgemeinschaf (German Research Agenc) for supporing his work hrough he priori program Cooperaive Mobile Robos in Dnamic Environmens as well as hrough he Transregional Collaboraive Research Cener Spaial Cogniion. Kewords Roboics, Noise, Modelling. Absrac In his paper we presen he applicaion of paricle filers for sae esimaion on a humanoid robo. These filers are used for self-localizaion and ball racking in a compeiive soccer scenario using robos wih limied percepual and processing capabiliies. Some exensions have been applied o he basic algorihms o adap hem o he special needs of his domain which is a subjec of high noise and dnamic changes. Differen experimens have been carried ou o confirm he applicabili and he precision of he approach. Inroducion The RoboCup iniiaive is an inernaional join projec o promoe arificial inelligence and roboics. I is an aemp o foser AI and inelligen roboics research b providing a sandard problem where a wide range of echnologies can be inegraed and examined 1]. The RoboCup domain is divided ino several differen caegories and leagues. The approaches described in his paper have been applied he RoboCup Soccer Humanoid Kid-Size League in which eams of humanoid robos pla soccer agains each oher. Two imporan sub-asks in his domain (among sable walking, acion selecion, and several ohers) are he esimaion of he own pose as well as he esimaion of he posiion and veloci of he ball. The main source of informaion abou he environmen is for our applicaion a camera inside he robo s pan-il head. Several properies of his se-up le accurae sae esimaion become a challenging ask: 1. The robo s field of view is limied and onl a secion of he environmen can be perceived a once. 2. All percepions are nois, perceiving false posiives is also possible. 3. Impercepible changes of he environmen ma occur, e.g. a replacemen of he ball or he robos b a referee. 4. The compuaional resources are limied, bu daa needs o be processed in real-ime o reac successfull on changes of he environmen caused b he opponen eam. One widespread approach for robo sae esimaion is he Mone Carlo Localizaion 2]. This probabilisic algorihm approximaes a sae b mainaining a se of hpoheses, denoed as paricles as well as samples. The approach is able o deal wih noise and non-linear changes of he environmen

2 (e.g. kicked balls or robo-kidnapping ). Differen implemenaions of his algorihm have been used for localizaion b several RoboCup eams before, e.g. b 3]. In his paper, we describe is applicaion on he wo above-menioned esimaion asks in he humanoid soccer scenario, realized on he robos of he B-Human eam 4,5]. A closel relaed approach for humanoid self-localizaion has recenl been published b 6], however using a robo wih superior percepual capabiliies. A sophisicaed bu for ou applicaion demanding oo high compuaional effors approach for racking a ball in a soccer environmen was presened b 7]. B using exensions 8] of he basic Mone Carlo Localizaion approach, we show ha i is possible o compue sufficienl accurae esimaes even on plaform wih comparabl low percepual capabiliies. The resuls of our robo experimens documen he precision of he approach and is performance in dnamic siuaions. This paper is organized as follows: Firs, we describe he scenario o which his work applies o, i.e. he environmen as well as he robos and heir percepual capabiliies. Thereafer, a shor inroducion on he Mone-Carlo-Localizaion algorihm and is exensions is given. This is followed b he descripion of heir adapion and applicaion o his domain. The paper is concluded b a presenaion of experimenal resuls. a) b) Fig. 1: a) A robo of he B-Human eam in deail. b) A scene from a robo soccer mach. The Domain of his Research As afore-menioned, his work is seled in a compeiive robo soccer scenario. This secion gives a shor inroducion ino he RoboCup Soccer Humanoid Kid-Size League and describes our robos and heir percepual capabiliies and limiaions. The RoboCup Soccer Humanoid Kid-Size League In his RoboCup league, wo eams of wo robos each pla agains each oher on a 5.7m x 4.4m large soccer field 1. To reduce complexi for compuer vision, all elemens of he environmen are colorcoded: he ball is orange, one goal is ellow, and he oher goal is blue. In he corners of he field, addiional beacons for localizaion are placed. The floor is an even green carpe wih wide whie field lines (see Fig. 1b) a specified posiions. To avoid disurbances wih his color scheme, all robos have o be mosl black. 1 For 2008, i is inended o enlarge he field o 7.4m x 5.4m and o increase he number of plaers o hree per eam.

3 One mach consiss of wo halves, 10 minues each. During his ime, he robos operae compleel auonomousl, no human inervenion is allowed. The plaers can o communicae wih each oher, bu addiional exernal conrol compuers are forbidden. The Humanoid Robos The robos have a maximum heigh of 60cm and mus have human proporions. This means ha he have o walk on wo legs and fulfill a se of consrains regarding, e.g., heir cener of mass and he size of heir fee. Special devices for holding or kicking he ball are no permied. Exernal sensing is onl allowed via cameras; acive sensors such as laser range finders are no allowed. For our research, we used he robos of our B-Human eam, which paricipaed in RoboCup compeiions in 2007; one of hese robos is shown in Fig. 1a. Each robo is equipped wih 20 servo moors (6 per leg o allow omni-direcional walking gais, 3 per arm, and 2 in a pan-il uni which carries he head). The oal heigh of he robo is 48cm; is weigh is 2.5kg. I is based upon a Bioloid consrucion ki which alread includes a microconroller for conrolling he servo moors. The main sofware runs an on a PDA (Fujisu-Siemens Pocke LOOX 720) ha has 128 MB RAM and an XScale processor wih 520 MHz. These are quie limied processing capabiliies, bu sill allow running he cogniive pars of he sofware (including vision, he localizaion algorihms presened in his paper, and acion selecion) wih 15 Hz and he moion conrol wih 50 Hz. The Robo s Percepual Capabiliies Our robo s onl exernal sensor is a camera inside he head. We use he PDA s original camera ha has been lead ouside he case. This camera provides 15 images per second wih a resoluion of 320 b 240 pixels; is opening angles are 45.1 b This is a quie limied field of view, as apparen in Fig. 2. To keep rack of he own pose as well as of he ball s posiion, he camera needs o be moved consanl b he pan-il uni. Currenl, man eams avoid his problem b using cameras poined a omni-direcional mirrors (ha provide a field of view of 360 ) or a se of cameras poining in differen direcions. Having hese percepual capabiliies, localizaion becomes rivial. Bu hese non-humanlike soluions will be disallowed in he fuure. The soluions presened in his paper anicipae hese changes. The vision sofware running on he PDA is able o exrac some basic feaures ha provide he base for he localizaion algorihms. These feaures (i.e. he ball and significan poins on he field) are depiced in Fig. 2. Their recogniion is based on he deecion of significan color changes in he picure. Since he camera s perspecive is known, i is possible o differeniae beween feaures which acuall belong o he field and hose ha don (e.g. specaors). Neverheless, he compuaion of he feaure posiions relaive o he robo is subjec o heav noise, since he camera is on op of a walking (and shaking) robo. Fig. 2: Two images from he robo s camera. Some drawings in he images depic perceived elemens of he environmen: orange circles for balls, whie dos for field line elemens, and ellow and blue dos for he lower edges of goals.

4 Mone-Carlo Localizaion This secion gives an overview abou he Mone-Carlo localizaion algorihm, which is he base for boh, he self-localizaion and he ball racking. Some exensions, which are crucial for he successful applicaion in a RoboCup scenario, are also presened. The General Algorihm for Localizaion The Mone-Carlo algorihm for robo localizaion has been inroduced b 2]. I is a probabilisic algorihm which approximaes a sae and is variance b a se of samples (also referred o as paricles), wih each sample consising of one possible sae and a weigh which represens he likelihood of his sae. This is illusraed b Fig. 3. Fig. 3: Illusraion of paricle-based represenaion of he robo pose and he ball posiion and veloci. Each gra box denoes one possible pose of he robo; ligh boxes are more likel han dark boxes. The black box shows he resuling robo pose from he filer. The dos wih arrows describe he ball samples (describing posiion and veloci of a ball). The orange one is he resuling ball esimae. This algorihm is in conras o sandard Kalman-filer-based 9] approaches able o deal wih nonlinear sae changes as well as b using an exension of he basic approach o efficienl cope wih he kidnapped-robo problem, i.e. replacing a robo which is no able o recognize his sae change and which has o re-esimae his posiion. The general algorihm for self-localizaion as well as for ball racking asks looks as follows (adaped from 10], who also provide a comprehensive descripion): 1: Algorihm_MCL(X -1, u, z, e): X (ø), X (ø) 2: for m = 1 o M do 3: x = moion_updae(u, x -1 ) 4: w = sensor_updae(z, x, e) 5: X = X + (x, w ) 6: for m = 1 o M do 7: i] draw i wih probabili w 8: add x i] o X 9: reurn X The algorihm processes he curren sample se X -1 in wo passes o generae an up-o-dae sample se X. During he firs pass, he sae of each sample x is modified according o he previousl performed acion u and hus resuling sae change (line 3: moion_updae). Aferwards, he weighing w of he samples is compued based on he curren sensor daa z (i.e. he perceps from he vision ssem in our case) and heir fi o he given sample sae and model e of he environmen (line 4: sensor_updae).

5 Boh acions are of course dependen on he curren domain and purpose of he filer. The are differen for self-localizaion and ball racking and herefore described in deail in he according laer secions. In he second pass, he new se X is made up b randoml drawing elemens from X -1 proporional o heir weigh. This implies ha samples ha are more likel according o he curren sensor daa are more likel o be added (some of hem even muliple imes) o he new sample se whils hose wih a low weighing migh drop ou. This pass is called resampling (lines 6-8). If no sensor updae was performed (because of no new inpu from he vision ssem) and herefore no weighings have been compued, he resampling sep is skipped. B he ime, he samples are disribued around he sae which should be esimaed. I is possible o ge a resul a an ime, e.g. b weighing-based averaging of all samples. Enhancemens for Resampling In heor, his algorihm is alread sufficien o e.g. esimae a soccer robo s pose (consising of a posiion and roaion on a wo-dimensional plane, boh in coninuous coordinaes). In pracice, problems arise when he iniial pose is no known or he robo is replaced during operaion. When using a low number of samples (<100), i migh ake a long ime unil a sample comes close o he real posiion (given he fac ha he moion model is nois and hus he variance of he disribuion increases b he ime) and ges duplicaed during resampling, since he sae space is oo large o be covered appropriael. Increasing he number of samples obviousl also increases he runime of he algorihm and herefore should be avoided. One common soluion for his problem is o add new samples which have no been drawn from a previous disribuion. Two crucial facors are he source and he number of new samples. New samples could be added b jus compuing random samples inside he given sae space. This is an appropriae soluion, bu migh also no be ver efficien since i could ake oo long, unil a sample comes across an adequae posiion. In his domain, i is possible o compue new samples direcl from he given sensor daa and hus move he disribuion o he real sae quie quickl. This procedure will be described in he laer secions for boh self-localizaion and ball racking. The number of new samples migh be se o a consan value. Bu his implicaes wo drawbacks: If he disribuion alread approximaes he sae quie well, hese new samples migh cause a higher variance, if heir number is oo high. On he oher hand, if he number is oo low, he paricle filer migh no be able o adap o he sae change fas enough. One soluion o overcome his issue is he Augmened_MCL algorihm proposed b 6]. The following descripion is adaped from 10]: 1: Algorihm_Augmened_MCL(X -1, u, z, e): X (ø), X (ø) 2: saic w slow, w fas 3: for m = 1 o M do 4: x = moion_updae(u, x -1 ) 5: w = sensor_updae(z, x, e) 6: X = X + (x, w ) 7: w avg = w avg + M -1 w 8: w slow = w slow + α slow (w avg - w slow ) 9: w fas = w fas + α fas (w avg - w fas ) 10: for m = 1 o M do 11: wih probabili max{0, 1 - w fas / w slow )} do 12: add new pose o X 13: else 14: i] draw i{1,,n}wih probabili w 15: add x i] o X 16: reurn X This exension of he base algorihm keeps rack of he overall weighing of he disribuion over ime. This weighing decreases, if he curren sensor daa does no mach wih he disribuion anmore, e.g.

6 afer replacing he robo or he ball. The weighing w slow adaps slower o such changes han w fas. Through heir quoien, a requiremen of new samples is compued (line 11). The adapiveness of his process is seered via he wo facors α slow and a α fas (wih 0 α slow < α fas cf. lines 8 and 9). Boh, he self-localizaion and he ball racking make use of his approach, which is laer referred o as sensor reseing. Self-Localizaion The paricle filer for self-localizaion esimaes he robo s pose. I uses he poins on field lines and on he edges beween he field and he beacons and goals as observaions, and he moion esimaed b he walking engine as inpu. The robo s pose x consiss of he (x, )-posiion and is orienaion on he field. Moion Model When appling he moion updae, each x -1 X -1 needs o be moved according o he robo s moion. An esimae of he robo s moion u is usuall provided as odomer. In he B-Human robo conrol sofware, he walking engine provides odomer informaion, i.e. he offses since he las moion updae x,, and. However, since his informaion is onl based on he moion of he legs, and no on he real moion of he robo, i is prone o large errors. Therefore, large amouns of noise are added o he pose of each sample during he moion updae: x x 1 1 R 1 x sample(max( x,, nw sample(max(, x, nw 1 1 )) )) (1) 1 x,, w )) sample(max(, (2) R -1 is he roaion marix corresponding o -1. sample(x) is a funcion ha reurns a random value in he inerval -x,x]. All λ are facors ha scale he noise raio depending on he robo s moion and he curren weighing of he sample. λ + models noise along same ranslaional direcion. λ - describes he influence of moion in he orhogonal direcion. λ scales roaional noise based on he robo s roaion. λ d models roaional noise based on he robos ranslaion. And finall λ n and λ r scale ranslaional and roaional noise based on he relaive weighing of each sample. w defines how he weighing of an individual sample relaes o he average of all samples. I is defined as: d r 1 w w i max Mw i] 1, 0 2 (3) As a resul, samples wih a less han average weighing are moved even if he robo is no in moion a all, allowing he samples o move oward he real posiion of he robo. Sensor Model The image processing ssem recognizes poins on field lines and poins on edges beween he field and he goals and he beacons. All hese poins are on he heigh of he field. Therefore, i is possible o deermine heir posiion relaive o he camera b inersecing he ra saring in he camera cener hrough heir posiion in he image wih he ground plane. Since he posiion of he camera relaive o he ground plane is onl roughl known, he resuling relaive posiions of he poins are prone o high levels of noise. Since he vision ssem connecs neighboring poins, he orienaion and a minimal lengh of he field line or edge are known for mos of he poins. For each image frame, a fixed number of such poins is seleced b random (he se of observaions z ). These poins are used o deermine for each sample how well he pose of he sample maches he curren observaions, resuling in he weighing w of he paricle:

7 1: Algorihm_sensor_updae(z, x, e) : w (1) 2: for each p rel z do 3: cam x x p abs R m cam R ] 4: p model = closes_poin(p abs, e) x error 5: cam 1 1 R R p p error abs cam p model xerror error 6: w w gaussian(, ) gaussian(, ) h x h x 7: reurn w Each poin is projeced o he field, given he curren pose of he sample and he curren pose of he camera relaive o he robo (line 3). Then he closes corresponding poin in he field model is deermined (line 4). For his purpose, a number of ables were precompued (called he environmen e). The map (x, )-posiions on he field o he closes model poin. Tables exis for field lines, green/blue edges, and green/ellow edges each of hem in varians for edges of unknown orienaion, edges along he field, and edges across he field, and also wheher or no an edge is longer han a minimum lengh. The laer disincion helps o separae goal poins from beacon poins and poins on he hrow-in and penal marks from regular field lines. Figure 4a depics a able for mapping green/ellow edge poins wih unknown orienaion and of an lengh. rel rel rel a) b) Fig. 4: a) Depicion of a able mapping poins o he closes green/ellow edge. b) Samples generaed from green/blue edge poins. The difference beween he closes model poin and he projeced measured poin is roaed back o he coordinae ssem relaive o he camera (line 5). As a resul and given ha he opening angles of he camera are raher small, x error roughl corresponds o he disance error, and error corresponds o he bearing error. Boh error disances are ransferred back ino pixel disance errors b dividing hem b he forward disance o he measured poin plus he heigh of he camera above he ground. Please noe ha hese are rough approximaions of he calculaions ha would be necessar, bu since hese operaions are performed for each sample and for each seleced poin, he simplificaions were necessar o achieve real-ime performance on a compuer wihou a floaing poin uni. The weigh w is deermined b modeling he errors as Gaussian normal disribuions based on he compued error values and a sandard deviaion (line 6). Sensor Reseing Since he camera onl perceives a small par of he field a once, sensor reseing has o be done wih cauion. I is possible ha he observaions made b he robo mach wih several posiions on he field. Therefore, adding new samples alwas increases he risk ha he achieve he highes weighing for several frames and herefore arac he whole disribuion. While a large prevens he

8 disribuion from being o reacive, conservaive values for α slow and α fas (0.05 and ) are used o making sensor reseing a rare even. New samples are onl generaed from green/ellow and green/blue edge poins (i.e. goals and beacons), because field line poins are oo ambiguous. Since he robo does no alwas perceive such poins, a buffer of he previous poins recognized is mainained. To generae a new sample posiion, a buffer enr is seleced b random. Then a random poin on a corresponding edge in he field model is seleced. Aferwards, a random pose maching he measuremen s disance and roaion from ha poin is consruced. Figure 4b shows such random poses for green/blue edge poins, i.e. he resul from he blue goal and beacons. Ball Tracking A paricle filer for racking he ball aims o esimaes he curren veloci of he ball o enable he robo o anicipae fuure game saes, e.g. o make a goalie jump o he righ corner of is goal in case of a sho. An addiional effec of he applicaion of a filer is he smoohing of he ball posiion s esimae. The rough percepions of he ball are especiall when walking or moving he head fas quie nois and would cause he robo s pan-il head o jier and also make he acion selecion more unsable. For our applicaion, he ball sae b is a four-dimensional vecor (x,, v x, v ) T wih x and represening is posiion and v x and v represening is veloci. The ball posiion and veloci are racked in he robo s coordinae ssem. Moion Model When appling he moion updae, each b X -1 needs o be moved according o he robo s moion as well as o is own veloci, boh in relaion o he las execuion of he filer. Le (x, ) T be a vecor describing he ranslaional par of he robo moion and ΔR -1 be a marix describing he roaion of he coordinae ssem according o he robo s roaion. The ime beween wo execuions of he filer is called Δ. The scalar values λ v and λ serve as user-defined parameers for conrolling he amoun of uncerain added in each moion updae. The updae according o he veloci provides a preliminar resul (x p, p ) T : x p p x 1 1 v v x1 1 sample( v v sample( v v Through he addiion of a random erm, he uncerain of he posiion increases dependen on he curren veloci of he ball. Aferwards, he posiion is adaped o he robos moion: x R 1 x p p x 1 x 1, v, v 1 1 ) ) x sample( x, ) (, ) sample x Again, a erm of uncerain is added; his ime depending on he speed of he robo. Finall, he robo s moion has o be incorporaed in he ball veloci ogeher wih a erm of uncerain dependan on he absolue veloci: v v x R 1 v v x1 1 sample( v v sample( v v In addiion o his sraigh-forward model, anoher feaure for decreasing he ball posiion s variance has been implemened. Through ofen occurring hardl perceivable robo insabiliies, he sensing of he ball posiion is subjec of srong variaions which canno be disinguished from real ball moions. This migh produce and advance samples wih high speeds and hus le he disribuion become oo flucuaing. In fac, he ball is no moving mos of he ime during a humanoid robo soccer mach. This siuaion can be considered b marking a subse of all samples as non-movable. When generaing new samples (cf. subsecion Sensor Reseing), a subse of hese will receive a flag which prevens all updaes considering ball velociies. Through he consan resampling process, hese samples sabilize he disribuion in case of ling balls and don inerfere in case of real ball moion. x 1 x 1, v, v 1 1 ) ) (4) (5) (6)

9 Sensor Model To compue a weighing for each sample, is curren posiion is se in relaion o he currenl perceived ball posiion. If no ball is perceived, his sep is as well as he following resampling sep skipped. Le d o and α o be he disance and he angle o he observed ball and d b and α b he disance and angle o of he currenl processed ball sample, hen he weighing w b can be compued as follows: wb gaussian( do db, d ) gaussian( o b, ) (7) The implemenaion uses differen sandard deviaions σ d and σ α since mos noise occurs in he percepion of he disance o he ball; in general, he angle is perceived quie precisel. Sensor Reseing Since he ball is a unique feaure, i is in conras o self-localizaion quie eas o generae new samples b jus using he curren percepion ha is ofen close o he real sae of he ball. In domains of low noise, he percepion ofen even serves direcl as informaion for he laer acion selecion; a filering of he posiion is no needed. In our implemenaion, he robo alwas sores all ball percepions made during he las ime (e.g. wo seconds). Whenever a new sample needs o be generaed, wo percepions p 1 and p 2 (wih p 2 having been sored a a laer poin of ime han p 1 ) are randoml drawn from he se. From hese percepions, a veloci for he new sample migh be compued direcl. An acual posiion is deermined b using p 1 and he veloci as in he ball veloci updae equaion in subsecion Moion Model. The resampling of he ball racking filer srongl benefis from he possibili o add a dnamic number of new samples as described in he subsecion Enhancemens for Resampling. If he ball is no moving on he field for a longer ime, onl ver few or no new samples need o be replaced in he disribuion. When i sars moving (afer a kick), he disribuion needs o be adaped quie quickl. This mechanism is depiced in Fig. 5. In addiion, i needs o be menioned ha during a robo soccer mach siuaions occur, in which he robo has los rack of he ball compleel (e.g. afer having been fallen down). When perceiving he ball again, his resampling feaure also helps o reesablish a proper disribuion quie fas. Fig. 5: Number of new samples in a sequence of consecuive execuions of he ball racking algorihm. In a simulaed experimen, he ball has been immediael replaced hree imes (frames 20, 50, and 80). The number of new samples alwas immediael increases and soon afer drops when he disribuion fis he new sensor readings. A oal of 40 samples has been used; his means ha abou 25% of he whole se ge replaced. Aferwards, he ball was moved around he field (frame 100 and following). Again, some comparabl lower peaks indicae changes of he moion direcion. Experimenal Resuls To evaluae he approaches described in his paper, several experimens have been carried ou. One of he humanoid robos and a ball were placed and moved on a sandard field (see Fig. 6a). To measure he correcness and precision of he robo s esimaes, an environmen for providing ground ruh informaion has been se up. A camera, insalled four meers above he field, provides a complee overview of he scenario. Is images are processed b he vision ssem of B-Smar 11], a RoboCup

10 eam from he Small Size League, where a global vision is he curren sandard. To idenif he robo and is orienaion, an addiional marker had o be placed on op of is head (see Fig. 6b). a) b) Fig. 6: The experimenal seup. a) The robo on a sandard soccer field. b) A close view on he robo carring he marker for racking. Self-Localizaion To evaluae he self-localizaion, he robo was conrolled around on he field using a josick for slighl more han wo minues, while he robo s head was coninuousl urning from lef o righ and back. During his ime, 2000 images were processed and he robo s esimae of is posiion was updaed. Figure 7 shows he rajecor raveled as well as he rajecor according he robo s odomer calculaion (cf. Fig. 7a) and when inegraing exernal sensor readings (cf. Fig. 7b). a) b) Fig. 7: Experimen conduced for self-localizaion. The real rajecor he robo walked wih up o 5cm/s is shown in blue. a) The rajecor onl based on odomer calculaion (in black). b) The esimaed rajecor based on he self-localizaion module (in black) Fig. 8: Posiion errors in mm during he 2000 frames of he experimen depiced in Fig. 7b.

11 In he experimen, he robo s pose was esimaed using 100 paricles. Five edge poins were used during he sensor updae. was quie large (0.9) so ha differences in he weighs of he paricles are kep small, resuling in a raher sable disribuion of paricles. During he 2000 frames of he experimen he mean disance error was 16.9 cm, i.e. 3% of he lengh of he field or 5.6% of is widh. Fig. 8 shows he disribuion of he error over ime. In fac, he deviaion is picall higher when he feaures used for localizaion are far awa or ou of sigh. The former is for insance he case when he robo faces he goal on he oher half of he field, while he laer happens when he robo is close o he sidelines and simpl looks over hem. In boh cases, he robo has mainl o rel on odomer onl, which is no ver precise, as shown in Fig. 7a. In a second experimen he same daa was fed ino he self-localizaion ssem, bu 500 frames were skipped, simulaing a kidnapped robo siuaion (cf. Fig. 9). I ook he robo abou 20 seconds o reesablish is posiion. Alhough his seems o be quie a while, please noe ha he robo s head could onl pan back and forh abou six imes during his period of ime. Since kidnapping of a robo happens rarel during games, he parameers of he self-localizaion mehod are uned owards sabili raher han quick adapaion Fig. 9: Experimen on a kidnapped robo. Using he same experimenal daa as shown in Fig. 8, bu skipping he frames 500 o Disance error again in mm. Ball Tracking To measure he precision of he ball racking, he robo has been placed a he cener circle of he field and he ball has been moved consanl around one half of he field. This has been done via a hin pole which is no perceivable b he robo s vision ssem. The whole rajecor of he ball is depiced in Fig. 10a. During he experimen, he robo s head was in is sandard racking mode for soccer maches, i.e. he robo ries o keep he ball in sigh mos of ime, bu occasionall looks around o keep localized. To avoid evaluaion errors which resul from changes of he ball veloci during a localizaion phase, we onl consider so-called complee racks. We define a rack as a sequence of ball observaions which is a leas wo seconds long and does no have an gaps (phases wihou an percepion of a ball) longer han 300ms. In Fig. 10b, an example rack is shown. a) b) Fig. 10: Experimen conduced for ball racking: a) The rajecor, along which he ball was moved and perceived b he ground ruh vision, is depiced as a gra line. b) A single rack observed b he robo. The real moion is again depiced in gra. The single percepions are shown as red dos. The black line shows he esimaed ball rajecor.

12 During he experimen, he ball was kep in moion all he ime. The average op speed of all racks was 1.27 m/s, he absolue op speed during he experimen was 2.66 m/s. This resuled in a mean posiion error of he ball of 26.6 cm. The mean veloci error was 0.28 m/s, he mean error of he ball moion s direcion was This appears o be quie significan, bu mos racks included srong changes of he ball direcion, which lead o quie high errors during he adapion phase of he filer. Some racks had been quie sraigh wih onl minimal direcional changes (e.g. he one in Fig. 10b); in hese cases, he mean error was 18.6 onl. This ball racking implemenaion has been used b he eam B-Human a RoboCup For all maches, he number of samples was se o 40 because of limied compuaional resources. Therefore, all experimens have been made wih he same amoun of samples. Conclusion and Fuure Work In his paper, we described he applicaion of paricle-filer algorihms in a humanoid soccer scenario. The experimenal resuls show, ha he enable even a percepual limied robo o compue reasonable sae esimaes. As afore-menioned, he implemenaion has alread been used in a real robo compeiion. While having some of he weakes robos off all eams, B-Human was sill able o reach he quarer finals wih a remarkabl well resul in he previous round robin group: hree wins and wo draws wih a oal goal raio of 8-1. The presened is inended o be kep for fuure applicaion. Neverheless, more compuing power would conribue o achieve beer resuls; a more complex vision module could provide more significan feaures for self-localizaion (e.g. field line crossing or goal poss) which enable a more deailed sample weighing or conribue o a beer generaion of new samples. The racking of oher robos is also a opic ha has no been reaed b us so far. The ransfer of he algorihms o his issue will be an ineresing subjec of invesigaion in he near fuure. Addiionall, cooperaive sae esimaion in a eam of humanoid robos becomes more imporan he larger he eams are. References 1] Kiano, H., Asada, M.: RoboCup Humanoid Challenge: Tha s One Small Sep for A Robo, One Gian Leap for Mankind, Inernaional Conference on Inelligen Robos and Ssems, Vicoria, ] D. Fox, W. Burgard, F. Dellaer, and S. Thrun: Mone Carlo Localizaion: Efficien Posiion Esimaion for Mobile Robos, Proc. of he Naional Conference on Arificial Inelligence, ] Röfer, T., Laue, T., Thomas, D.: Paricle-filer-based self-localizaion using landmarks and direced lines, RoboCup 2005: Robo Soccer World Cup IX, Lecure Noes in Arificial Inelligence (LNCS 4020), Springer, ] Laue, T., Röfer, T.: Geing Uprigh: Migraing Conceps and Sofware from Four-Legged o Humanoid Soccer Robos, Proceedings of he Workshop on Humanoid Soccer Robos in Conjuncion wih he 2006 IEEE Inernaional Conference on Humanoid Robos, Genova, ] T. Röfer, C. Budelmann, M. Frische, T. Laue, J. Müller, C. Niehaus, and F. Penqui: B-Human - Team Descripion for RoboCup 2007, RoboCup 2007: Robo Soccer World Cup XI Preproceedings, RoboCup Federaion, ] J.-S. Gumann and D. Fox: An Experimenal Comparison of Localizaion Mehods Coninued, Proceedings of he IEEE/RSJ Inernaional Conference on Inelligen Robos and Ssems (IROS'02), Lausanne, Swizerland, Ocober ] H. Srasda, M. Bennewiz, and S. Behnke: Muli-Cue Localizaion for Soccer Plaing Humanoid Robos, RoboCup 2006: Robo Soccer World Cup X, Lecure Noes in Arificial Inelligence (LNCS 4434), Springer, ] C. Kwok and D. Fox: Map-based muliple model racking of a moving objec, RoboCup 2004: Robo Soccer World Cup VIII, Lecure Noes in Arificial Inelligence (LNCS 3276), Springer, ] R.E. Kalman: A new approach o linear filering and predicion problems, Transacions of he ASME Journal of Basic Engineering 82, ] S. Thrun, W. Burgard, D. Fox: Probabilisic Roboics, MIT Press, ] A. Burchard, K. Cierpka, S. Frisch, N. Göde, K. Huhn, T. Kirilov, B. Lassen, T. Laue, M. Miezal, E. Laif, M. Schwaring, A. Seekircher, and R. Sein: B-Smar - Team Descripion for RoboCup 2007, RoboCup 2007: Robo Soccer World Cup XI Preproceedings, RoboCup Federaion, 2007.

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