Improved Rao-Blackwellized H filter based mobile robot SLAM

Transcription

1 Ocober 216, 23(5): The Journal of China Universiies of Poss and Telecommunicaions hp://jcup.bup.edu.cn Improved Rao-Blackwellized H filer based mobile robo SLAM Luo Yuan, Su Qin (), Zhang Yi, Zheng Xiaofeng Research Cener of Informaion Accessibiliy and Roboics, Chongqing Universiy of Poss and Telecommunicaions, Chongqing 465, China Absrac For he problems of esimaion accuracy, inconsisencies and robusness in mobile robo simulaneous localizaion and mapping (SLAM), a novel SLAM based on improved Rao-Blackwellized H paricle filer (IRBHF-SLAM) algorihm is proposed. The ieraed unscened H filer (IUHF) is uilized o accuraely calculae he imporance densiy funcion, repeaedly correcing he sae mean and he covariance marix by he ieraive updae mehod. The laser sensor s observaion informaion is inroduced ino sequenial imporance sampling rouine. I can avoid he calculaion of Jacobian marix and linearizaion error accumulaion; meanwhile, he robusness of he algorihm is enhanced. IRBHF-SLAM is compared wih FasSLAM2. and he unscened FasSLAM (UFasSLAM) under differen noises in simulaion experimens. Resuls show he algorihm can improve he esimaion accuracy and sabiliy. The improved approach, based on he robo operaion sysem (ROS), runs on he Pioneer3-DX robo equipped wih a HOKUYO URG-4LX (URG) laser range finder. Experimenal resuls show he improved algorihm can reduce he required number of paricles and he operaing ime; and creae online 2 dimensional (2-D) grid-map wih high precision in differen environmens. Keywords SLAM, Rao-Blackwellized paricle filer, ieraed unscened H filer, ROS 1 Inroducion SLAM was firs proposed by Smih and Cheeseman in 1988, uilized o solve he problem of mobile robo s localizaion and mapping. The problem can be described in a way ha a mobile robo perceives an unknown environmen by he equipped sensors, and hen gradually builds a map of he surrounding environmen while using he map o esimae is pose [1]. I is he key in he roboic field o perform auonomous asks and has araced increasing aenion wih broad applicaion prospec [2]. SLAM algorihm based on Rao-Blackwellized paricle filer (RBPF) [3] showed by Monemerlo e al. firs is named FasSLAM1. as well, decomposing he problem ino he robo pose esimaion and map esimaion. Gaussian disribuion consruced by exended Kalman filer (EKF) is used as proposal disribuion in FasSLAM2., which adds he robo laes observaion Received dae: Corresponding auhor: Su Qin, grace_suqin@163.com DOI: 1.116/S (16)657-2 informaion. Grisei e al. represened a grid-based SLAM wih RBPF by adding he curren laser scan daa under he grid map model o avoid he paricle degradaion and improve he esimaion accuracy o some exen [4]. However, hese algorihms suffer from numerous problems and hey are a consequence of he derivaion of Jacobian marix and he linear approximaions of he nonlinear funcions. Therefore, EKF-SLAM proposed by Mallios e al. uilized wo EKFs [5] for SLAM. An improved FasSLAM described by Wang e al. used ieraed EKF o calculae proposal disribuion while modifying resampling o avoid paricle degradaion [6], so he esimaion accuracy was improved. However, EKF-SLAM is weak o linearizaion. To overcome hese drawbacks, UFasSLAM represened by Kim e al. improved he SLAM accuracy by uilizing unscened ransform (UT) o esimae he ransiion probabilisic densiy and updaing he robo sae and corresponding feaure landmarks [7]. A square roo unscened Kalman filer (SRUKF) based SLAM algorihm described by Zhao e al. used he square roo unscened paricle filer (SRUPF) o esimae robo sae and he

2 48 The Journal of China Universiies of Poss and Telecommunicaions 216 SRUKF o esimae relevan landmarks [8]. Neverheless, all enormously amelioraive performances are based on he hypohesis of known noise saisics and precise sysem model, limiing pracical applicaion. As a resul, H filer (HF) served as an efficien approach o solve he roublesome shorcomings [9 1]. Ahmad e al. researched on he convergence of HF based SLAM and pu forward he expansion of variance mehods o furher improve he performance of his algorihm under much noise [11]. Pham e al. proposed a compressed HF based SLAM algorihm o improve he sabiliy and decrease compuaional complexiy [12]. In order o apply RBPF-SLAM o large-scale environmens, a new Jacobian-free RBPF-SLAM algorihm [13] proposed by Song e al. using 5h-order conjugae unscened ransform o obain a beer disribuion of he paricle filer (PF). To furher alleviae he noise influence on performance and improve he esimaion accuracy as well as robusness of he RBPF-SLAM algorihm, IRBHF-SLAM algorihm is advanced. The algorihm uilizes IUHF o accuraely calculae he imporance densiy funcion, inroducing he laser sensor s observaion informaion ino sequenial imporance sampling rouine. I avoids he calculaion of Jacobian marix and linearizaion error accumulaion. Meanwhile, he robusness of he algorihm is enhanced. IRBHF-SLAM is compared wih FasSLAM2. and UFasSLAM under differen noises in simulaion experimens. Resuls show he algorihm can improve he esimaion accuracy and sabiliy. The improved approach, based on he ROS, runs on he Pioneer3-DX robo equipped wih a URG laser range finder. Experimenal resuls show he improved algorihm can reduce he required number of paricles, lower operaing ime, and creae online 2-D grid-map wih high precision in differen environmens. The remainder of he paper is organized as follows. The basic RBPF-SLAM framework is reviewed in he nex secion. Sec. 3 presens he IRBHF-SLAM. Simulaion resuls and performance analysis of IRBHF-SLAM are compared o ha of FasSLAM2. and UFasSLAM in Sec. 4. Finally, Sec. 5 concludes he work of his paper. 2 RBPF-SLAM framework The purpose of SLAM is o achieve a robo s locaion and mapping simulaneously. To explain SLAM algorihm for a robo, suppose he robo kinemaic model and environmen observaion model as x = f ( x 1, u) + w (1) z = h( x ) + v (2) where x is he sae vecor composed of he robo pose and he posiion of he landmarks. u is he conrol inpu daa in he ime inerval [ 1, ]. z is he observaion measuremen. Boh process noise w and measuremen noise v are Gaussian whie noise wih variance Q and R respecively. f () and h() are sysem funcion and observaion funcion. The core idea of he RBPF-SLAM is o esimae robo s x = x x x given a se poenial rajecories 1: [ ] of hisorical observaions z1: = [ z1 z2... ] odomeer conrol inpu daa = [... ] z and is u u u u, 1: namely poserior p( x1: z1:, u 1: 1), hen o uilize he poserior o calculae a join poserior probabiliy disribuion over map Θ and rajecories x 1: p( x, Θ z, u ) = p( x z, u ) pθ ( x, z ) (3) 1: 1: 1: 1 1: 1: 1: 1 1: 1: Eq. (3) based on condiional independence propery of SLAM algorihm permis us o calculae availably join poserior probabiliy disribuion p( x1:, Θ z1:, u 1: 1). Meanwhile, in accordance wih he knowledge of x 1: and z 1:, poserior probabiliy based on maps pθ ( x1:, z 1: ) can be calculaed effecively. The algorihm uilizes PF o esimae robo s poserior probabiliy over is rajecories p( x z, u ). Every paricle represens a poenial 1: 1: 1: 1 rajecory. The Kalman filers (KFs) are used o updae he maps over he rajecories x1:and he observaions z 1:. 3 IRBHF-SLAM framework The HF is an available approach o deal wih he non-gassian measuremen noise. Wih max-min crierion adoped, i is unnecessary o know he prior knowledge of any saisics assumpions of he process noise and measuremen noise. The purpose of HF is o ensure he minimizaion of he esimaion error in a variey of he noise disurbances while enhancing he sysem robusness. Hence IUHF is embedded ino RBPF algorihm o accuraely calculae he imporance densiy funcion of PF in he imporance sampling sep, and curren environmenal observaion informaion from sensors is added ino he imporance densiy funcion. Therefore, IRBHF-SLAM is inroduced, uilizing IUHF o accuraely

3 Issue 5 Luo Yuan, e al. / Improved Rao-Blackwellized H filer based mobile robo SLAM 49 calculae he imporance densiy funcion, repeaedly correcing he sae mean and he covariance marix by he ieraive updae mehod. The aim is o avoid degradaion of he paricles and increase consisency while improving he accuracy of he esimaed pah of he robo in beer performance and more robusness. The key of he proposed algorihm is he imporance sampling including wo seps: unscened paricles predicion and sae updae. The imporance densiy funcion is expressed as a Gaussian disribuion q( x x, z, u ) = N ( x, P) (4) 1 1 where P is he covariance of he paricle. 3.1 Imporance sampling Unscened paricles predicion 1) In order o implemen IRBHF-SLAM, combining he conrol inpu u 1 and he process noise covariance Q, he sae x and covariance P of paricle are ˆ m1 1 augmened respecively as ˆ a x 1 xˆ 1 = a P 1 P 1 = Q where m is he index of some paricle, x and ˆa m 1 (5) a P 1 are he augmened vecor and he augmened sae covariance marix of mh paricle a ime 1, respecively. x and P represen he sae ˆ m1 1 esimaion and is covariance of he robo pose respecively. 2) (+1) sigma poins are deermined as follows The esimaion uncerainy is calculaed by a group of symmerical sigma poins represening he Gaussian probabiliy densiy. Sigma poins are defined as a xˆ 1 ; a[ s] a a χ ˆ 1 = x 1 + ( ( n + κ ) P 1 ) ; s = 1,2,... n (6) s a a xˆ 1 ( ( n + κ ) P 1 ) ; s = n + 1,..., sn where κ R is a scaling facor and influence he disribuion of sigma poins in he viciniy of he sample a ( ) 1 mean. ( n κ ) + P is he sh row or column of he marix squares roo of ( n κ ) s + P. a 1 3) The predicion of paricle sae and covariance a[ s] Subsiuing a series of sigma poins χ ino 1 moion model using he curren conrol u and χ [ s] 1 can be obained as [ s] a[ s] χ = f ( χ, u ) (7) 1 1 where χ [ s] 1 is he sigma poin se of he robo sae calculaed hrough nonlinear moion model funcion. The predicions of paricle sae mean and covariance marix are compued as = s [ s] 1 ω 1 xˆ χ (8) s [ s] [ s] Τ ˆ ˆ 1 ω s ω P = χ x χ x + Q (9) where he weighed is deermined by κ ; s = s n+ κ ω = 1 ; s = 1,2,..., 2( n+ κ) Sae updae (1) Combining he robo pose sae wih feaure posiion vecor obained from observaion (suppose he jh feaure is observed), augmened predicion paricle sae is obained as xˆ m a 1 x 1 = u 1 (11) a P 1 P 1 = = R The symmerical sigma poins are generaed as ( ( n κ ) ) χ a [ s ][ m ] a [ m ] a [ m ] a [ m ] 1 = 1 1 ± + 1 x x P s (12) where he definiion of each parameer as in Eq. (6). Sigma poins is uilized o predic observaion a s m ( 1 ) Z =h χ (13) = s a[ s] 1 ω h 1 z ( χ ) (14) where Z is he sigma poins calculaed by [ m ] non-linear observaion equaion, including he observaion noise componen. z is observaion predicion for 1 environmen feaure of mh paricle. The measuremen covariance marix and is crosscorrelaion coefficien covariance marix can be acquired

4 5 The Journal of China Universiies of Poss and Telecommunicaions 216 wih he predicable sigma poins zz s Τ 1 = ω 1 1 P Z z Z z (15) xz s a[ s] T 1 = ω P χ x Z z (16) Therefore, he robo sae a ime is updaed as follows ( ) xz zz 1 ˆ = x ˆ x P R P z z (17) xz 1 xz Τ e, 1 1 P = P P P R P P (18) where xz xz Τ R + P 1 P 1 Re, = xz 2 1 γ + P I P 1 (19) where he derivaion of parameer γ is as follows. Since he parameer γ should be compued o adjus he marix P o posiive definie, i can be easily shown 1 ha 1 1 Τ 1 P = P + H R H 2 γ I > (2) T 1 γ max( 1 ) > + P H R H (21) where max( A ) is he maximum eigenvalue of he marix A. The value of γ can be seleced as γ = α max( P + H R H ) (22) γ 2 1 T Subsiue H = P P ino he Eq. (22) o derive T 1 xz 1 1 T ( ) = α P + P P R P P (23) xz 1 1 xz max where he scalar parameer α is larger han 1. The ieraion crierion is denoed as zˆ =h x ˆ (24) ( d ) d,, ɶz = z z ˆ (25) d, d, d, ɶx = xˆ x ˆ (26) d, d, d 1, Τ Τ 1 Τ 1 ɶ ɶ d, d, d, d, d, d, d 1, x ˆ P xˆ + zˆ R zˆ < z R z (27) where z d, represens he measuremen value a ime. d is he ieraive number less han 3 in general. [ m ] ˆ m x and P are obained from Eqs. (17) and (18) respecively. Then hey are subsiued ino he Eqs. (24) (26). And Eq. (27) is calculaed o judge wheher or no i works. Reurn o Sec o coninue o execue filering if i does and d is less han 3. Oherwise, he ieraion is erminaed and reurn he sae value xˆ m and he covariance P. [ m ] If muli-feaure poins are observed a some ime, i can be defined as xˆ = xˆ and P P, hen repea he 1 1 = above seps. Afer accomplishing he sae updae, imporan sampling sep is execued as x N ( xˆ, P ) (28) 3.2 The procedure of IRBHF-SLAM algorihm The procedure of he designed IRBHF-SLAM algorihm is summarized as follows: Sep 1 Iniializaion. The relevan parameers are denoed, such as he number of paricles N, he iniial N x, P, process noise Q, disribuion of robo sae ( ) measuremen noise R, sigma ieraion number d, α, γ, N, κ, ec. Then N paricles are capured from ( x, P ) namely x m N ( x, P ). For each ime insan For m = 1,2,..., N do Sep 2 Imporance sampling. Subsep 1 Perform he algorihm. Predic paricles sae: predic robo sae mean x ˆ m and is covariance 1 1 P wih u, Q and f () via he Eqs. (5) (1). Subsep 2 If environmen informaion is no observed, go o Sep 5; oherwise, coninue wih Subsep 3. Subsep 3 Updae he sae of every prediced paricle wih x ˆ m, P and z via he Eqs. (11) (27), and obain he approximae proposal disribuion P. ) N ] ( xˆ[ m, Subsep 4 Sample from updaed proposal disribuion via he Eq. (28). Sep 3 Calculae and normalize he paricle weighs as ˆ ˆ M m m p( z Θ 1, x ) p( x x 1, u 1) ω = ω 1, q( xˆ ω = 1 x, z, u ) 1: 1 1: 1 Sep 4 Resample. Decide wheher or no a resampling sep should be performed over he number of he effecive N 2 paricles Neff = 1 ( ɶ ω ) i= 1. While N eff drops below a given hreshold value N, resample from wih probabiliy ; oherwise, go o Sep 5. [ m ] ω Sep 5 Compue and updae maps robo pose x m and observaions z. 4 Simulaion resuls and analysis 4.1 Simulaion using Malab h i= 1 Θ in line wih To verify he superioriy of he proposed algorihm, IRBHF-SLAM is developed and compared wih

5 Issue 5 Luo Yuan, e al. / Improved Rao-Blackwellized H filer based mobile robo SLAM 51 FasSLAM2. and UFasSLAM for he same simulaion condiion. For he compuaional simplificaion, he daa associaion is assumed o be known. The parameers are se as follows: he experimenal area is recangular shaped rajecories of 1 m 1 m, including 117 landmarks and 55 waypoins. The robo runs from he global coordinae poin (, ) wih a couner-clockwise direcion. The vehicle has a.8 m wheel base and is equipped wih a range-bearing sensor wih a maximum deecion range of 8 m and a 18 fronal field-of-view. The robo moves a a speed.3 m/s and wih a maximum seering angle of 2. Sysemaic sampling inerval is T =.1 s. Observaion scans are obained a.5 Hz. Ten paricles are used o observe he esimae accuracy. In IUHF, γ = 1, α = 1.1 and d =2. Three algorihms are esed on he hardware wih 3.3 GHz Inel Core i3 CPU and 3.19 GB RAM under he above simulaion environmen respecively. A conrasive quaniaive analysis of he performance is carried ou. Fig. 1 shows simulaion resuls of hree algorihms wih known Gaussian noise, i.e, he process noise is σ =.3 m/s, σ = 1 ; and he observaion noise is v θ σ =.5 m in range and σ = 1 in bearing. r ξ (c) IRBHF-SLAM Fig. 1 Esimaed robo pah and esimaed landmark wih rue robo pah and rue landmark wih known Gaussian noise From Fig. 1, i is clearly seen ha wih known Gaussian noise, he esimaed pah from FasSLAM2. is sill far away from robo acual pah, showing a serious inconsisency. By applying UT, he esimaed robo pah of UFasLAM is much mismached wih he acual pah. Moreover, due o he good esimaion propery, he esimaed robo pah of IRBHF-SLAM quie maches wih rue pah wih high esimaion accuracy. To evaluae he performance of algorihms, hey are measured over 2 Mone Carlo runs. The posiion error of robo wih respec o ime is used as a way of evaluaion. I is shown in Fig. 2. (a) FasSLAM2. Fig. 2 Posiion error wih respec o ime wih known Gaussian noise (b) UFasSLAM As is shown as Fig. 2, IRBHF-SLAM ouperforms he ohers, since IRBHF-SLAM can esimae he mean and covariance wih higher accuracy and consisency han FasSLAM2. and UFasSLAM. The posiion error for IRBHF-SLAM is less han 1 m, however, he posiion error of posiion for UFasSLAM is less han 2.3 m, and he posiion error for FasSLAM2. is up o 4.5 m. To indicae superioriy of IRBHF-SLAM under

6 52 The Journal of China Universiies of Poss and Telecommunicaions 216 non-gaussian noise condiion, he measuremen noise is supposed o be non-gaussian noise drawn from a Gamma disribuion wih non-gaussian and non-zero mean noises. However, he process noise is he same as Gaussian noise. Fig. 3 describes he simulaion resuls of algorihms in he above condiion. depiced in Fig. 4. Fig. 4 Posiion error wih respec o ime wih non-gaussian noise (a) FasSLAM2. (b) UFasSLAM As can be seen from he above, under he errible noise environmen, wih he good robusness for exernal environmen noise, he posiion error for IRBHF-SLAM remains less han 2 m sably. On he conrary, he reason why he posiion error for UFasSLAM and FasSLAM2. come o 4.2 m and 6.8 m respecively is ha boh of hem are exremely vulnerable wihou he hypohesis ha he noises are known whie Gaussian disribuion. Meanwhile, he margin of error of IRBHF-SLAM flucuaes smaller han ha of ohers, demonsraing he significan sabiliy. To evaluae he performance of algorihms, he roo mean square error (RMSE) of posiion is used as a way of evaluaion. RMSE and average elapsed ime (AET) of wo simulaions are lised in Table 1. As can be seen, RMSE of posiion for IRBHF-SLAM is he smalles, he nex is UFasSLAM. Adding UT, he AET for IRBHF-SLAM is almos he same as ha of UFasSLAM while slighly longer han ha of FasSLAM2.. Table 1 Comparison of simulaion experimen daa for 3 algorihms Simulaion environmen Wih known Gaussian noise Wih non-gaussian noise Algorihm RMSE/m AET/s FasSLAM UFasSLAM IRBHF-SLAM FasSLAM UFasSLAM IRBHF-SLAM (c) IRBHF-SLAM Fig. 3 Esimaed robo pah and esimaed landmark wih rue robo pah and rue landmark wih non-gaussian noise The corresponding posiion error wih respec o ime is To furher demonsrae opimum robusness of he improved algorihm under diverse noise condiions, he process noise is assumed as σ =.3 m/s, σ = 1, which is Gaussian noise. The measuremen noises of each simulaion are as 1) The measuremen noise is Gaussian noise, lised as σ r1 =.3 m, σ ξ1 =.7 ; σ r2 =.6 m, σ ξ2 =.9. v θ

7 Issue 5 Luo Yuan, e al. / Improved Rao-Blackwellized H filer based mobile robo SLAM 53 2) The measuremen noise is wrongly considered as Gaussian noise, lised as σ r3 =.2 m, σ ξ3 = 1 ; σ r4 =.3 m, σ ξ4 = 2. 3) The measuremen noise is non-gaussian noise, drown from a Weibull disribuion (WB) and a Bae disribuion (BB) respecively. For each se of measuremen noise, hree algorihms are esed 1 imes in simulaion. RMSE for robo posiion and heading as he evaluaion crieria is shown in Fig. 5. To prove he performance of IRBHF-SLAM when he differen numbers of paricles are uilized, i.e. he numbers of paricles are se as 5, 1, 2, 4 and 8. The process noise is σ =.3 m/s and σ = 3 ; he measuremen noise is v θ σ =.3 m, σ =.1. Every algorihm is r ξ performed 1 imes. Then simulaion resuls are shown in Fig. 6. (a) RMSE of posiion (a) RMSE of posiion (b) RMSE of heading Fig. 5 RMSE of pose wih differen measuremen noise for hree algorihms In Fig. 5, he line bars represen he sandard deviaion for RMSE and he columns represen he mean for RMSE. Wih he increase of measuremen noise, mean and sandard deviaion for RMSE of robo pose esimaion increase gradually, whereas he rae of increase for IRBHF-SLAM is relaively slower and lower han ha of ohers. Therefore, IRBHF-SLAM possesses he higher esimaion accuracy, srong abiliy of noise suppression and robusness. (b) RMSE of heading Fig. 6 RMSE of pose wih differen number of paricles for hree algorihms Wih he number of paricles increasing, RMSE of robo posiion esimaion and heading esimaion for algorihms are gradually reduced, ha is, he posiion esimaion accuracy is increasingly higher. Therefore, o achieve he consisency of pose esimaion accuracy, he required number of paricles for IRBHF-SLAM is fewer han ha of ohers, indicaing he high-qualiy paricles are able o express robo s rajecories precisely. As a resul, IRBHF-SLAM can use fewer paricles o achieve higher accuracy and guaranee compuaional efficiency.

8 54 The Journal of China Universiies of Poss and Telecommunicaions Implemenaion of IRBHF-SLAM on ROS Gmapping 1 is an implemenaion of he RBPF-SLAM approach and open source ready-o-use algorihm available in he ROS [14]. In order o implemen he IRBHF-SLAM algorihm compared he performance wih RBPF-SLAM, he original Gmapping package is direcly modified. The experimens are performed using a Pioneer3-DX robo equipped wih a URG laser range finder and a PC wih 2.9 GHz Inel Core i5 CPU wih 4 GB RAM. The sysem of PC is 12.4 Ubunu Linux wih ROS of Hydro version. Pioneer3-DX robo moves a he speed of.3 m/s and i is driven by a joysick. 2-D grid maps wih he resoluion of 5 cm 5 cm are consruced wih odomeer conrol inpu informaion and online laser daa informaion in real ime and displayed in he Rivz which is a visualizaion ool in he ROS. Environmen 1 The firs experimen is execued in he arificial environmen. The size of he environmen is abou 1 m 15 m. Wih he condiion ha 8 paricles are uilized o encode robo pose and he corresponding laser scan, he maps capured form wo algorihms based on he odomeer daa provide by robo and laser daa are showed in Fig. 7. I is easily seen ha he map creaed by RBPF-SLAM reveals a bi of inconsisencies, such as 1, 2, 3 in Fig. 7(a), alhough he local srucures of he map show grea accuracy. The reason why he phenomenon appears is ha in spie of RBPF-SLAM adops moion model as he proposal disribuion and adds he laes observaion from laser senor, he proposed disribuion canno accuraely express robo poserior probabiliy disribuion, hus lowering he robo esimaion accuracy. On he conrary, in he imporance sampling procedure of RBPF, IRBHF- SLAM applies measuremen updaes of he IUHF o design precisely he imporance densiy funcion and inegraes he observaion informaion of laser sensor scan maching, leading sampling paricles concenraing in he high observaion likelihood area. Hence he furher improved performance of sae esimaion accuracy conribues o he creaed map maching high wih acual environmen framework. Environmen 2 Anoher experimen is carried ou in he firs floor of he Research Cener of Informaion Accessibiliy Projec and Roboics, Chongqing Universiy of Poss and Telecommunicaions. The size of his environmen is abou 2 m 3 m. The maps obained by wo algorihms are depiced in Fig. 8. (a) Map buil by RBPF-SLAM (a) Map buil by RBPF-SLAM (b) Map buil by IRBHF-SLAM Fig. 7 Map of Environmen 1 from RBPF-SLAM and IRBHF-SLAM 1 Gerkey B. Slam_gmapping. (21-8-5).[ ]. hp://wiki.ros.org/slam_gmapping (b) Map buil by IRBHF-SLAM Fig. 8 Map of Environmen 2 from RBPF-SLAM and IRBHF-SLAM

9 Issue 5 Luo Yuan, e al. / Improved Rao-Blackwellized H filer based mobile robo SLAM 55 When environmen is lager, he resuling map in Fig. 8(a) buil by RBPF-SLAM wih 2 paricles shows obvious inconsisencies, such as 1, 2 and 3. Whereas, he high consisen map in Fig. 8(b) creaed by IRBHF-SLAM wih only 1 paricles indicaes he improved algorihm can enhance he esimaion precision for SLAM and avoid paricle degradaion, which are a consequence of he fac i can provide precise predicion and simulaneously keeps he robo pose uncerainy in he poserior. In addiion, since he paricles almos disribue in he high likelihood field, he imporance facors of paricles are exraordinarily approximae, alleviaing he difference of he variance of he imporance facors of paricles, increasing he number of imporance paricles, mainaining he paricle diversiy. To validae IRBHF-SLAM can reduce he required number of paricles as well as he elapsed ime, experimens are operaed in Environmen 12 using wo algorihms for 1 imes. Table 2 compares he number of paricles (NOP) and AET when he same consisency map is creaed wih wo algorihms. As can be seen in Table 2, compared wih RBPF-SLAM, he modified algorihm is able o creae high accuracy maps using fewer paricles, while reducing he AET, for he reason ha wih fewer paricles used, he compuaional complexiy is lower, which conribues o less running ime, hereby improving he efficiency of he sysem. Table 2 Parameers lis when building he same consisency map Environmen Algorihm NOP AET/s 1 RBPF-SLAM IRBHF-SLAM RBPF-SLAM IRBHF-SLAM Conclusions An IRBHF-SLAM algorihm is proposed in his sudy o enhance he robusness for he errible noises as well as he esimaion accuracy. This algorihm uilizes IUHF o accuraely calculae he imporance densiy funcion, and embed he laser sensor s measuremen daa ino sequenial imporance sampling rouine. The improved algorihm is esed in simulaion experimens compared wih FasSLAM2. and UFasSLAM. Resuls show he algorihm can improve he esimaion accuracy and noise robusness. The improved approach is verified in Pioneer3-DX robo wih a URG laser range finder compared wih RBPF-SLAM. High-precision 2-D grid-map is creaed online in differen environmens, demonsraing he feasibiliy and superioriy of IRBHF-SLAM. Acknowledgemens This work was suppored by he Scienific and Technological Research Projec Funds of Chongqing Municipal Educaion Commission (KJ13512), he Projec Funds of Chongqing Science and Technology Commission (csc215jcyjb241). References 1. Chen B F, Cai Z X, Hu D W. Approach of simulaneous localizaion and mapping based on local maps for robo. Journal of Cenral Souh Universiy of Technology, 26, 13(6): Chen C, Cheng Y H. Simulaion research of SLAM algorihm based on ieraed unscened Kalman filer. Journal of Sysem Simulaion, 212, 24(8): (in Chinese) 3. Monemerlo M, Thrun S, Koller D, e al. FasSLAM: a facored soluion o he simulaneous localizaion and mapping problem. Proceedings of he AAAI Naional Conference on Arificial Inelligence (AAAI 2), Jul 28Au 1, 22, Edmonon, Canada. Menlo Park,CA, USA: American Associaion for Arificial Inelligence, 23: Grisei G, Sachniss C, Burgard W. Improved echniques for grid mapping wih Rao-Blackwellized paricle filers. IEEE Transacions on Roboics, 27, 23(1): Mallios A, Ridao P, Ribas D, e al. EKF-SLAM for AUV navigaion under probabilisic sonar scan-maching. Proceedings of he 21 IEEE/RSJ Inernaional Conference on Inelligen Robos & Sysems (IROS 1), Oc 1822, 21, Taipei, China. Piscaaway, NJ, USA: IEEE, 21: Wang H J, Wang J, Liu Z Y. Fas simulaneous localizaion and mapping based on ieraive exended Kalman filer proposal disribuion and linear opimizaion resampling. Journal of Elecronics and Informaion Technology, 214, 36(2): (in Chinese) 7. Kim C, Sakhivel R, Chung W K. Unscened FasSLAM: a robus and efficien soluion o he SLAM problem. IEEE Transacions on Roboics, 28, 24(4): Zhao L J, Sun L N, Li R F, e al. On an improved SLAM algorihm in indoor environmen. Robo, 29, 31(5): (in Chinese) 9. Hu J S, Lee M T, Yang C H. Robus adapive beamformer for speech enhancemen using he second-order exended filer. IEEE Transacions on Audio Speech and Language Processing, 213, 21(1): Okawa Y, Namerikawa T. Simulaneous localizaion and mapping problem via he H filer wih a known landmark. Proceedings of he SICE Annual Conference (SICE 13), Sep 1417, 213, Nagoya, Japan. Piscaaway, NJ, USA: IEEE, 213: Ahmad H, Namerikawa T. Covariance inflaion efficiency in H filer based SLAM. Proceedings of he 211 Inernaional Conference on Elecrical, Conrol and Compuer Engineering, Jun 2122, 211, Pahang, Malaysia. Piscaaway, NJ, USA: IEEE, 211: Pham V C, Juang J C. Robus and efficien slam via compressed H filering. Asian Journal of Conrol, 214, 16(3): Song Y, Li Q L, Kang Y F. Conjugae unscened FasSLAM for auonomous mobile robos in large-scale environmens. Cogniive Compuaion, 214, 6(3): Zhang J W, Zhang L W, Hu Y, e al. Open source robo operaion sysem. Beijing, China: Science Press, 212 (in Chinese) (Edior: Wang Xuying)