Research Article Localization of Outdoor Mobile Robots...

Research ArticleLocalization of Outdoor Mobile Robots Using Curb Features inUrban Road Environments

Hyunsuk Lee1 Jooyoung Park2 and Woojin Chung1

1 Department of Mechanical Engineering Korea University Anam-dong Seongbuk-gu Seoul 136-713 Republic of Korea2Department of Control and Instrumentation Korea University Anam-dong Seongbuk-gu Seoul 136-713 Republic of Korea

Correspondence should be addressed to Woojin Chung smartrobotkoreaackr

Received 12 December 2013 Revised 13 February 2014 Accepted 13 February 2014 Published 8 April 2014

Academic Editor Leo Chen

Copyright copy 2014 Hyunsuk Lee et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Urban road environments that have pavement and curb are characterized as semistructured road environments In semistructuredroad environments the curb provides useful information for robot navigation In this paper we present a practical localizationmethod for outdoor mobile robots using the curb features in semistructured road environments The curb features are especiallyuseful in urban environment where the GPS failures take place frequently A curb extraction is conducted on the basis of the KernelFisher Discriminant Analysis (KFDA) to minimize false detection We adopt the Extended Kalman Filter (EKF) to combine thecurb information with odometry and Differential Global Positioning System (DGPS) The uncertainty models for the sensors arequantitatively analyzed to provide a practical solution

1 Introduction

Outdoor environments have irregular shapes and changesin geometry and illumination due to the weather conditionTherefore environmental uncertainty is relatively highThereare numerous studies for autonomous navigation of mobilerobot in outdoor environments Typical examples are theautonomous vehicles that were developed through DARPAGrandUrban Challenges [1 2] Most of the vehicles wereequipped with a variety of high cost sensors in order toovercome various uncertainties

The aim of this work is to develop a practical localizationmethod for outdoor mobile robots In particular this studyfocuses on surveillance robots in urban road environmentsA localization method using a small number of sensors isproposed instead of using multiple high cost sensors

The fusion of a global positioning system (GPS) andinertial measurement unit (IMU) has been widely used forthe outdoor localization of mobile robots [3 4] Howeverit is difficult to ensure the accurate pose estimation indense urban environment where GPS signal is degraded bythe multipath errors and satellite blockage Therefore theuse of environmental features has been studied to enhancethe precision of the estimated robot pose in dense urban

environment [5 6] In [7] a 3D representation of the localenvironment is used to detect obstruction of the GPS signalswhich is blocked by buildings In [8 9] the extracted linefeatures of buildings are used to estimate the robot positionHowever the available information regarding buildings issparse in many places and the slow update rate limits theperformance of localization In [10] the road centerlineis extracted to correct the lateral position of the vehiclein mountainous forested paths However the correction ofthe heading error is not considered by the extracted roadcenterline

Generally urban road environments are paved and thecurbs act as the boundaries of the roads Therefore urbanroad environments are characterized as semistructured roadenvironments In semistructured road environments thecurb provides useful information for robot navigationThere-fore the curb features have been widely used for navigationstrategies and localization methods In [11] Wijesoma et alpropose amethod based on EKF for detection and tracking ofthe curbsThe range and angle of the curbs are obtained froman LRF measurement However quantitative performanceanalysis of the curb detection was not clearly shown In[12 13] the curb on one side of the road is extracted usinga vertical LRF for vehicle localization The lateral error of

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 368961 12 pageshttpdxdoiorg1011552014368961

2 Mathematical Problems in Engineering

a vehicle is reduced by map matching approach using theextracted curb point However the correction of the headingangle is not considered because there is no angle informationof the curb

A method for traversable region detection using roadfeatures such as road surface curbs and obstacles is pro-posed in our previous works [14ndash16] The curb features arederived by the geometric features of the road to obtain curbcandidates In order to extract the correct curb among thecurb candidates a validation gate is derived from principalcomponent analysis (PCA)The curb extraction is performedsuccessfully in a road environment However there was afundamental limitation on PCA The validation gate doesnot consider the classification of the curb and noncurbdata Consequently false detection where noncurb data areextracted as curbs may occur The precision of estimatedpose is decreased when the false detection data are usedfor localization Therefore it is important to reduce the falsedetection rate

The contribution of this paper can be summarized by twoschemes The first contribution is the robust curb extractionscheme by using a single Laser Range Finder (LRF) Inorder to reduce the number of false detection of the curbsthe classification of the curb data and the noncurb datais conducted by using Kernel Fisher Discriminant Analysis(KFDA) in [17ndash19] On the basis of our previous worksgeometrical features of the curb are defined The secondcontribution is the integrated localization scheme using curbfeatures on the basis of quantitative sensor uncertainty mod-els In particular the uncertaintymodel for the extracted curbis quantitatively determined from experiments ExtendedKalman Filter (EKF) is exploited to combine the curb featureswith odometry and Differential Global Positioning System(DGPS) information The extracted curbs enable accurateestimation of the pose of the robot even when the temporalGPS blackout takes place

The remainder of this paper is organized as followsA method for curb extraction is presented in Section 2Section 3 describes the localization method for an outdoormobile robot using the extracted curb It also introducesthe uncertainty models for the sensor measurements Theexperimental results of the proposedmethod are presented inSection 4 Finally the conclusion of this research is presentedin Section 5

2 Road Feature Extraction

21 System Configuration Figure 1 shows the configurationof the mobile robot and the LRF coordinate configurationA single onboard LRF with a tilting angle of 120572

119905is used to

extract road features such as the road surface and curbsThe following list shows the nomenclature for road featureextraction The variables are described with respect to therobot coordinate frame

119908119903 road width

120572119905 nominal tilt angle of LRF

120579119891 angle between the detected road surface points

and 119884119877-axis

119889119891 horizontal look-ahead distance from the robot to

the road surface points(119909C119877 119910C119877) coordinates of the right curb edge (pointC)120579C119877 angle between the right curb and 119884

119877-axis

(119909C119871 119910C119871) coordinates of the left curb edge (point B)120579C119871 angle between the left curb and 119884

119877-axis

22 Road Feature Detection A road feature detection schemewas proposed in our previous works [14 15] The previousworks on road feature detection are briefly reviewed Thefirst step for the road feature detection is the road surfaceextraction In order to identify the road surface the LRFmeasurements in expected road region 119877

119910are selected as

candidates for the road surface 119871119903 Multiple line segments

are constructed by combining consecutive data points of 119871119903

The angle of the road surface is parallel with the 119883119877-axis

in the ideal case Therefore the range data 119871119903are saved as

road surface points 119871119891if the angle of the line segment is

within threshold 120579119890 The road surface is extracted as a line

by using the least square method The extracted road surfaceprovides 120579

119891and 119889

119891from the robotThe overall algorithm can

be summarized in Algorithm 1Figure 2 shows the ideal model of a semistructured road

environment The geometrical features of the road can beused to extract the curb features The curb has the followingfour attributes

(Att 1) The angular difference between the curb ori-entation (120579

119888) and road surface angle (120579

119891) is close to

90∘(Att 2) The gap between the horizon distance of theroad surface (119889

119891) and the 119910 value of the curb point (B

or C) is close to 0(Att 3) The angular difference between the left curb( AB) and the right curb ( CD) is close to 0(Att 4)The difference between the roadwidth and thegap between two curbs is close to 0 It is assumed thatthe road width is known

It is commonly assumed that the robot navigates parallelto the curb It is reasonable to assume that the robot ismovingalong the road without significant change of orientationin most cases Moreover the vertical surfaces of the curbare perpendicular to the road surface When we scan theroad environments using the LRF the road features arecomposed of straight lines with different orientations Inorder to distinguish different line segments that correspondto the road surface the curbs and the sidewalk it is helpfulto assume that the robotrsquos heading direction points forwardalong the road The road width is assumed to be known bygiven map information

Thefirst attribute is used to select the curb candidatesTheline segments that satisfy the following condition are selectedas the curb candidates

1198861=

120587

2

plusmn 120576 (1)

Mathematical Problems in Engineering 3

(1) 119871119894larr the LRF measurement

(2) 119871119884119894

larr 119910 coordinate of the LRF measurement(3)119873 larrThe number of the LRF measurement points(4)119877119884larr Expected 119910 range of the road surface points

(5) for 119894 larr 1 to119873

(6) if 119871119884119894

isin 119877119884 then

(7) 119871119903larr save 119871

119894as candidate for the road surface

(8) 120579119903larr angle of candidate for the road surface

(9) 119872 larrThe number of candidates for the road surface(10) end if(11) end for(12) for 119895 larr 1 to119872

(13) if 10038171003817100381710038171003817120579119903119895

10038171003817100381710038171003817le 120579119890 then

(14) 119871119891larr save 119871

119903119895as the road surface

(15) end if(16) end for(17) return (119871

119891)

Algorithm 1 Road surface extraction

LRF coordinate

Robot coordinate

Curb

Curb

Road

A

B

C

DF

ZL

YL

df

120572tXL

XR

YR

ZR

120579f

wr

O

Figure 1 The configuration of a robot and installation of a LRF

where 1198861= |120579119891minus 120579119888| 120576 = tolerance

Once the curb candidates are determined attributes 2 3and 4 are used to extract the correct curb out of the curbcandidatesThe attribute values 119886

2 1198863 and 119886

4that correspond

to each attribute are numerically calculated for the pair ofright and left curb candidates as follows

1198862= 119889119891minus avg (119910C119877 119910C119871)

1198863= 120579C119877 minus 120579C119871

1198864= 119908119903minus 119908119888

(2)

CurbRoadLRF

A

B C

D

Extracted road surface

Figure 2 Ideal model of semiconstructed environment (blue dottedline LRF data red line extracted road surface)

119908119888is the gap between the right and left curb points (119908

119888=

119909C119877 minus 119909C119871) When a curb exists on only one side 1198862and

1198863are computed from the curb candidates for one side 119886

4is

assumed to be 0 The data vector of the curb candidates isgiven as follows

x119894= [1198862

1198863

1198864]

119879

(3)

23 Curb Extraction Using Kernel Fisher Discriminant Anal-ysis (KFDA) KFDA is applied to extract the correct curbfrom the curb candidates KFDA aims to find a discriminantfunction for optimal data classification Therefore the dis-criminant function can be used to classify the curb candidatesas curb and noncurb class The curb extraction is conductedby the following procedure First the training data withclass information are selected The discriminant function isderived from the offline computation of the training dataWhen the discriminant function is obtained classificationof the curb candidates is carried out by the discriminantfunction in real time


The discriminant function 120572 is defined as a vector tomaximize the following object function in the kernel featurespaceF Consider the following

119869 (120572) =

120572119879119878Φ

119861120572

120572119879119878Φ

119882120572

(4)

The ldquobetween-class variance matrixrdquo 119878Φ119861and the ldquowithin-

class variance matrixrdquo 119878Φ119882are defined as follows

119878Φ

119861= sum

119888

ℓ119888(120581119888120581119879

119888minus 120581120581119879)

119878Φ

119882= 119870119870

119879minus sum

119888

ℓ119888120581119888120581119888

119879

(5)

with 120581119888

= (1ℓ119888) sum119894isin119888

119870119894119895and 120581 = (1ℓ)sum

119894119870119894119895 ℓ is the

number of total training samples and ℓ119888is the number of class

samplesTraining data 119909

1 1199092 119909

ℓ consist of data with obvious

class information Each sample xtraining119894 isin R3 belongs to oneof two classes that include curb and noncurb class In order toobtain equivalent effects on classification the components ofeach sample should be normalized Consider the following

x(119896)119894

=

x(119896)119894

minus 120583(119896)

120590(119896)

(6)

Here 120583(119896) and 120590(119896) are themean and standard deviation of

each attribute respectivelyThe training data that aremappedto the kernel feature space are represented by an ℓ times ℓmatrix119870 The Gaussian kernel is used for mapping the data ontokernel feature spaceF Consider the following

119870119894119895= 119896 (x

119894 x119895) = exp(minus

10038171003817100381710038171003817x119894minus x119895

10038171003817100381710038171003817

2

21205902

) (7)

120590 is the control parameter that needs to be tuned toimprove classification performance [19] If 120590 is too small theoverfitting problem may take place Although the classifi-cation accuracy with respect to the training data increasesthe classification performance with respect to the test databecomes poor under the occurrence of the overfitting If 120590is too large the underfitting problem may take place Theclassification performance will not be satisfactory at all caseswhen the underfitting takes place Therefore 120590 should becarefully selected In this paper 120590 is manually tuned underthe consideration of experimental performances

The discriminant function that maximizes the objectfunction in (4) is derived by an eigenvalue problem In orderto project the training data onto a one-dimensional (1D)solution space the eigenvector that corresponds to the largesteigenvalue is defined as the discriminant function 120572 for dataclassificationThe discriminant function 120572 is given by an ℓtimes1

vector Consider the following

119878Φ

119861120572 = 120582119878

Φ

119882120572 (8)

The classification of the training data is conducted byan inner product of the data matrix 119870 and the discriminant

function120572The projected training data119910training are distributedin the 1D solution space Consider the following

119910training = 120572 sdot 119870 (9)

The class of test data can be predicted by using thediscriminant function 120572 The test data denote the curbcandidates The test data xtest is projected to the 1D solutionspace as shown in the following equation

119910test = sum

119894

120572119894119896 (xtraining119894 xtest) (10)

The class properties of the training data are used to predictthe class of the test data 119910test The Mahalanobis distancesbetween each class and the test data are computed by thefollowing equation

119889 (119910test 120583Φ

119888) =

(119910test minus 120583Φ

119888)

2

(120590Φ

119888)2

(11)

where 120583Φ

119888and 120590

Φ

119888denote the mean and standard deviation

of the class distribution respectively The class of the testdata is determined as the class with the smallest Mahalanobisdistance When the test data are classified as the curb classthey are extracted as the curb

3 Outdoor Localization Using Curb Feature

31 System Design This paper adopts EKF to estimate therobot pose using curb features EKF is a well-known methodfor mobile robot localization and sensor fusion [20ndash22]When the initial pose of the robot and adequate observationsare provided the pose of the robot can be estimated bycorrecting the odometry error The EKF process consists of aprediction step and an update step in sampling time 119896 DGPSand an LRF are used to correct odometry errors Figure 3shows a block diagram of the localization process

32 Measurement Uncertainty Model The GPS error mainlyoccurs due to the following two factors One is the pseu-dorange errors caused by systematic factors Another is thegeometric constellation of satellites In this paper DGPS isused to minimize the pseudorange errors The uncertaintymodel for DGPS is computed under the consideration of theldquodilution of precisionrdquo in relation to the geometric constella-tion of satellites and the pseudorange error or so-called ldquouser-equivalent range errorrdquo [23] Consider the following

RDGPS119896 = [

1205902

119909120590119909119910

120590119909119910

1205902

119910

]1205902

UERE (12)

The error covarianceRDGPS119896 is given as (12)The elementsof the covariance matrix are provided by the DGPS receiverin real time

Several studies were proposed to define the error covari-ance of line features [24 25] However the uncertaintymodels are appropriate for a static condition or a low-speeddriving condition on a flat surface However the outdoor


DGPS

Robot

Laser rangefinder

Position(xDGPS yDGPS )

Incrementaldisplacement

(ΔsΔ120579)

Curb information

Map

PredictionCorrectedrobot pose

Localizer

1st measurementcorrection

2nd measurementcorrection

(R120572Rr)

(W120572iWri)

xminusk

Pminusk

x+k2x+k1

zDGPS k

RDGPS k

zcurb k

Rcurb k

P+k2P+k1

Figure 3 A block diagram of localization process

Extracted curb

Actual curb

120572i

ri120579i

di

Figure 4 Noise model of the extracted curb

mobile robots are usually driven in the uneven terrain Themeasurement noise of the extracted curb occurs due to thewobble of the robot Therefore the uncertainty model forthe curb needs to be defined by experiments under resultantdriving conditions

In order to define the error covariance Rcurb we considerthe noise model of the extracted curb as shown in Figure 4The information of the extracted curb contains estimationerrors in the range and angle Therefore the angle andrange measurements for the extracted curb are composed ofthe ldquotruerdquo angle 120579

119894and the ldquotruerdquo range 119889

119894 along with the

estimation errors Consider the following

120572119894= 120579119894+ 120576120572119894

119903119894= 119889119894+ 120576119903119894

(13)

where 120576120572119894

and 120576119903119894are the estimation errors for a curb and

have random variances 1205902120572and 120590

2

119903 respectively The ground

truth of the curb locations can be measured by an additionalLRF which is attached to the side of the robot Because theadditional LRF is directly facing the curb the range data fromthe additional LRF provide reliable geometric informationof the curb during robotrsquos movement The measurement ofthe curb from the additional LRF is more accurate than theforward-pointing tilted LRF because the number of rangedata points that correspond to the curb is much larger Thecurb is represented as a straight line by the application of theleast square method The ground truth implies the relativerange and orientation of the curb The estimation errorsare computed for the extracted curbs Therefore the errorcovariance of the curb is defined by the distribution of theestimation errors By using a large number of measurementsof the estimation errors 120576

120572and 120576

119903 the error covariance is

calculated as follows

Rcurb = [

1205902

120572120590120572119903

120590119903120572

1205902

119903

] = [

119864 (120576120572120576119879

120572) 119864 (120576

120572120576119879

119903)

119864 (120576119903120576119879

120572) 119864 (120576

119903120576119879

119903)

] (14)

The covariance matrices are experimentally defined asconstant values for the left and right curbs

33 Extended Kalman Filter Localization Using Curb FeatureThe odometry data from the wheel encoders are used topredict the robot pose By using the incremental distanceΔ119904119896minus1

and orientationΔ120579119896minus1

the predicted robot pose is givenby the following equation

xminus119896= 119891 (x

119896minus1 u119896minus1

) =

[

[

[

[

[

[

119909minus

119896minus1+ Δ119904119896minus1

cos(120579minus

119896minus1+

Δ120579119896minus1

2

)

119910minus

119896minus1+ Δ119904119896minus1

sin(120579minus

119896minus1+

Δ120579119896minus1

2

)

120579minus

119896minus1+ Δ120579119896minus1

]

]

]

]

]

]

(15)


Extracted curb(from 1st estimated robot perspective)

Actual curb(curb line map)

W

R

Wri

W120572i

Rrk

R120572k

W+

k1

Wy+k1

Wx+k1

Figure 5 Extracted curb features and a line map with respect to theglobal coordinate frame

The state vector xminus119896= [119909minus

119896119910minus

119896

120579minus

119896]

119879

is the predicted robotpose at sampling time 119896 When the initial pose of the robot isgiven the robot pose is represented by 119909 119910 and 120579 in a globalcoordinate frameTheuncertainty of the predicted robot poseconsistently increases because of the accumulative errors ofthe odometry

In order to correct the odometry error the first measure-ment correction is performed using DGPS measurementsThe update frequency is set to 1Hz on the basis of theDGPS measurement frequency When the available positionmeasurement is provided the observation vector is given inglobal coordinates Consider the following

zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879

(16)

The observation model for the current state is describedas follows

hDGPS (xminus

119896 119896) = [119909

minus

119896119910minus

119896]

119879

(17)

The measurement Jacobian matrixH119896is given as follows

HDGPS119896 =120597h (xminus119896 119896)

120597xminus119896

= [

1 0 0

0 1 0] (18)

zcurb119896 = [120572119896

119903119896]

119879

(19)

The second measurement correction is conducted byusing the curb features The observation vector for theextracted curb is given by (19) When the curbs are extractedon both sides there are two measurement vectors for the leftand right curbs as shown in Figure 5 The sequence of thesecond measurement correction is from the right curb to theleft curbThe update rate is 5Hz if the curbs are continuouslyextracted

The robot pose is corrected by comparing the curb withthe map The extracted curb is matched with the 119894th line ofthe curb map The observation model for the 119894th line 119882z

119894=

[119882120572119894

119882119903119894]

119879

and the robot pose at time 119896 is given by thefollowing equation

hcurb (x+

1198961 119896 119894)

= [

119882120572119894minus120579+

1198961

119882119903119894minus 119909+

1198961cos 119882120572

119894+ 119910+

1198961sin 119882120572

119894

]

(20)

The Jacobian matrixH119896is defined as follows

Hcurb119896 =120597h (x+1198961

119896 119894)

120597x+1198961

= [

0 0 minus1

minus cos 119882120572119894minus sin 119882120572

1198940

]

(21)

The consistency of EKF relies on the observation modelIf an erroneous sensor observation is provided the systemdoes not provide a consistent result Therefore the outliersthat lie outside of the uncertainty bounds should be rejectedA normalized innovation squared (NIS) test is implementedin order to confirm the consistency of the filter NIS valuehas a 120594

2 distribution with respect to 119899 degrees of freedomConsider the following

NIS119896= (z119896minus h (x+

119896 119896))

119879Sminus1119896

(z119896minus h (x+

119896 119896)) le 120594

2 (22)

where S119896is the innovation matrix which is defined as S

119896=

H119896Pminus119896H119879119896+R119896 The NIS value for valid measurements should

be within the threshold of the 1205942 distribution However the

erroneous measurements are discarded when the NIS valuelies outside the threshold boundary A threshold value thatcorresponds to a 95 confidence region is used for outlierrejection

4 Experimental Results

41 Experimental Setup Figure 6 shows the sensor systemattached to the mobile robot The outdoor mobile robotis a Pioneer P3-AT a commercial outdoor platform ofMobileRobots The wheel encoders attached to the drivingmotors provide odometry information SICK LMS-100 wasused to detect the curb The LRF was tilted by 5∘ towardthe ground A Novatel DGPS system was used to measurethe global position The robot was equipped with a roverantenna and a base stationwas located on the roof of a nearbybuilding The ldquotruerdquo value for the curb and the ground truthwere measured using an additional LRF (HOKUYO URG-04lx) attached to the side of the robot

The experiment was performed in Korea University inSeoul Korea as shown in Figure 7 The robot was drivenmanually along the yellow dashed line from ldquoSrdquo to ldquoGrdquoThe curbs along the experimental path are represented assolid green lines The target environment has semistructuredgeometry that is composed of paved roads and curbs inmost of the region Furthermore there are tall buildings andtunnels that degrade the DGPS precisionThe travel distancealong the experimental path was 775m and average speed ofthe robot was 05ms


DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate

Figure 6 Sensor system attached to mobile robot

Reference pathCurb map

SG

Figure 7 Experimental environment

42 Curb Extraction Results The curb extraction process ina semistructured road environment is shown in Figure 8Figure 8(a) shows the road environment where the experi-ment was performed The red dotted line represents the scanarea of the tilted LRF Figure 8(b) shows the extracted roadsurface on the basis of the scanned LRF data in the roadenvironment When the road surface is extracted the linesegments that satisfy attribute 1 in Section 22 are selected asthe curb candidates Figure 8(c) shows the line segments thatcorrespond to the curb candidates The first and the secondcandidates for each side of the curbs are represented by blueand green lines respectively There are two candidates oneach sideTherefore four pairs of candidates can be extractedas curbs (R1 L1) (R1 L2) (R2 L1) and (R2 L2) The classprediction results for each pair of curb candidates are listedin Table 1 The pairs of candidates (R1 L1) and (R1 L2)are classified as the curb class Finally candidate (R1 L1) isextracted as the curbs as shown in Figure 8(d) which hasthe smallest Mahalanobis distance with respect to the curb

Table 1 Class prediction for pairs of curb candidates

Candidates Mahalanobis distance Class predictionCurb class Noncurb class

1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb

Table 2 Classification results including confusion matrix

Instance PCA KFDAClass correct 4338 913 4683 986Class incorrect 413 87 68 14Total 4751 100 4751 100

Classified as Classified asTrue curb False curb True curb False curb

True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)

class If the LRF data that correspond to the vertical surfaceare detected the proposed method will perform successfullydespite the small and less distinct curbs

The curb extraction was performed while the robotnavigates through the experimental path Figure 9 showsthe curb mapping result from the curb extraction The curbmap is shown in the right bottom in Figure 9 The extractedcurbs are denoted by the magenta dots The results indicatethat most of the curbs along the experimental path weresuccessfully extracted In order to demonstrate the robust-ness of the proposed method comparison of classificationperformance between our previousmethod and the proposedmethod is summarized in Table 2 The accuracy of the curbextractionwith PCAwas 913 for 4751 scanned datasetsTheaccuracy was improved to 986 with the proposed KFDAA confusion matrix is presented below The conventionalmethod and the proposed method show 971 and 982of true positive rate respectively The curb extraction isperformed successfully by the application of both methodsHowever the most important factor in the curb extraction isto reduce the false detection rate False detection is that thenoncurb data are misclassified as the curb dataThe accuracyof the estimated pose can be decreased when the false curbsare used for localization The false detection rate was 274with PCA The false detection rate was reduced to 04 withthe proposed KFDA The result implies that most of thenoncurb data were classified as noncurb data correctly

43 Uncertainty Measurement Results The DGPS measure-ments are represented by red dots along the experimentalpath in Figure 10(a) The areas with large DGPS errors arerepresented by AndashF Figure 10(b) shows the standard devia-tion of the DGPS measurements The standard deviation ofthe DGPS is about 2m in open area There were temporalblackouts in areas B D and E due to satellite blockage


(a)

0 1 2 3

0

1

2

3

4

5

6

7

Detected road surface

minus1minus2

minus1

minus2minus3minus4minus5minus6

y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)

Figure 8 Curb extraction results (a) Road environment (b) Road surface detection (c) Curb feature candidates on both sides (d) Extractedcurb

0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100

Figure 9 Curb mapping result on experimental path


Reference pathDGPS measurements

SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)

Figure 10 (a) DGPS measurement and (b) DGPS uncertainty measurement (1120590 bound)

CurbAdditional LRF

Figure 11 Additional LRF for ground truth of the curbs

The uncertainty measurements in areas B D and E werealmost infinite as shown in Figure 10(b) Furthermore largeDGPS errors occurred in areas A C and F due to thedegraded satellite signals In particular measurement errorswere 21m on average in area F The standard deviation thatwas measured in area F was 64m on average The resultimplies that the regional properties ofDGPSwere obtained bymeasuring the DGPS uncertainty in real time However theprecision of the localization only by DGPS can be decreasedwhen the robot navigates near the buildings

The curb estimation errors are considered in order todefine the error covariance The most accurate result forthe quantitative curb uncertainty is obtained by measuringthe estimation errors in experimental environments Theestimation errors were measured while the robot navigatesthrough the road with curbs Ground truth for the curb wasprovided by an additional LRF that is attached to the sideof the robot as shown in Figure 11 Ground truth of thecurb was provided by line feature from the additional LRFdata Experiments were conducted in order to measure theestimation errors prior to the localization experiment The

Table 3 Error covariance of extracted curb

Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572

Right curb 01620m 00575 rad 00035msdotradLeft curb 01614m 00649 rad minus00034msdotrad

following results show the estimation errors for the range andangle of the extracted curb

Figure 12 shows the histogram of the curb estimationerrors for each sideThe number of the estimation error mea-surements is approximately 5000 The covariance matrix ofthe curb was computed from the distributions of estimationerrors The elements of error covariance for each side of thecurb are listed in Table 3

The covariance representation for the extracted curbs isshown in Figure 13 The extracted curbs are represented byblue lines and the error bounds for the curbs are representedby green dotted lines The resultant curbs exist within theerror bounds with 95 confidence

44 Outdoor Localization Results The localization results areshown in Figure 14 The proposed method was comparedwith the conventional framework for outdoor localizationthat combines DGPS measurement with odometry The bluedash-dot line represents the localization results correctedonly by the DGPS measurements The estimated paths showsome difference with respect to the reference path (yellowdotted line) in area AndashF due to theDGPS errorsThemagentaline represents the localization results corrected byDGPS andthe extracted curb When the curb information is appliedthe results show that the robot position well matches thereference path even if the DGPS errors are large or a blackoutoccurs (area AndashF) It is clear that the curb information plays adominant role The following part presents the localizationerrors in area AndashF as shown in Figure 14 The localizationerrors were compared with the conventional framework thatcombines DGPS measurement with odometry The ground


0

100

200

300Histogram of left curb range errors

Estimation error (m)

N(c

ount

)

040302010minus01minus02minus03minus04

0

100

200

300

400Histogram of left curb angle errors

Estimation error (rad)

N(c

ount

)

010050minus005minus01

(a)


0

200

400

600

800Histogram of right curb range errors

N(c

ount

)


0

200

400

600

800Histogram of right curb angle errors


N(c

ount

)


(b)

Figure 12 Distribution of estimation errors for (a) left and (b) right curbs

0 1 2 3

0

1

2

3

4

5

6

7

Range dataExtracted curbCovariance (95 confidence)

minus1minus2

minus1


y(m

)

x (m)

Figure 13 Extracted curbs and covariance representation

truth was computed using the additional LRF attached to theside of the robot

Figure 15 shows the lateral errors of the localizationresults The position errors when using the fusion of theodometry and DGPS are shown in Figure 15(a) The lateralerrors in each areawere usually greater than 1m In particularthe maximum error in area F was 5m In contrast thelocalization result which was corrected by odometry DGPSand curb information shows that the lateral errors werewithin 06m across the entire area as shown in Figure 15(b)

SG

A

B

DE

C

F

Reference pathEKF (odometry + DGPS)EKF (odometry + DGPS + curb)

Figure 14 Localization results in semistructured road environment

Therefore the proposed method shows robust performancein terms of lateral position estimation errors despite the largeDGPS errorsTheheading errors of the localization results arerepresented in Figure 16 The result that was corrected usingonly the DGPS data is shown in Figure 16(a) The headingerrors were greater than 1∘ on averageThe variancewas largerthan 2∘ However when the curb information is used forcorrection the heading errors were remarkably decreasedFurthermore the errors rarely exceed 3∘ in the entire areaIn experiments the proposed method showed precise androbust performance for the lateral and heading errors despitethe large DGPS errors and a temporal blackout


0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection

EKF (odometry + DGPS)

minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section

EKF (odometry + DGPS + curb)

minus1

minus2

minus3

minus4

(b)

Figure 15 Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb

A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)

Figure 16 Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb

5 Conclusion

This paper presents a localization method for outdoor robotsusing curb features in semistructured road environmentsA reliable curb extraction scheme is proposed to classifythe curb candidates as curb and noncurb classes Mostof the curbs in an experimental path are extracted withhigh accuracy An EKF-based localization is also proposed

to combine the extracted curbs with odometry and DGPSmeasurements The uncertainty models of the sensors aredefined by experiments to provide a practical solution forlocalization From experimental results the robustness of theproposed method is demonstrated in real road experimentsThe curb features can correct significantly the lateral positionand heading errors in dense area where the DGPS signal getsdegraded by buildings


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported in part by the MKE (TheMinis-try of Knowledge Economy) Korea under the HumanResources Development Program for Convergence RobotSpecialists Support Program supervised by the NIPA(National IT Industry Promotion Agency) (NIPA-2013-H1502-13-1001) This work was also supported by theNational Research Foundation of Korea (NRF) Grant fundedby Korea Government (MEST) (2013-029812)

References

[1] S Thrun M Montemerlo H Dahlkamp et al ldquoStanley therobot that won the DARPA Grand Challengerdquo Journal of FieldRobotics vol 23 no 9 pp 661ndash692 2006

[2] M Buehler K Lagnemma and S Singh The DARPA UrbanChallenge Autonomous Vehicles in City Traffic Springer NewYork NY USA 2009

[3] A Soloviev ldquoTight coupling of GPS laser scanner and iner-tial measurements for navigation in urban environmentsrdquo inProceedings of the IEEEION Position Location and NavigationSymposium pp 511ndash525 Monterey Calif USA May 2008

[4] S Panzieri F Pascucci and G Ulivi ldquoAn outdoor navigationsystem using GPS and inertial platformrdquo IEEEASME Transac-tions on Mechatronics vol 7 no 2 pp 134ndash142 2002

[5] E-J Jung andD-J Yi ldquoTask-oriented navigation algorithms foran outdoor environment with colored borders and obstaclesrdquoIntelligent Service Robotics vol 6 no 2 pp 69ndash77 2013

[6] S Kim J Kang andM Jin Chung ldquoProbabilistic voxelmappingusing an adaptive confidence measure of stereo matchingrdquoIntelligent Service Robotics vol 6 no 2 pp 89ndash99 2013

[7] M Joerger and B Pervan ldquoRange-domain integration of GPSand laser-scanner measurements for outdoor navigationrdquo inProceedings of the 19th International Technical Meeting of theSatellite Division of The Institute of Navigation (ION GNSS rsquo06)pp 1115ndash1123 Fort Worth Tex USA September 2006

[8] M Hentschel O Wulf and B Wagner ldquoA GPS and laser-basedlocalization for urban and non-urban outdoor environmentsrdquoin Proceedings of the IEEERSJ International Conference on Intel-ligent Robots and Systems pp 149ndash154 Nice France September2008

[9] A Georgiev and P K Allen ldquoLocalizationmethods for amobilerobot in urban environmentsrdquo IEEE Transactions on Roboticsvol 20 no 5 pp 851ndash864 2004

[10] Y Morales T Tsubouchi and S Yuta ldquoVehicle localizationin outdoor mountainous forested paths and extension of two-dimensional road centerline maps to three-dimensional mapsrdquoAdvanced Robotics vol 24 no 4 pp 489ndash513 2010

[11] W SWijesoma K R S Kodagoda andA P Balasuriya ldquoRoad-boundary detection and tracking using ladar sensingrdquo IEEETransactions onRobotics andAutomation vol 20 no 3 pp 456ndash464 2004

[12] M Jabbour and P Bonnifait ldquoGlobal localization robust toGPS outages using a vertical ladarrdquo in Proceedings of the 9th

International Conference on Control Automation Robotics andVision pp 1ndash6 December 2006

[13] P Bonnifait M Jabbour and V Cherfaoui ldquoAutonomousnavigation in urban areas using GIS-managed informationrdquoInternational Journal of Vehicle Autonomous Systems vol 6 no5 pp 83ndash103 2008

[14] Y Shin D Kim H Lee J Park and W Chung ldquoAutonomousnavigation of a surveillance robot in harsh outdoor environ-mentsrdquo Advances in Mechanical Engineering vol 2013 ArticleID 837484 15 pages 2013

[15] Y Shin C Jung andWChung ldquoDrivable road region detectionusing a single laser range finder for outdoor patrol robotsrdquo inProceedings of the IEEE Intelligent Vehicles Symposium (IV rsquo10)pp 877ndash882 San Diego Calif USA June 2010

[16] D Kim and W Chung ldquoLocalization of outdoor mobile robotsusing road featuresrdquo in Proceedings of the 8th International Con-ference on Ubiquitous Robots and Ambient Intelligence (URAIrsquo11) pp 363ndash365 Incheon Republic of Korea November 2011

[17] S Mika G Ratsch J Weston B Scholkopf and K MullerldquoFisher discriminant analysis with kernelsrdquoNeural Networks forSignal Processing vol 9 pp 41ndash48 1999

[18] S Mika G Ratsch and K R Muller ldquoA mathematical pro-gramming approach to the kernel fisher algorithmrdquo Advancesin Neural Information Processing vol 13 pp 591ndash597 2001

[19] G Camps-Valls and L Bruzzone Kernel Methods for RemoteSensing Data Analysis JohnWiley amp Sons New York NY USA2009

[20] R E Kalman ldquoA new approach to linear filtering and predictionproblemsrdquo Journal of Basic Engineering vol 82 no 1 pp 35ndash451960

[21] R E Kalman and R S Bucy ldquoNew results in linear filtering andprediction theoryrdquo Journal of Basic Engineering vol 83 no 3pp 95ndash108 1961

[22] J J Leonard and H F Durrant-Whyte Directed Sonar Sensingfor Mobile Robot Navigation Kluwer Academic DordrechtTheNetherlands 1992

[23] B W Parkinson and J J Spilker Global Positioning SystemTheory and ApplicationsThe American Institute of Aeronauticsand Astronautics Washington DC USA 1996

[24] K O Arras and R Y Siegwart ldquoFeature extraction and sceneinterpretation for map-based navigation and map buildingrdquo in12th Mobile Robots Conference vol 3210 of Proceedings of SPIEpp 42ndash53 Pittsburgh Pa USA January 1998

[25] S T Pfister S I Roumeliotis and J W Burdick ldquoWeighted linefitting algorithms for mobile robot map building and efficientdata representationrdquo in Proceedings of the IEEE InternationalConference on Robotics and Automation pp 1304ndash1311 Septem-ber 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


a vehicle is reduced by map matching approach using theextracted curb point However the correction of the headingangle is not considered because there is no angle informationof the curb

A method for traversable region detection using roadfeatures such as road surface curbs and obstacles is pro-posed in our previous works [14ndash16] The curb features arederived by the geometric features of the road to obtain curbcandidates In order to extract the correct curb among thecurb candidates a validation gate is derived from principalcomponent analysis (PCA)The curb extraction is performedsuccessfully in a road environment However there was afundamental limitation on PCA The validation gate doesnot consider the classification of the curb and noncurbdata Consequently false detection where noncurb data areextracted as curbs may occur The precision of estimatedpose is decreased when the false detection data are usedfor localization Therefore it is important to reduce the falsedetection rate

The contribution of this paper can be summarized by twoschemes The first contribution is the robust curb extractionscheme by using a single Laser Range Finder (LRF) Inorder to reduce the number of false detection of the curbsthe classification of the curb data and the noncurb datais conducted by using Kernel Fisher Discriminant Analysis(KFDA) in [17ndash19] On the basis of our previous worksgeometrical features of the curb are defined The secondcontribution is the integrated localization scheme using curbfeatures on the basis of quantitative sensor uncertainty mod-els In particular the uncertaintymodel for the extracted curbis quantitatively determined from experiments ExtendedKalman Filter (EKF) is exploited to combine the curb featureswith odometry and Differential Global Positioning System(DGPS) information The extracted curbs enable accurateestimation of the pose of the robot even when the temporalGPS blackout takes place

The remainder of this paper is organized as followsA method for curb extraction is presented in Section 2Section 3 describes the localization method for an outdoormobile robot using the extracted curb It also introducesthe uncertainty models for the sensor measurements Theexperimental results of the proposedmethod are presented inSection 4 Finally the conclusion of this research is presentedin Section 5

2 Road Feature Extraction

21 System Configuration Figure 1 shows the configurationof the mobile robot and the LRF coordinate configurationA single onboard LRF with a tilting angle of 120572

119905is used to

extract road features such as the road surface and curbsThe following list shows the nomenclature for road featureextraction The variables are described with respect to therobot coordinate frame

119908119903 road width

120572119905 nominal tilt angle of LRF

120579119891 angle between the detected road surface points

and 119884119877-axis

119889119891 horizontal look-ahead distance from the robot to

the road surface points(119909C119877 119910C119877) coordinates of the right curb edge (pointC)120579C119877 angle between the right curb and 119884

119877-axis

(119909C119871 119910C119871) coordinates of the left curb edge (point B)120579C119871 angle between the left curb and 119884

119877-axis

22 Road Feature Detection A road feature detection schemewas proposed in our previous works [14 15] The previousworks on road feature detection are briefly reviewed Thefirst step for the road feature detection is the road surfaceextraction In order to identify the road surface the LRFmeasurements in expected road region 119877

119910are selected as

candidates for the road surface 119871119903 Multiple line segments

are constructed by combining consecutive data points of 119871119903

The angle of the road surface is parallel with the 119883119877-axis

in the ideal case Therefore the range data 119871119903are saved as

road surface points 119871119891if the angle of the line segment is

within threshold 120579119890 The road surface is extracted as a line

by using the least square method The extracted road surfaceprovides 120579

119891and 119889

119891from the robotThe overall algorithm can

be summarized in Algorithm 1Figure 2 shows the ideal model of a semistructured road

environment The geometrical features of the road can beused to extract the curb features The curb has the followingfour attributes

(Att 1) The angular difference between the curb ori-entation (120579

119888) and road surface angle (120579

119891) is close to

90∘(Att 2) The gap between the horizon distance of theroad surface (119889

119891) and the 119910 value of the curb point (B

or C) is close to 0(Att 3) The angular difference between the left curb( AB) and the right curb ( CD) is close to 0(Att 4)The difference between the roadwidth and thegap between two curbs is close to 0 It is assumed thatthe road width is known

It is commonly assumed that the robot navigates parallelto the curb It is reasonable to assume that the robot ismovingalong the road without significant change of orientationin most cases Moreover the vertical surfaces of the curbare perpendicular to the road surface When we scan theroad environments using the LRF the road features arecomposed of straight lines with different orientations Inorder to distinguish different line segments that correspondto the road surface the curbs and the sidewalk it is helpfulto assume that the robotrsquos heading direction points forwardalong the road The road width is assumed to be known bygiven map information

Thefirst attribute is used to select the curb candidatesTheline segments that satisfy the following condition are selectedas the curb candidates

1198861=

120587

2

plusmn 120576 (1)



(2) 119871119884119894


(5) for 119894 larr 1 to119873

(6) if 119871119884119894

isin 119877119884 then

(7) 119871119903larr save 119871




(13) if 10038171003817100381710038171003817120579119903119895

10038171003817100381710038171003817le 120579119890 then

(14) 119871119891larr save 119871



119891)


LRF coordinate

Robot coordinate

Curb

Curb

Road

A

B

C

DF

ZL

YL

df

120572tXL

XR

YR

ZR

120579f

wr

O




2 1198863 and 119886

4that correspond


1198862= 119889119891minus avg (119910C119877 119910C119871)

1198863= 120579C119877 minus 120579C119871

1198864= 119908119903minus 119908119888

(2)

CurbRoadLRF

A

B C

D




119888=



4is


x119894= [1198862

1198863

1198864]

119879

(3)




119869 (120572) =

120572119879119878Φ

119861120572

120572119879119878Φ

119882120572

(4)



119878Φ

119861= sum

119888

ℓ119888(120581119888120581119879

119888minus 120581120581119879)

119878Φ

119882= 119870119870

119879minus sum

119888

ℓ119888120581119888120581119888

119879

(5)

with 120581119888

= (1ℓ119888) sum119894isin119888

119870119894119895and 120581 = (1ℓ)sum

119894119870119894119895 ℓ is the



1 1199092 119909



x(119896)119894

=

x(119896)119894

minus 120583(119896)

120590(119896)

(6)



119870119894119895= 119896 (x

119894 x119895) = exp(minus

10038171003817100381710038171003817x119894minus x119895

10038171003817100381710038171003817

2

21205902

) (7)




119878Φ

119861120572 = 120582119878

Φ

119882120572 (8)



119910training = 120572 sdot 119870 (9)


119910test = sum

119894

120572119894119896 (xtraining119894 xtest) (10)


119889 (119910test 120583Φ

119888) =


119888)

2

(120590Φ

119888)2

(11)

where 120583Φ

119888and 120590

Φ






RDGPS119896 = [

1205902

119909120590119909119910

120590119909119910

1205902

119910

]1205902

UERE (12)




DGPS

Robot

Laser rangefinder



(ΔsΔ120579)

Curb information

Map


Localizer



(R120572Rr)

(W120572iWri)

xminusk

Pminusk

x+k2x+k1

zDGPS k

RDGPS k

zcurb k

Rcurb k

P+k2P+k1


Extracted curb

Actual curb

120572i

ri120579i

di







120572119894= 120579119894+ 120576120572119894

119903119894= 119889119894+ 120576119903119894

(13)

where 120576120572119894



2



120572and 120576



Rcurb = [

1205902

120572120590120572119903

120590119903120572

1205902

119903

] = [

119864 (120576120572120576119879

120572) 119864 (120576

120572120576119879

119903)

119864 (120576119903120576119879

120572) 119864 (120576

119903120576119879

119903)

] (14)





xminus119896= 119891 (x


) =

[

[

[

[

[

[

119909minus

119896minus1+ Δ119904119896minus1

cos(120579minus

119896minus1+

Δ120579119896minus1

2

)

119910minus

119896minus1+ Δ119904119896minus1

sin(120579minus

119896minus1+

Δ120579119896minus1

2

)

120579minus

119896minus1+ Δ120579119896minus1

]

]

]

]

]

]

(15)




W

R

Wri

W120572i

Rrk

R120572k

W+

k1

Wy+k1

Wx+k1



119896119910minus

119896

120579minus

119896]

119879



zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879

(16)


hDGPS (xminus

119896 119896) = [119909

minus

119896119910minus

119896]

119879

(17)


HDGPS119896 =120597h (xminus119896 119896)

120597xminus119896

= [

1 0 0

0 1 0] (18)

zcurb119896 = [120572119896

119903119896]

119879

(19)



119894=

[119882120572119894

119882119903119894]

119879


hcurb (x+

1198961 119896 119894)

= [

119882120572119894minus120579+

1198961

119882119903119894minus 119909+

1198961cos 119882120572

119894+ 119910+

1198961sin 119882120572

119894

]

(20)


Hcurb119896 =120597h (x+1198961

119896 119894)

120597x+1198961

= [

0 0 minus1


1198940

]

(21)



NIS119896= (z119896minus h (x+

119896 119896))

119879Sminus1119896

(z119896minus h (x+

119896 119896)) le 120594

2 (22)


119896=








DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate



SG





1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb




True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)





(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











(2) 119871119884119894


(5) for 119894 larr 1 to119873

(6) if 119871119884119894

isin 119877119884 then

(7) 119871119903larr save 119871




(13) if 10038171003817100381710038171003817120579119903119895

10038171003817100381710038171003817le 120579119890 then

(14) 119871119891larr save 119871



119891)


LRF coordinate

Robot coordinate

Curb

Curb

Road

A

B

C

DF

ZL

YL

df

120572tXL

XR

YR

ZR

120579f

wr

O




2 1198863 and 119886

4that correspond


1198862= 119889119891minus avg (119910C119877 119910C119871)

1198863= 120579C119877 minus 120579C119871

1198864= 119908119903minus 119908119888

(2)

CurbRoadLRF

A

B C

D




119888=



4is


x119894= [1198862

1198863

1198864]

119879

(3)




119869 (120572) =

120572119879119878Φ

119861120572

120572119879119878Φ

119882120572

(4)



119878Φ

119861= sum

119888

ℓ119888(120581119888120581119879

119888minus 120581120581119879)

119878Φ

119882= 119870119870

119879minus sum

119888

ℓ119888120581119888120581119888

119879

(5)

with 120581119888

= (1ℓ119888) sum119894isin119888

119870119894119895and 120581 = (1ℓ)sum

119894119870119894119895 ℓ is the



1 1199092 119909



x(119896)119894

=

x(119896)119894

minus 120583(119896)

120590(119896)

(6)



119870119894119895= 119896 (x

119894 x119895) = exp(minus

10038171003817100381710038171003817x119894minus x119895

10038171003817100381710038171003817

2

21205902

) (7)




119878Φ

119861120572 = 120582119878

Φ

119882120572 (8)



119910training = 120572 sdot 119870 (9)


119910test = sum

119894

120572119894119896 (xtraining119894 xtest) (10)


119889 (119910test 120583Φ

119888) =


119888)

2

(120590Φ

119888)2

(11)

where 120583Φ

119888and 120590

Φ






RDGPS119896 = [

1205902

119909120590119909119910

120590119909119910

1205902

119910

]1205902

UERE (12)




DGPS

Robot

Laser rangefinder



(ΔsΔ120579)

Curb information

Map


Localizer



(R120572Rr)

(W120572iWri)

xminusk

Pminusk

x+k2x+k1

zDGPS k

RDGPS k

zcurb k

Rcurb k

P+k2P+k1


Extracted curb

Actual curb

120572i

ri120579i

di







120572119894= 120579119894+ 120576120572119894

119903119894= 119889119894+ 120576119903119894

(13)

where 120576120572119894



2



120572and 120576



Rcurb = [

1205902

120572120590120572119903

120590119903120572

1205902

119903

] = [

119864 (120576120572120576119879

120572) 119864 (120576

120572120576119879

119903)

119864 (120576119903120576119879

120572) 119864 (120576

119903120576119879

119903)

] (14)





xminus119896= 119891 (x


) =

[

[

[

[

[

[

119909minus

119896minus1+ Δ119904119896minus1

cos(120579minus

119896minus1+

Δ120579119896minus1

2

)

119910minus

119896minus1+ Δ119904119896minus1

sin(120579minus

119896minus1+

Δ120579119896minus1

2

)

120579minus

119896minus1+ Δ120579119896minus1

]

]

]

]

]

]

(15)




W

R

Wri

W120572i

Rrk

R120572k

W+

k1

Wy+k1

Wx+k1



119896119910minus

119896

120579minus

119896]

119879



zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879

(16)


hDGPS (xminus

119896 119896) = [119909

minus

119896119910minus

119896]

119879

(17)


HDGPS119896 =120597h (xminus119896 119896)

120597xminus119896

= [

1 0 0

0 1 0] (18)

zcurb119896 = [120572119896

119903119896]

119879

(19)



119894=

[119882120572119894

119882119903119894]

119879


hcurb (x+

1198961 119896 119894)

= [

119882120572119894minus120579+

1198961

119882119903119894minus 119909+

1198961cos 119882120572

119894+ 119910+

1198961sin 119882120572

119894

]

(20)


Hcurb119896 =120597h (x+1198961

119896 119894)

120597x+1198961

= [

0 0 minus1


1198940

]

(21)



NIS119896= (z119896minus h (x+

119896 119896))

119879Sminus1119896

(z119896minus h (x+

119896 119896)) le 120594

2 (22)


119896=








DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate



SG





1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb




True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)





(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119869 (120572) =

120572119879119878Φ

119861120572

120572119879119878Φ

119882120572

(4)



119878Φ

119861= sum

119888

ℓ119888(120581119888120581119879

119888minus 120581120581119879)

119878Φ

119882= 119870119870

119879minus sum

119888

ℓ119888120581119888120581119888

119879

(5)

with 120581119888

= (1ℓ119888) sum119894isin119888

119870119894119895and 120581 = (1ℓ)sum

119894119870119894119895 ℓ is the



1 1199092 119909



x(119896)119894

=

x(119896)119894

minus 120583(119896)

120590(119896)

(6)



119870119894119895= 119896 (x

119894 x119895) = exp(minus

10038171003817100381710038171003817x119894minus x119895

10038171003817100381710038171003817

2

21205902

) (7)




119878Φ

119861120572 = 120582119878

Φ

119882120572 (8)



119910training = 120572 sdot 119870 (9)


119910test = sum

119894

120572119894119896 (xtraining119894 xtest) (10)


119889 (119910test 120583Φ

119888) =


119888)

2

(120590Φ

119888)2

(11)

where 120583Φ

119888and 120590

Φ






RDGPS119896 = [

1205902

119909120590119909119910

120590119909119910

1205902

119910

]1205902

UERE (12)




DGPS

Robot

Laser rangefinder



(ΔsΔ120579)

Curb information

Map


Localizer



(R120572Rr)

(W120572iWri)

xminusk

Pminusk

x+k2x+k1

zDGPS k

RDGPS k

zcurb k

Rcurb k

P+k2P+k1


Extracted curb

Actual curb

120572i

ri120579i

di







120572119894= 120579119894+ 120576120572119894

119903119894= 119889119894+ 120576119903119894

(13)

where 120576120572119894



2



120572and 120576



Rcurb = [

1205902

120572120590120572119903

120590119903120572

1205902

119903

] = [

119864 (120576120572120576119879

120572) 119864 (120576

120572120576119879

119903)

119864 (120576119903120576119879

120572) 119864 (120576

119903120576119879

119903)

] (14)





xminus119896= 119891 (x


) =

[

[

[

[

[

[

119909minus

119896minus1+ Δ119904119896minus1

cos(120579minus

119896minus1+

Δ120579119896minus1

2

)

119910minus

119896minus1+ Δ119904119896minus1

sin(120579minus

119896minus1+

Δ120579119896minus1

2

)

120579minus

119896minus1+ Δ120579119896minus1

]

]

]

]

]

]

(15)




W

R

Wri

W120572i

Rrk

R120572k

W+

k1

Wy+k1

Wx+k1



119896119910minus

119896

120579minus

119896]

119879



zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879

(16)


hDGPS (xminus

119896 119896) = [119909

minus

119896119910minus

119896]

119879

(17)


HDGPS119896 =120597h (xminus119896 119896)

120597xminus119896

= [

1 0 0

0 1 0] (18)

zcurb119896 = [120572119896

119903119896]

119879

(19)



119894=

[119882120572119894

119882119903119894]

119879


hcurb (x+

1198961 119896 119894)

= [

119882120572119894minus120579+

1198961

119882119903119894minus 119909+

1198961cos 119882120572

119894+ 119910+

1198961sin 119882120572

119894

]

(20)


Hcurb119896 =120597h (x+1198961

119896 119894)

120597x+1198961

= [

0 0 minus1


1198940

]

(21)



NIS119896= (z119896minus h (x+

119896 119896))

119879Sminus1119896

(z119896minus h (x+

119896 119896)) le 120594

2 (22)


119896=








DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate



SG





1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb




True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)





(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










DGPS

Robot

Laser rangefinder



(ΔsΔ120579)

Curb information

Map


Localizer



(R120572Rr)

(W120572iWri)

xminusk

Pminusk

x+k2x+k1

zDGPS k

RDGPS k

zcurb k

Rcurb k

P+k2P+k1


Extracted curb

Actual curb

120572i

ri120579i

di







120572119894= 120579119894+ 120576120572119894

119903119894= 119889119894+ 120576119903119894

(13)

where 120576120572119894



2



120572and 120576



Rcurb = [

1205902

120572120590120572119903

120590119903120572

1205902

119903

] = [

119864 (120576120572120576119879

120572) 119864 (120576

120572120576119879

119903)

119864 (120576119903120576119879

120572) 119864 (120576

119903120576119879

119903)

] (14)





xminus119896= 119891 (x


) =

[

[

[

[

[

[

119909minus

119896minus1+ Δ119904119896minus1

cos(120579minus

119896minus1+

Δ120579119896minus1

2

)

119910minus

119896minus1+ Δ119904119896minus1

sin(120579minus

119896minus1+

Δ120579119896minus1

2

)

120579minus

119896minus1+ Δ120579119896minus1

]

]

]

]

]

]

(15)




W

R

Wri

W120572i

Rrk

R120572k

W+

k1

Wy+k1

Wx+k1



119896119910minus

119896

120579minus

119896]

119879



zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879

(16)


hDGPS (xminus

119896 119896) = [119909

minus

119896119910minus

119896]

119879

(17)


HDGPS119896 =120597h (xminus119896 119896)

120597xminus119896

= [

1 0 0

0 1 0] (18)

zcurb119896 = [120572119896

119903119896]

119879

(19)



119894=

[119882120572119894

119882119903119894]

119879


hcurb (x+

1198961 119896 119894)

= [

119882120572119894minus120579+

1198961

119882119903119894minus 119909+

1198961cos 119882120572

119894+ 119910+

1198961sin 119882120572

119894

]

(20)


Hcurb119896 =120597h (x+1198961

119896 119894)

120597x+1198961

= [

0 0 minus1


1198940

]

(21)



NIS119896= (z119896minus h (x+

119896 119896))

119879Sminus1119896

(z119896minus h (x+

119896 119896)) le 120594

2 (22)


119896=








DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate



SG





1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb




True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)





(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












W

R

Wri

W120572i

Rrk

R120572k

W+

k1

Wy+k1

Wx+k1



119896119910minus

119896

120579minus

119896]

119879



zDGPS119896 = [119909DGPS119896 119910DGPS119896]119879

(16)


hDGPS (xminus

119896 119896) = [119909

minus

119896119910minus

119896]

119879

(17)


HDGPS119896 =120597h (xminus119896 119896)

120597xminus119896

= [

1 0 0

0 1 0] (18)

zcurb119896 = [120572119896

119903119896]

119879

(19)



119894=

[119882120572119894

119882119903119894]

119879


hcurb (x+

1198961 119896 119894)

= [

119882120572119894minus120579+

1198961

119882119903119894minus 119909+

1198961cos 119882120572

119894+ 119910+

1198961sin 119882120572

119894

]

(20)


Hcurb119896 =120597h (x+1198961

119896 119894)

120597x+1198961

= [

0 0 minus1


1198940

]

(21)



NIS119896= (z119896minus h (x+

119896 119896))

119879Sminus1119896

(z119896minus h (x+

119896 119896)) le 120594

2 (22)


119896=








DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate



SG





1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb




True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)





(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










DGPS baseDGPS rover

Pioneer P3-AT

LaptopLaser range

finder

Communicate



SG





1198831(R1 L1) 00005 1634922 True Curb

1198832(R1 L2) 19779 2025195 True Curb

1198833(R2 L1) 1056307 41180 False Curb

1198834(R2 L2) 1102497 32296 False Curb




True curb 3524(971)

106(29)

3566(982)

64(18)

False curb 307(274)

814(726)

4(04)

1117(996)





(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a)

0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)

(b)

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

R2

L1 R1

L2

(c)

Extracted curbs

0 1 2 3

0

1

2

3

4

5

6

7

minus1minus2

minus1


y(m

)

x (m)

(d)


0 50 100 150

0

50

100

150

y(m

)

x (m)

minus50

minus50minus100




SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











SG

A

B

DE

C

F

(a)

0 5 10 15 20 25 300

2

4

6

8

Time (min)

Dist

ance

(m)

A B C D E F

120590DGPS

(b)


CurbAdditional LRF





Range std 120590119903

Angle std 120590120572

Correlation 120590119903120572







0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

100

200



N(c

ount

)


0

100

200

300



N(c

ount

)


(a)


0

200

400

600


N(c

ount

)


0

200

400

600



N(c

ount

)


(b)


0 1 2 3

0

1

2

3

4

5

6

7


minus1minus2

minus1


y(m

)

x (m)




SG

A

B

DE

C

F





0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

1

2

3

4

5

Late

ral e

rror

s (m

)

A B C D E FSection


minus1

minus2

minus3

minus4

(a)

A B C D E F

0

1

2

3

4

5

Late

ral e

rror

s (m

)Section


minus1

minus2

minus3

minus4

(b)


A B C D E FSection


0

5

10

15

Ang

ular

erro

rs (d

eg)

minus5

minus10

(a)

A B C D E F

0

5

10

15

Ang

ular

erro

rs (d

eg)

Section


minus5

minus10

(b)


5 Conclusion






Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Acknowledgments


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Localization of Outdoor Mobile Robots...

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