Urban road environments that have pavement and curb are characterized as semistructured road environments. In semistructured road environments, the curb provides useful information for robot navigation. In this paper, we present a practical localization method for outdoor mobile robots using the curb features in semistructured road environments. The curb features are especially useful in urban environment, where the GPS failures take place frequently. A curb extraction is conducted on the basis of the Kernel Fisher Discriminant Analysis (KFDA) to minimize false detection. We adopt the Extended Kalman Filter (EKF) to combine the curb information with odometry and Differential Global Positioning System (DGPS). The uncertainty models for the sensors are quantitatively analyzed to provide a practical solution.
Outdoor environments have irregular shapes and changes in geometry and illumination due to the weather condition. Therefore, environmental uncertainty is relatively high. There are numerous studies for autonomous navigation of mobile robot in outdoor environments. Typical examples are the autonomous vehicles that were developed through DARPA Grand/Urban Challenges [
The aim of this work is to develop a practical localization method for outdoor mobile robots. In particular, this study focuses on surveillance robots in urban road environments. A localization method using a small number of sensors is proposed instead of using multiple high cost sensors.
The fusion of a global positioning system (GPS) and inertial measurement unit (IMU) has been widely used for the outdoor localization of mobile robots [
Generally, urban road environments are paved, and the curbs act as the boundaries of the roads. Therefore, urban road environments are characterized as semistructured road environments. In semistructured road environments, the curb provides useful information for robot navigation. Therefore, the curb features have been widely used for navigation strategies and localization methods. In [
A method for traversable region detection using road features such as road surface, curbs, and obstacles is proposed in our previous works [
The contribution of this paper can be summarized by two schemes. The first contribution is the robust curb extraction scheme by using a single Laser Range Finder (LRF). In order to reduce the number of false detection of the curbs, the classification of the curb data and the noncurb data is conducted by using Kernel Fisher Discriminant Analysis (KFDA) in [
The remainder of this paper is organized as follows. A method for curb extraction is presented in Section
Figure
The configuration of a robot and installation of a LRF.
A road feature detection scheme was proposed in our previous works [
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Figure
(Att_1) The angular difference between the curb orientation (
(Att_2) The gap between the horizon distance of the road surface (
(Att_3) The angular difference between the left curb (
(Att_4) The difference between the road width and the gap between two curbs is close to 0. It is assumed that the road width is known.
Ideal model of semiconstructed environment (blue dotted line: LRF data, red line: extracted road surface).
It is commonly assumed that the robot navigates parallel to the curb. It is reasonable to assume that the robot is moving along the road without significant change of orientation in most cases. Moreover, the vertical surfaces of the curb are perpendicular to the road surface. When we scan the road environments using the LRF, the road features are composed of straight lines with different orientations. In order to distinguish different line segments that correspond to the road surface, the curbs, and the sidewalk, it is helpful to assume that the robot’s heading direction points forward along the road. The road width is assumed to be known by given map information.
The first attribute is used to select the curb candidates. The line segments that satisfy the following condition are selected as the curb candidates:
Once the curb candidates are determined, attributes 2, 3, and 4 are used to extract the correct curb out of the curb candidates. The attribute values
KFDA is applied to extract the correct curb from the curb candidates. KFDA aims to find a discriminant function for optimal data classification. Therefore, the discriminant function can be used to classify the curb candidates as curb and noncurb class. The curb extraction is conducted by the following procedure. First, the training data with class information are selected. The discriminant function is derived from the offline computation of the training data. When the discriminant function is obtained, classification of the curb candidates is carried out by the discriminant function in real time.
The discriminant function
The “betweenclass variance matrix”
Training data
Here,
The discriminant function that maximizes the object function in (
The classification of the training data is conducted by an inner product of the data matrix
The class of test data can be predicted by using the discriminant function
The class properties of the training data are used to predict the class of the test data
This paper adopts EKF to estimate the robot pose using curb features. EKF is a wellknown method for mobile robot localization and sensor fusion [
A block diagram of localization process.
The GPS error mainly occurs due to the following two factors. One is the pseudorange errors caused by systematic factors. Another is the geometric constellation of satellites. In this paper, DGPS is used to minimize the pseudorange errors. The uncertainty model for DGPS is computed under the consideration of the “dilution of precision” in relation to the geometric constellation of satellites and the pseudorange error or socalled “userequivalent range error” [
The error covariance
Several studies were proposed to define the error covariance of line features [
In order to define the error covariance
Noise model of the extracted curb.
The covariance matrices are experimentally defined as constant values for the left and right curbs.
The odometry data from the wheel encoders are used to predict the robot pose. By using the incremental distance
The state vector
In order to correct the odometry error, the first measurement correction is performed using DGPS measurements. The update frequency is set to 1 Hz on the basis of the DGPS measurement frequency. When the available position measurement is provided, the observation vector is given in global coordinates. Consider the following:
The observation model for the current state is described as follows:
The measurement Jacobian matrix
The second measurement correction is conducted by using the curb features. The observation vector for the extracted curb is given by (
Extracted curb features and a line map with respect to the global coordinate frame.
The robot pose is corrected by comparing the curb with the map. The extracted curb is matched with the
The Jacobian matrix
The consistency of EKF relies on the observation model. If an erroneous sensor observation is provided, the system does not provide a consistent result. Therefore, the outliers that lie outside of the uncertainty bounds should be rejected. A normalized innovation squared (NIS) test is implemented in order to confirm the consistency of the filter. NIS value has a
Figure
Sensor system attached to mobile robot.
The experiment was performed in Korea University in Seoul, Korea, as shown in Figure
Experimental environment.
The curb extraction process in a semistructured road environment is shown in Figure
Class prediction for pairs of curb candidates.
Candidates  Mahalanobis distance  Class prediction  

Curb class  Noncurb class  

0.0005  163.4922  True Curb 

1.9779  202.5195  True Curb 

105.6307  4.1180  False Curb 

110.2497  3.2296  False Curb 
Curb extraction results. (a) Road environment. (b) Road surface detection. (c) Curb feature candidates on both sides. (d) Extracted curb.
The curb extraction was performed while the robot navigates through the experimental path. Figure
Classification results including confusion matrix.
Instance  PCA  KFDA  

Class correct  4338  91.3%  4683  98.6% 
Class incorrect  413  8.7%  68  1.4% 
Total 






Classified as  Classified as  
True curb  False curb  True curb  False curb  


True curb  3524 
106 
3566 
64 
False curb  307 
814 
4 
1117 
Curb mapping result on experimental path.
The DGPS measurements are represented by red dots along the experimental path in Figure
(a) DGPS measurement and (b) DGPS uncertainty measurement (
The curb estimation errors are considered in order to define the error covariance. The most accurate result for the quantitative curb uncertainty is obtained by measuring the estimation errors in experimental environments. The estimation errors were measured while the robot navigates through the road with curbs. Ground truth for the curb was provided by an additional LRF that is attached to the side of the robot as shown in Figure
Additional LRF for ground truth of the curbs.
Figure
Error covariance of extracted curb.
Range std. 
Angle std. 
Correlation  

Right curb  0.1620 m  0.0575 rad  0.0035 m·rad 
Left curb  0.1614 m  0.0649 rad  −0.0034 m·rad 
Distribution of estimation errors for (a) left and (b) right curbs.
The covariance representation for the extracted curbs is shown in Figure
Extracted curbs and covariance representation.
The localization results are shown in Figure
Localization results in semistructured road environment.
Figure
Lateral errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb.
Heading errors (a) corrected by DGPS and (b) corrected by DGPS and extracted curb.
This paper presents a localization method for outdoor robots using curb features in semistructured road environments. A reliable curb extraction scheme is proposed to classify the curb candidates as curb and noncurb classes. Most of the curbs in an experimental path are extracted with high accuracy. An EKFbased localization is also proposed to combine the extracted curbs with odometry and DGPS measurements. The uncertainty models of the sensors are defined by experiments to provide a practical solution for localization. From experimental results, the robustness of the proposed method is demonstrated in real road experiments. The curb features can correct significantly the lateral position and heading errors in dense area, where the DGPS signal gets degraded by buildings.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported in part by the MKE (The Ministry of Knowledge Economy), Korea, under the Human Resources Development Program for Convergence Robot Specialists Support Program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA2013H1502131001). This work was also supported by the National Research Foundation of Korea (NRF) Grant funded by Korea Government (MEST) (2013029812).