2013 Seventh International Conference on Image and Graphics
Curb Detection Using 2D Range Data in a Campus Environment
Zhao Liu, Daxue Liu, Tongtong Chen, Chongyang Wei College of Mechatronic Engineering and Automation National University of Defense Technology Changsha, China
[email protected]
Abstract—Curb detection is an important research topic for unmanned ground vehicle (UGV) navigation. In this paper, a new curb detection method is proposed using a 2D laser range finder in a campus environment. Firstly, a local Digital Elevation Map (DEM) is built with 2D sequential laser range finder data and vehicle state information. Then, the curb candidate points are extracted considering the moving direction of the vehicle in the local DEM. Finally, the 1D Gaussian process regression is firstly used for curb detection, and the initial training curb data are obtained online by the extracted straight curbs. The proposed method has been verified in different scenes with the real vehicle platform, and it can detect the straight and curved curbs robustly in a campus environment.
II.
The geometrical features of a curb are not clear in a real structural environment, as curb height varies only from 5cm to 25cm in general. Therefore, curb detection is a challenging task, because the geometrical features of a curb might be contaminated by random noise and measurement errors. According to the idea of curb detection, such algorithms based on the geometrical feature can be divided into two classes: one idea is that range data are processed individually per frame and the algorithm can obtain curb candidate points, then the curb points are tracked using the filter method, such as Kalman filter and Extend Kalman filter; the other idea is that the algorithm extracts ground surface or obstacle-free area in a local map to obtain local curb information. In [1, 2], Kodagoda et al. used a tilted 2D laser range finder to detect road curbs. In this approach, the result of the measurement is predicted with the Kalman filter algorithm. If the measurement is far away from the prediction, it is considered as a curb candidate. Prior knowledge assumptions have to be made to find the right curbs. For example, the UGV needs to move in parallel to the curb, the street width is known, and the curbs are locally straight. Smadja L et al. also presented a curb detection approach using a 2D laser range finder [3]. Firstly, the road surface points are extracted by the RANSAC algorithm and are projected onto a global map; secondly, the boundaries of the obstacle-free area are fitted by the RANSAC algorithm, and then the curb candidate points are picked out by a multi-frame accumulated map. In [4], the author detected road curbs using HDL64-E LIDAR which contains 64 scan lines, but the algorithm deals with the data to be one line as a unit. In [5, 6], the stereo vision is used for detecting the curbs. A straight curb is detected by the Hough transform, and a curved curb is extracted by chains of segments in [5]. In [6], the author changed the curbs model to cubic polynomial curves, and then used the RANSAC algorithm to compute the parameters of the model. The authors built a DEM to detect curbs by Conditional Random Field (CRF) in [7]. The approach can detect and reconstruct different curvature and height curbs, but the algorithm assumes that the curb is visible in front of the vehicle. If the curb is occluded by other object on the road, the performance of the algorithm will be decrease. Orazio Gallo et al. proposed a modified RANSAC algorithm (dubbed CC-RANSAC) for detecting street
Keywords-curb detection; 1D Gaussian process regression; 2D laser range finder
I.
INTRODUCTION
Environment perception is a key research direction in the areas of unmanned ground vehicle (UGV) developments. The UGV is expected to navigate autonomously in a structure or semi-structured environment such as campus sites, parks, and urban environment. It is important for a UGV to detect all kinds of obstacles around it correctly in order to avoid the risks of collision. The road curb is a special sub-category of the obstacles. The road curbs usually represent the boundary of the road between driving lane and sidewalk so as to calculate the obstacle-free areas. Furthermore, the vehicle and pedestrian detection can be improved by the road curb. Secondly, a collision is a potential risk of the tire damage, although curbs in general are of low height. The damage may result in accidents in critical situations. In this paper, we propose a new curb detection method based on a local Digital Elevation Map (DEM) which is built with 2D sequential laser range finder data and vehicle state information. The 1D Gaussian process regression is firstly used for curb detection. The initial training curb data are obtained online by the extracted straight curbs, and the training data will be updated step by step based on the new curb points. The proposed method can detect the straight and curved curbs robustly in the campus environment. The rest of the paper is structured as follows. The related works are given in the next section. In Section 3, the curb detection method is described. The experimental results are shown in Section 4 and conclusion in Section 5. 978-0-7695-5050-3/13 $26.00 © 2013 IEEE DOI 10.1109/ICIG.2013.64
RELATED WORK
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the local DEM using 2D sequential laser rangefinder data and vehicle state data which contain global position and Euler rotation angles information. Our algorithm detects the road curb based on the local DEM in the global coordinate system. According to environmental complexity, vehicle navigation requirement and computing power of the system, we build an 80 × 80 m local DEM, and the grid size is 20 × 20 cm. Fig. 2(a) shows an example of the local DEM in the static environment. The gray level denotes the height of the terrain, and the larger gray level represents the higher height. The position of vehicle is denoted by a yellow point in Fig. 2(a) which located in the center area of the map. The road region and roadside can be distinguished in Fig. 2(a). We can find that the local DEM can represent the surrounding environment of a vehicle accurately in the static environment.
surface and pavement surface using Canesta TOF Camera [8, 9]. The algorithm can detect two nearby surfaces by the largest connected components of inliers. The above approaches [5-9] belong to the second class algorithms based on geometrical feature. The proposed method belongs to the second class based on geometrical feature algorithms. Compared with the first class algorithms, our method can obtain the robust curb detection results, because the historical and current sensor information is considered in the process of the curb detection. Namely, our method uses the local DEM information which includes multiple laser data frames to detect the curb. But the first class algorithms only use the limited information, so these algorithms are sensitive to data noise. In addition, the curb model and the curb tracking step is not available in our method. Instead of it, the 1D Gaussian process regression can detect the new curb points. To our knowledge, the 1D Gaussian process regression is firstly used for curb detection. III.
THE CURB DETECTION METHOD
A. The Overview of the Method The schematic of the proposed curb detection method is shown in Fig. 1. There are four steps in the proposed new method. First, a local DEM is built in real-time by 2D laser range finder and vehicle state data which denote the surrounding environment information of the vehicle. Second, curb candidate points are extracted in the local DEM. Third, the training data are selected from the straight curbs which are obtained by the Hough transform algorithm and some constraint conditions. Finally, the new curb points are detected by 1D Gaussian process regression. Each step is discussed in detail in the following.
(a) Figure 2.
(b)
The results of the curb candidate detection. (a)The local DEM. (b) The curb candidate points.
C. Curb Candidate Detection In our method, it is assumed that the height of the ground surface varies continuously and slowly. The curb candidate point has a main feature: elevation gradient variation in the local DEM. We design a curb candidate point detection algorithm based on the vehicle moving direction. The algorithm assumes that the vehicle is located on the road surface, and chooses the appropriate direction to detect the elevation gradient variation in the adjacent grids. The above detected directions of the grid depend on the vehicle moving direction, but not equal to the vehicle moving direction. The curb candidate point should meet the needs of the following conditions: (a) The slope between the curb candidate grid (point) and the adjacent grids is large enough. The formula for slope calculation is as follows:
Figure 1. Flowchart of the new curb detection method.
tan θ =
B. Environment Representation The construction of models of the environment is crucial in UGV operations. There are many environment models, such as elevation grids, point clouds, 3-D grids, and meshes [10]. In this research, the elevation grid model is chosen to represent the surrounding environment of a UGV. We build
z1 − z2 ( x1 − x2 ) 2 + ( y1 − y2 )2
(1)
where ( x1䯸 y1 ) and ( x2䯸 y2 ) denote grid coordinates in the local DEM; z1 and z 2 are the height of the grid. (b) The height difference which is denoted Δh 1 in a same curb candidate grid is larger than a given threshold T2 .
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where μ* is the best estimation for f∗ , and is the mean of the above distribution. Σ∗ is the uncertainty in the best estimation, and is the variance of the above distribution. p( f∗ | X ∗ , X , f ) denotes that the posterior predictive density. In this paper, the squared-exponential covariance function in one dimension is used, and it has the following form
(c) The height variance Δh2 between the curb candidate grid and the adjacent grid meet the following formula: hmin ≤ Δh2 ≤ hmax
(2)
where hmin denotes the lower limit of height variance, hmax denotes the upper limit of height variance. The result of curb candidates is shown in Fig. 2(b), and the current local DEM around the vehicle is represented in Fig. 2(a). The white points denote curb candidate points in Fig. 2(b). We can find that our algorithm can detect the straight curb candidate points. But some false candidate points arise in the red rectangle areas of Fig. 2(b).
k ( x p , xq ) = σ 2f exp(−
which is one iff p = q and zero otherwise. x p , xq ∈ X , and p, q are the index of the matrix K .
E. The Curb Detection Based on the 1D Gaussian Process Regression In general, the road curb arise in real environment continuously. The historical and current curb points have the relationship in the process of the curb detection. We want to use the relationship to detect the new curb points. The 1D Gaussian process regression can predict the function output on the basis of some training data. In other words, the 1D Gaussian process regression uses the relationship of the training data to make predictions. Based on the above reason, we design the online curb detection algorithm by the 1D Gaussian process regression. There are four steps in the proposed algorithm: extraction of the initial training data, Gaussian process regression, evaluation of the curb points and training data update. 1) Extraction of the initial training data by straight curbs Due to Gaussian process regression belongs to supervised learning, the most important thing is how to obtain the reliable training data. In this paper, the initial training data are obtained by the straight curbs which are detected using the Hough transform and multiple constraints. The straight curbs are divided into two categories: the left straight curbs and the right straight curbs according to the position and direction of the vehicle. According to the receipt time of the data, the latest left and right straight curb points of each category is selected as the training data, respectively. There are two reasons to adopt the Hough transform to detect the reliable straight curb. The first reason is that the Hough transform have a good adaption in the noisy environment. Compared with it, the traditional method such as the least squares can be easily affected by gross errors, leading to wrong results. The second reason is that the Hough transform considers the entire distribution of the data set, so it can give more accurate result than the incremental line algorithms which use the local data distribution. The best straight curbs are selected by three constraints based on the results of the Hough transform. The constraints are introduced as follows: (a) The direction constraint:
(3)
For notational simplicity we will take the mean function m( x) to be zero, although this need not be done. A Gaussian process defines a prior over functions, which can be converted into a posterior over functions based on some known data [12]. If the characteristic of the output is continuous, it is a Gaussian process regression problem. Suppose we observe a training set D = {( xi , f i ), xi ∈ X , i = 1...n} , where f i = f ( xi ) + ε .
ε denotes the noise term, and ε N (0, σ n2 ) , where σ n2 denotes the noise variance. Given a test set X ∗ which include n points, the goal of the Gaussian process regression is to predict the function output f∗ . The joint distribution has the following form
§ § K K∗ · · §f · ¸ ¸¸ ¨ ¸ N ¨¨ 0, ¨ T © f∗ ¹ © © K∗ K∗∗ ¹ ¹
(4)
where K = k ( X , X ) is n × n , K∗ = k ( X , X ∗ ) is n × n∗ , and K∗∗ = k ( X ∗ , X ∗ ) is n∗ × n∗ .The key predictive equations of Gaussian process regression is as follows: p( f∗ | X ∗ , X , f ) = N ( f∗ | μ* , Σ∗ )
(5)
μ* = K∗T K −1 f
(6)
Σ∗ = K∗∗ − K∗T K −1 K∗
(7)
(8)
where σ 2f denotes the signal variance, δ pq is a Kronecker delta
D. Gaussian Process Regression A Gaussian process is defined as a collection of random variables, any finite number of which has a joint Gaussian distribution [11]. A Gaussian process is completely specified by its mean function m( x) and covariance function k ( x, x′) . The Gaussian process is represented as f ( x) GP(m( x), k ( x, x ′))
1 ( x p − xq ) 2 ) + σ n2δ pq 2l 2
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φc − θi < δ1
0
