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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Curb detection is an important research topic in environment perception, which is an essential part of unmanned ground vehicle (UGV) operations. In this paper, a new curb detection method using a 2D laser range finder in a semi-structured environment is presented. In the proposed method, firstly, a local Digital Elevation Map (DEM) is built using 2D sequential laser rangefinder data and vehicle state data in a dynamic environment and a probabilistic moving object deletion approach is proposed to cope with the effect of moving objects. Secondly, the curb candidate points are extracted based on the moving direction of the vehicle in the local DEM. Finally, the straight and curved curbs are detected by the Hough transform and the multi-model RANSAC algorithm, respectively. The proposed method can detect the curbs robustly in both static and typical dynamic environments. The proposed method has been verified in real vehicle experiments.

Environment perception is a key research direction in the area of UGV development. The UGV is expected to navigate autonomously in semi-structured environments such as campus sites, parks, and the urban environment. It is important for an UGV to be able to detect obstacles around it correctly in order to avoid the risks of collision. The road curb is a special sub-category that can represent the boundary of the road so as to calculate the obstacle-free areas.

According to the different features of the curb detection, the existing algorithms are divided into two categories: the first is based on detection of the geometrical features of the curb; the second category is based on image context derived from the monocular vision field. The main merit of the second method is that it contains rich information, such as color, texture,

The geometrical features of a curb are not clear in a real structural environment, as curb height varies only from 5 cm to 25 cm 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. In recent years, researchers have presented some curb detection algorithms using geometrical features which are obtained by laser range finder [

In [

In [

In this paper, we propose a new curb detection method based on a local DEM which is built from 2D sequential laser range finder data and vehicle state data. The algorithm can detect road curbs accurately and quickly in both static and typical dynamic environments where a few objects may move on the road or roadside, and it belongs to the second class based on geometrical feature algorithms. Compared with the first class algorithms, our method has three main merits. Firstly, our method can obtain robust curb detection results, because the historical and current sensor information is considered in the process of the curb detection. To be precise, our method uses the local DEM information which includes multiple laser data frames to detect the curb. The first class algorithms only use limited information, so these algorithms are sensitive to data noise. Secondly, we only select the suitable curb model in our method, and the curb tracking step is not available. The reason is that the curb model implies knowledge of the geometric information of the road. If we obtain the parameters of the curb model, we will not need to track the new curb. However, curb tracking is an important step after the curb detection in the first class algorithms, because it can check the validation of the new result based on the filter which includes the former curb information. In general, curb tracking is a difficult task using the traditional tracking methods such as the Kalman filter. The main reason is that the traditional tracking methods need to know the accurate process model and estimate the error model, which are hard to obtain in practice. Thirdly, our method can detect the curbs in a typical dynamic environment, which reduces the influence of moving objects in the process of the building the local DEM.

The paper is structured as follows: in Section 2, the proposed method is described, and the curb detection algorithm will be presented; the experimental results are shown in Section 3 and conclusions in Section 4.

The basic idea of the proposed curb detection method based on the geometrical features are mentioned in Section 1. There are four steps in the proposed new method. The schematic of the new curb detection method is shown in

First, a local DEM is built in real-time by a 2D laser range finder and vehicle state data which denotes the surrounding environment information of the vehicle. Second, curb candidate points are extracted in the local DEM and we accumulate the multiple results of curb candidate points. Third, the straight curbs are obtained by the Hough transform algorithm and some constraint conditions in the accumulated curb candidates. Then, the residual curb candidate points, except straight curbs, are processed by the multi-model RANSAC algorithm which uses the suitable model to represent the curved curb. Each step is discussed in detail in the following.

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 [

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.

Building the DEM is a challenge task with 2D laser range finder in a dynamic environment. We not only have to determine the position of the vehicle and the map of the environment, but also identify and deal with possible moving objects in the environment. Compared with the static environment, there are some difficulties of building the DEM in a dynamic environment. The first one is that some spurious objects appear in the passing area of moving objects. The phenomenon is shown in the blue rectangle areas of this Section. The long white trace is a spurious object in blue rectangle areas which will have a serious influence on the curb detection. The second one is that the occlusion problem that happens more frequently in a dynamic environment than that in a static environment. This will cause missing data for some parts of the curb information in the DEM. The missing data cannot be obtained again by the 2D laser range finder, because of the scan principle and the way of installation of the 2D laser range finder which is shown in _{1} in position 1 in _{2} cannot be detected because of the occlusion of the right vehicle. The curb point _{1} cannot be detected even during this moving process because the 2D laser range finder has only one scanning plane which is shown in _{1} in position 1, it has no chance to scan _{1} again. The occlusion can bring about difficulties in the curb detection. The situation of the missing data appears in the red rectangle areas due to the occlusion of the moving object in

A probabilistic moving objects deletion approach is proposed in this paper which can delete most of spurious objects caused by moving objects in the process of building the DEM. The purpose of the approach is to decrease the influence of moving objects in the DEM and to keep the geometric feature of the road areas which are the passing areas of moving objects at the same time. In other words, we want to build the static environment map in the dynamic environment. The main idea behind the proposed method is to use the time cue based on the probability approach to detect the data of the moving objects.

We define the function which is called data permit mapping probability function (DPMPF). Firstly, the DPMPF of the each cell is initialized: _{i,j}_{i,j}_{i,j}_{new}_{last}_{last}_{new}_{last}_{1} is the threshold, and is defined by the prior knowledge. Here, we choose _{1} = 0.5 s. If _{last}

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's direction of movement. 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:

The slope between the curb candidate grid (point) and the adjacent grids is large enough. The formula for slope calculation is as follows:
_{1}, _{1}) and (_{2}, _{2}) denote grid coordinates in the local DEM; _{1} and _{2} are the height of the grid.

The height difference which is denoted Δ_{1}_{2}.

The height variance Δ_{2}_{min} denotes the lower limit of height variance, _{max} denotes the upper limit of height variance.

The results of the curb candidate detection are shown in

However some false candidate points arise in the red rectangle area in

Note that the results of the curb candidate detection only have the right part in

In this section, the real road curbs are extracted from the result of the accumulated curb candidates. The curbs are divided into two classes: straight and curved curbs. According to the different characteristics of the straight and curved curbs, we use the Hough transform to extract the straight curbs and the multi-model RANSAC algorithm to extract the curved curbs.

Firstly, the candidate straight curb is detected by the Hough transform after the accumulated results of the curb candidates are handled by the isolated point filter algorithm to eliminate random noise. There are two reasons to adopt the Hough transform to detect the straight curbs. The first reason is that the Hough transform has a good adaption to a 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. Although the processing time of the Hough transform is longer than the least squares algorithm and incremental algorithms, it still satisfies the real-time operation requirement. The average and the worst computational time of our algorithm are about 2.45 ms and 4.91 ms, respectively.

Secondly, the real straight curb is selected from the candidate straight curbs based on the results of the Hough transform. We have designed a two-stage scheme to choose the best straight curb: (1) the candidate straight curbs are divided into three categories: the left straight curbs, the right straight curbs and other curbs according to the position and direction of the vehicle; (2) we will use three constraints to choose the best straight curbs in the first two categories. Based on the above classification, we have designed the following constraint conditions:

The direction constraint:
_{c}_{i}_{1} denotes an angle threshold.

The constraint of the historical straight curb information:
_{old}_{2} denotes an angle threshold. It is assumed that the straight curbs vary regularly and continuously.

The life cycle constraint:
_{new}_{old}_{1} denotes the life cycle. The constraint means that the validation of the historical straight curb information is restricted in our algorithm. In other words, the historical straight curb information has a life cycle. If _{new}_{old} T_{1}, the historical straight curb information will be invalid.

The curved curb detection is an important research area, because curved curbs usually appear in practice. In this part, the multi-model RANSAC algorithm is proposed to detect the curved curbs. RANSAC [

The ordinary RANSAC algorithm is unsuitable for extraction of the curved curb because of the above drawbacks. There are two reasons. The first one is that the number of the curved curbs is equal or greater than one when the curb exists. The second one is that the shape of the curved road is complex. Namely, with a one curved curb model it is hard to describe the entire curved road. In this paper, the multi-model RANSAC algorithm is proposed to deal with the above problems. The merit of our algorithm is that it can cope with multiple models at the same time and select a suitable curved curb model. The flowchart of our algorithm is shown in

There are two purposes of setting up a data cluster. The first purpose is that the multiple curved curb candidates are divided into different clusters before fitting the parameters of the model; the second purpose is to reduce the noise points in the data set.

According to the complexity of curbs in the real road environment, we have selected the quadratic polynomial model and cubic polynomial model to represent the curved curb. The adaptive model selection step can choose the suitable curved curb model online from these models in our algorithm. Formally, the four models are split into two groups as follows:
_{0}, _{1}, _{1}, _{3} and _{0}, _{1}, _{2}, _{3} denote the coefficients of cubic polynomial models individually; the parameters _{0}, _{1}, _{2} and _{0}, _{1}, _{2} denote the coefficients of quadratic polynomial models individually. Note that only one model is valid when we use it to a sample from the data set.

In our algorithm, the adaptive model selection step includes two parts in _{i}_{i}

In order to increase the efficiency of our algorithm, we evaluate and modify the iterations which denotes _{inliers}_{all}^{n}^{n}_{0} = 50. We can see that the majority of the iterations less than 20, and only a few iterations close to _{0}. According to our calculation, in comparison with the original algorithm, the efficiency of the multi-model RANSAC algorithm has been increased by 47.64%. The average and the worst computational time of our algorithm are about 2.44 ms and 24.89 ms, respectively. The details of the computer and software are introduced in Section 3.

The experimental platform is a light off-road vehicle. A forward-looking laser range finder is mounted on the front top of the vehicle and tilts down a little, and it is shown in the red ellipse area in

The first experimental site is shown in

Typical straight curbs exist in Scene 1, and the vehicle drove from the East to the West.

In Scene 2, the right curved curb and the left straight curb were seen in

Scene 3 is a typical dynamic environment, and vehicle can be seen on the road in

Scene 4 is a typical dynamic environment too, but it is more complex than Scene 3. Some dynamic objects which include the car and the bicycles appear in the local DEM in

In [

The results of the data cluster, bad detection and our algorithm are shown in the first, second and third column respectively. The red rectangle region denotes the same cluster in the same row. We use the quadratic polynomial model to obtain the result in

In the second experiment, the travelled distance of the vehicle is 3.2 km. The hardware and software specification in our system is shown in

The average and the worst computational time of our algorithm are about 58.5 ms and 81.9 ms, respectively. In

In this paper, a new curb detection method has been developed based on a local DEM which can be established with 2D sequential laser data and vehicle state data. The robustness and efficiency of the method have been demonstrated through various experiments. According to the experimental results of the four scenes, the proposed algorithm can not only detect road curbs in a static environment, but also in a typical dynamic environment.

Future research will focus on the fusion of camera and laser range finder data to extract the road surface, and on extending the curb information with recognized and classified obstacles and obstacle-free areas on the road.

This work was supported in part by the National Nature Science Foundation of China under Grant Nos. 90820302, 61075072 and 61075043. The first author would like to acknowledge the financial support from the China Scholarship Council to support his joint Ph.D. research training at the University of New South Wales, Sydney, Australia.

Flowchart of the new curb detection method.

The local DEM in static environment.

The schematic of the laser scanning on the road.

The local DEM in dynamic environment. (

The results of the curb candidate detection. (

The accumulated results of the curb candidates. (

The flowchart of the multi-model RANSAC algorithm.

The iterative number of the RANSAC algorithm.

The position of the laser range finder.

The running route of the vehicle in first experiment. (

The result of the straight curb detection. (

The result of the curb detection. (

The curb detection in typical dynamic environment. (

The contrastive result of the curb detection. (

The contrastive result of the curved curb detection. (

The execution time of our algorithm.

The curb detection results in the second experiment. (

The hardware and software specification.

Memory(RAM) | 2 GB |

Operating system | Windows XP Professional SP2 |

Programming language | C++ |

The confusion matrix.

Actual curb | 23248 | 3574 |

Actual no curb | 341 | 4837 |