CN109188459A - A kind of small obstacle recognition method in ramp based on multi-line laser radar - Google Patents

A kind of small obstacle recognition method in ramp based on multi-line laser radar Download PDF

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CN109188459A
CN109188459A CN201811000910.4A CN201811000910A CN109188459A CN 109188459 A CN109188459 A CN 109188459A CN 201811000910 A CN201811000910 A CN 201811000910A CN 109188459 A CN109188459 A CN 109188459A
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point cloud
road
road surface
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point
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CN109188459B (en
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殷国栋
吴丛磊
刘帅鹏
叶建伟
庄伟超
张宁
王金湘
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Southeast University
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    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S17/00Systems using the reflection or reradiation of electromagnetic waves other than radio waves, e.g. lidar systems
    • G01S17/88Lidar systems specially adapted for specific applications
    • G01S17/93Lidar systems specially adapted for specific applications for anti-collision purposes
    • G01S17/931Lidar systems specially adapted for specific applications for anti-collision purposes of land vehicles

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Abstract

本发明涉及一种基于多线激光雷达的坡道小障碍物识别方法,实现了坡道路面的小障碍物识别,快速准确,节省运算资源,保证了实时性;有效避免了传统障碍物识别方法在即将下坡路段障碍物的漏检以及上坡路段把路面识别为障碍物的弊端,提高了智能驾驶汽车的行车安全性和对复杂路况的适应性。

The invention relates to a method for identifying small obstacles on a slope based on a multi-line laser radar, which realizes the identification of small obstacles on a slope road surface, is fast and accurate, saves computing resources, and ensures real-time performance, and effectively avoids the traditional obstacle identification method. The missed detection of obstacles in the upcoming downhill section and the disadvantages of identifying the road surface as an obstacle in the uphill section improve the driving safety of intelligent driving vehicles and the adaptability to complex road conditions.

Description

A kind of small obstacle recognition method in ramp based on multi-line laser radar
Technical field
The present invention relates to a kind of small obstacle recognition methods in the ramp based on multi-line laser radar, belong to unmanned obstacle Object identifies field.
Background technique
Detection of obstacles on vehicle driving road is in pilotless automobile surrounding enviroment cognition technology research field The effect of important component, detection of obstacles is directly related to the traffic safety of pilotless automobile.Tradition is based on multi-thread thunder The obstacle detection method reached is all the point cloud that filters out all z coordinates be less than-h rough according to the mounting height h of radar, this Method can be identified as ramp large obstacle in the section that will be gone up a slope, and can filter out downhill path section on ramp Small obstacle.So a kind of obstacle recognition method that can be suitably used for ramp road conditions is particularly important.
Summary of the invention
The present invention provides a kind of small obstacle recognition method in the ramp based on multi-line laser radar, is applicable not only to horizontal road Face, and it is suitable for ramp road surface, accurately road surface and barrier can be distinguished, there is stronger practicability and wide Application prospect.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of small obstacle recognition method in ramp based on multi-line laser radar, comprising the following steps:
The first step is carried out road-edge detection to original point cloud, filters out the region on the outside of road based on Hough transformation, obtain In to road with the reference point cloud of obstacle recognition;
Second step is projected to the reference point cloud on the road surface of ramp with obstacle recognition and road based on projection dimension reduction method On the vertical perpendicular XOZ in face, ramp road identify and filter out ramp road surface, Hough straight line is recycled to become Swap-in row detection, so that all reference point clouds for belonging to road surface scanning element are accurately found out, then in the phase for belonging to road surface scanning element It closes and all road surface points is filtered out again in point cloud;
Third step carries out outlier to the range within ten meters on the road surface of ramp and filters out, filters out road surface zero according to outlier Scattered point cloud makes the point cloud after filtering out belong to barrier scanning element;
4th step, the barrier scanning element after being filtered out using the DBCSAN clustering algorithm based on density to outlier carry out into One step filters out noise spot, realizes barrier cluster;
As present invention further optimization, by the region segmentation inside and outside road, the point cloud in region forms image coordinate Space, using Hough transformation by point Cloud transform conllinear in image coordinate space into parameter space, these clouds parameter sky Between in intersect at same point, the straight line that intersects with ramp pavement edge is excluded by Hough transformation, with this to road on the outside of Region is filtered out, and the reference point cloud in road with obstacle recognition is obtained;
As present invention further optimization, if not finding road edge, i.e. selection two lateral extent of automobile body is each Five meters of inner regions are as cut zone;
As present invention further optimization, based on projection dimension reduction method, by the phase on the road surface of ramp with obstacle recognition It closes point cloud to project on the perpendicular XOZ vertical with road surface, the projection plane of reference point cloud is formed, on a projection plane from thunder A continuous straight line is formed up to nearest stretch face, intermediate one section of ramp is the straight line of segmentation, and remaining stretch face exists It is not shown on projection plane;Hough transformation is carried out for the point cloud number after aforementioned all projections, the length to be formed is found out and is greater than 0.5 meter of straight line, so that the straight line for road surface is found, to accurately find out all reference point clouds for belonging to road surface scanning element;
As present invention further optimization, in the range of within ten meters on the road surface of ramp, in input data to point The range distribution of cloud to point of proximity cloud is calculated, and show that a cloud to the average distance of its point of proximity cloud, is in this average departure From average value ranges in point cloud be barrier scanning element, incongruent cloud is rejected;
As present invention further optimization, it is circular conical surface by the region that every line of radar scans, uses DBCSAN clustering algorithm judges this by calculating the density value in the Euclidean distance and its place sweep radius between each point A little points are to belong to core point, boundary point either noise spot.
By above technical scheme, compared with the existing technology, the invention has the following advantages:
The present invention realizes the small obstacle recognition on ramp road surface, quick and precisely, saves calculation resources, ensure that in real time Property;Traditional obstacle recognition method is effectively prevented road surface to be known the missing inspection of downhill path section barrier and uphill way Not Wei barrier the drawbacks of, improve the travel safety of intelligent driving automobile and the adaptability to complex road condition.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples.
It is the small obstacle recognition flow chart in ramp of the preferred embodiment of the present invention shown in Fig. 1;
It is the confirmatory experiment scene figure of the preferred embodiment of the present invention shown in Fig. 2;
In Fig. 3,3a is that Hough transformation detects the straight line schematic diagram in image coordinate space, and 3b is that straight line schematic diagram is mapped to Sine curve in parameter space;
In Fig. 4,4a is road-edge detection effect picture, and 4b filters out the related point cloud chart after Independent Point cloud;
It is the xoz projecting method schematic diagram of the preferred embodiment of the present invention shown in Fig. 5;
It is the reference point cloud xoz drop shadow effect figure of the preferred embodiment of the present invention shown in Fig. 6;
It is the road surface recognition effect figure of the preferred embodiment of the present invention shown in Fig. 7;
It is the effect picture filtered out behind road surface of the preferred embodiment of the present invention shown in Fig. 8;
It is the effect picture rejected after outlier of the preferred embodiment of the present invention shown in Fig. 9;
It is the BSDCAN algorithm principle figure of the preferred embodiment of the present invention shown in Figure 10;
Be shown in Figure 11 the preferred embodiment of the present invention cluster after point cloud effect and each class mass center position.
In figure: 1-10 indicates the multiple cone buckets being distributed on the ground as small obstacle.
Specific embodiment
In conjunction with the accompanying drawings, the present invention is further explained in detail.These attached drawings are simplified schematic diagram, only with Illustration illustrates basic structure of the invention, therefore it only shows the composition relevant to the invention.
As shown in Figure 1, a kind of small obstacle recognition method in ramp based on multi-line laser radar of the invention, including it is following Step:
The first step is carried out road-edge detection to original point cloud, filters out the region on the outside of road based on Hough transformation, obtain In to road with the reference point cloud of obstacle recognition;
Second step is projected to the reference point cloud on the road surface of ramp with obstacle recognition and road based on projection dimension reduction method On the vertical perpendicular XOZ in face, ramp road identify and filter out ramp road surface, Hough straight line is recycled to become Swap-in row detection, so that all reference point clouds for belonging to road surface scanning element are accurately found out, then in the phase for belonging to road surface scanning element It closes and all road surface points is filtered out again in point cloud;
Third step carries out outlier to the range within ten meters on the road surface of ramp and filters out, filters out road surface zero according to outlier Scattered point cloud makes the point cloud after filtering out belong to barrier scanning element;
4th step, the barrier scanning element after being filtered out using the DBCSAN clustering algorithm based on density to outlier carry out into One step filters out noise spot, realizes barrier cluster;
As present invention further optimization, by the region segmentation inside and outside road, the point cloud in region forms image coordinate Space, using Hough transformation by point Cloud transform conllinear in image coordinate space into parameter space, these clouds parameter sky Between in intersect at same point, the straight line that intersects with ramp pavement edge is excluded by Hough transformation, with this to road on the outside of Region is filtered out, and the reference point cloud in road with obstacle recognition is obtained;
As present invention further optimization, if not finding road edge, i.e. selection two lateral extent of automobile body is each Five meters of inner regions are as cut zone;
As present invention further optimization, based on projection dimension reduction method, by the phase on the road surface of ramp with obstacle recognition It closes point cloud to project on the perpendicular XOZ vertical with road surface, the projection plane of reference point cloud is formed, on a projection plane from thunder A continuous straight line is formed up to nearest stretch face, intermediate one section of ramp is the straight line of segmentation, and remaining stretch face exists It is not shown on projection plane;Hough transformation is carried out for the point cloud number after aforementioned all projections, the length to be formed is found out and is greater than 0.5 meter of straight line, so that the straight line for road surface is found, to accurately find out all reference point clouds for belonging to road surface scanning element;
As present invention further optimization, in the range of within ten meters on the road surface of ramp, in input data to point The range distribution of cloud to point of proximity cloud is calculated, and show that a cloud to the average distance of its point of proximity cloud, is in this average departure From average value ranges in point cloud be barrier scanning element, incongruent cloud is rejected;
As present invention further optimization, it is circular conical surface by the region that every line of radar scans, uses DBCSAN clustering algorithm judges this by calculating the density value in the Euclidean distance and its place sweep radius between each point A little points are to belong to core point, boundary point either noise spot.
Specific operating process is as follows:
The first step shown in Fig. 2, is distributed multiple cone buckets on the ground, will be unrelated with small obstacle detection as small obstacle Point cloud in region is first filtered out, to reduce the calculation resources consumption of points cloud processing below;Extraneous areas referred to herein For the region on the outside of road, this system only detects the barrier on road;
Straight line is detected first with Hough transformation, searches road edge, Hough transformation detects straight line schematic diagram, in Fig. 3,3a With shown in 3b: Hough transformation by the point transformation in image coordinate space into parameter space, conllinear point in image coordinate space After transforming in parameter space, same point is all intersected in parameter space, at this time obtained ρ, θ, ρ, θ are required straight line Pole coordinate parameter, the conllinear two o'clock (x of image coordinate spacei,yi) and (xj,yj), (xi,yi) and (xj,yj) it is mapped to parameter Space is two sine curves, intersects at point (ρ00), as shown in 3b in Fig. 3;Conversely, intersecting at same point in parameter space All sine curves have conllinear point to be corresponding to it in image coordinate space;According to this characteristic, given image coordinate space Some marginal points, so that it may pass through Hough transformation determine connection these point linear equation;When using Hough transformation here, Here we limit θ ∈ (- 45 °, 45 °), to exclude the straight line intersected with road edge as far as possible.
If finding road edge, as shown in 4a in Fig. 4, two straight lines in figure are the road edge detected; Then the point cloud data on the outside of road is filtered out, as shown in 4b in Fig. 4;Wherein, the method for filtering out a cloud is, is point with road edge Boundary line is the point cloud on the inside of road close to middle line, such as straight line " x=0 " in figure, otherwise is the point cloud on the outside of road, will put cloud X, y, z coordinate value is set as INF, and (preset infinitely large quantity is herein 10000.0, i.e., 10000.0 meters are considered as nothing in systems It is poor big), coordinate is that can all be ignored in operation of the point of INF below, that is, is filtered out, side point cloud is not dealt in road; If not finding road edge, using each 5 meters of inner regions of distance at left and right sides of automobile body as relevant range (with two Body width is safe distance);In addition, passing through detection road edge, it is known that, there is 4.7 ° of drift angle immediately ahead of road and radar, Radar center point is deviated to the right 0.2 meter of lane center.
Second step, general detection of obstacles is will not specially to go to filter out road surface point cloud, because of general detection of obstacles Object be mostly large obstacle, they included point cloud signal it is more much more than the point cloud signal on the ground near them, So road surface point cloud is very small on large obstacle detection influence;And in the process of multi-line laser radar identification small obstacle In, road surface filtering is extremely important, it is unobvious with road surface differentiation because the point cloud quantity that small barrier itself includes is considerably less, By 3b in Fig. 3 as it can be seen that small barrier almost combines together with ground, road surface point cloud is maximum noise in entire point cloud signal, In order to preferably carry out further work, first have to filter out in road surface point cloud, to improve signal-to-noise ratio;But accurately filter out ground ratio More difficult, 3b can be seen that in a top view from Fig. 3, and the point cloud shape on road surface is circular arc or ellipse, be unfavorable for unified Feature screened, need to go out ground point cloud from new angle extraction thus, and this paper presents one kind in cloud signal Definition goes out the new method on road surface, this process employs the method for projection dimensionality reduction and Hough transformation, projection drop herein Dimension is different from the projection dimensionality reduction in most papers, and the projection dimensionality reduction of most papers is all that 3D point cloud is projected to 2D water Plane forms 2D map, and herein then from new angle, all the points cloud is projected into the perpendicular perpendicular to road surface On, it is specific as shown in Figure 4;
In Fig. 5, using the central point of multi-line laser radar as coordinate origin, cartesian coordinate system is established, wherein o ' (x0,y0, z0) it is corresponding points of the radar center point on lane center, o ' o " is the tangent line at the place lane center o ', and θ is o ' o " in y-axis Angle;The plane perpendicular to road surface where o ' o " is the projection plane of all the points cloud;Herein with matrix A storage region point The three-dimensional coordinate information for cutting rear all the points cloud, then have
Enable the point cloud coordinate matrix of projectionIt indicates, then has
For the point cloud in 4b in Fig. 4, θ=4.7 °, x0=-0.2, y0=0, projection result, as shown in Figure 6;
For figure after Binding experiment projection it is found that shown in Fig. 7, road surface is approximately straight line, and nearest from radar one Road section surface forms a continuous straight line, intermediate one section of ramp, because sweeping to road surface since radar point cloud data is than comparatively dense Harness it is less, so be segmentation straight line, and last stretch face inherently without point cloud distribution, so from projection It is displayed without road surface.After projection, Hough transformation is carried out herein for the 2D point cloud data, the inside length is found out and is greater than 0.5 meter Straight line because the diameter of small barrier circumsphere be no more than 0.5 meter, find straight line herein and be only possible to be road surface;Hough After transformation, the point cloud below the point cloud and the direction straight line z that all straight lines for meeting length include is filtered out;Effect after filtering out road surface For fruit as shown in figure 8, after the filtering of road surface, ground point cloud has filtered out the position that completely can clearly be observed that cone bucket completely.Third In step, how outlier filters out scattered point;
After the point cloud for having filtered out road surface and extraneous areas, still have as shown in Figure 8, in point cloud chart some very scattered Point cloud noise, at this point, the application will filter out scattered point cloud according to outlier, to guarantee that remaining cloud is barrier institute The point cloud for including;Specific algorithm used in this application is that statistics outlier rejects algorithm, and the analysis of this algorithm execution point cloud is simultaneously And the point cloud for being unsatisfactory for designated statistics feature can be rejected;Statistical nature in the application is in being averaged for distance between a cloud Within the scope of one near value, and reject the too many point of those deviation averages.One statistics is carried out to the neighborhood of each cloud Analysis, and trim those point clouds for not meeting certain standard;
Specifically, being calculated herein each point the calculating of the range distribution of cloud to point of proximity cloud in input data It arrives the average distance of its all point of proximity clouds.Assuming that obtain the result is that a Gaussian Profile, shape is by mean value and mark Quasi- difference determines, point of the average distance except critical field (being defined by global distance average and variance), can be defined as from Group puts and can get rid of from data set;After this algorithm, the point isolated in point cloud chart is also filtered out, to prevent from filtering The cone bucket of distant place is removed, only the carry out outlier in 10 meters is filtered out, as shown in Figure 9:
In 4th step, the region of the every line scanning of multi-line laser radar is a circular conical surface, therefore even if radar scanning is arrived The object of rule, an even plane, point cloud distribution on this plane is also non-uniform.Complicated in face of motor vehicle environment When environment, the point cloud distribution scanned is that extremely unevenly, shape also calculate by irregular, classical Kmeans algorithm and hierarchical clustering Method will face huge failure risk, use the BDSCAN algorithm based on density herein to adapt to such case, BDSCAN algorithm Barrier can be effectively clustered out, and noise spot can be further filtered out, accomplishes quick and precisely, calculation resources to be saved, to protect Demonstrate,prove real-time.The schematic diagram of BDSCAN algorithm, as shown in Figure 10:
Judge that these points belong to by calculating the density value in the Euclidean distance and its place sweep radius between each point In core point, boundary point or noise spot.It is 1.5 that sweep radius is set in Figure 10, density threshold 3, so:
(1) P0 point is boundary point, because only there are two point P0 and P1 in the sweep radius centered on it;
(2) P1 point is core point, because there are four point P0, P1, P2, P4 in the sweep radius centered on it;
(3) P8 is noise spot, because it is neither core point nor boundary point;
(4) other are put.
After point cloud tracking BDSCAN in Fig. 9 is clustered, obtained effect is as shown in figure 11, the effect of comparative diagram 11 with And the position in kind of Fig. 2, it is known that all cone buckets are detected.
After BDSCAN algorithm according to third step step by further cancelling noise point cloud (i.e. by the XYZ coordinate assignment of cloud For INF).
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (including technology art Language and scientific term) there is meaning identical with the general understanding of those of ordinary skill in the application fields.Should also Understand, those terms such as defined in the general dictionary, which should be understood that, to be had and the meaning in the context of the prior art The consistent meaning of justice, and unless defined as here, it will not be explained in an idealized or overly formal meaning.
The meaning of "and/or" described herein refers to that the case where respective individualism or both exists simultaneously wraps Including including.
The meaning of " connection " described herein can be between component be directly connected to be also possible to pass through between component Other components are indirectly connected with.
Taking the above-mentioned ideal embodiment according to the present invention as inspiration, through the above description, relevant staff is complete Various changes and amendments can be carried out without departing from the scope of the technological thought of the present invention' entirely.The technology of this invention Property range is not limited to the contents of the specification, it is necessary to which the technical scope thereof is determined according to the scope of the claim.

Claims (6)

1.一种基于多线激光雷达的坡道小障碍物识别方法,其特征在于:包括以下步骤:1. a method for identifying small obstacles on a ramp based on multi-line laser radar, it is characterized in that: comprise the following steps: 第一步,对原始点云进行道路边缘检测,基于霍夫变换将道路外侧的区域滤除,得到道路内与障碍物识别的相关点云;The first step is to perform road edge detection on the original point cloud, filter out the area outside the road based on the Hough transform, and obtain the relevant point cloud for identification of obstacles in the road; 第二步,基于投影降维方法,将坡道路面上与障碍物识别的相关点云投影到与路面垂直的竖直平面XOZ上,对坡道道路进行识别并将坡道路面进行滤除,再利用霍夫直线变换进行检测,从而准确求出所有属于路面扫描点的相关点云,然后在属于路面扫描点的相关点云中对所有路面点再次进行滤除;In the second step, based on the projection dimensionality reduction method, the relevant point cloud identified with the obstacles on the slope road surface is projected onto the vertical plane XOZ perpendicular to the road surface, the slope road is identified and the slope road surface is filtered out. Then use the Hough straight line transformation to detect, so as to accurately obtain all relevant point clouds belonging to the road scanning points, and then filter out all the road points in the relevant point clouds belonging to the road scanning points again; 第三步,对坡道路面上十米以内的范围进行离群值滤除,根据离群值滤除路面零散的点云,使滤除后的点云均属于障碍物扫描点;The third step is to filter out outliers within ten meters of the slope road surface, and filter out scattered point clouds on the road according to the outliers, so that the filtered point clouds belong to obstacle scanning points; 第四步,利用基于密度的DBCSAN聚类算法对离群值滤除后的障碍物扫描点进行进一步滤除噪声点,实现障碍物聚类。The fourth step is to use the density-based DBCSAN clustering algorithm to further filter out the noise points from the obstacle scanning points after the outliers have been filtered out, so as to realize the obstacle clustering. 2.根据权利要求1所述的基于多线激光雷达的坡道小障碍物识别方法,其特征在于:将道路内外的区域分割,区域内的点云形成图像坐标空间,采用霍夫变换将图像坐标空间中共线的点云变换至参数空间中,这些点云在参数空间中均相交于同一点,通过霍夫变换排除与坡道路面边缘相交的直线,以此对道路外侧的区域进行滤除,得到道路内与障碍物识别的相关点云。2. The method for identifying small obstacles on a ramp based on multi-line laser radar according to claim 1, wherein the area inside and outside the road is divided, the point cloud in the area forms an image coordinate space, and the image is converted by Hough transform. The point cloud that is collinear in the coordinate space is transformed into the parameter space. These point clouds all intersect at the same point in the parameter space. The Hough transform is used to exclude the straight line that intersects with the edge of the slope road surface, so as to filter out the area outside the road. , to get the relevant point cloud of road and obstacle recognition. 3.根据权利要求2所述的基于多线激光雷达的坡道小障碍物识别方法,其特征在于:若没有查找到道路边缘,即选用车辆车身两侧距离各五米内区域作为分割区域。3 . The method for identifying small obstacles on a ramp based on multi-line laser radar according to claim 2 , wherein if the road edge is not found, the area within five meters from each side of the vehicle body is selected as the segmentation area. 4 . 4.根据权利要求1所述的基于多线激光雷达的坡道小障碍物识别方法,其特征在于:基于投影降维方法,将坡道路面上与障碍物识别的相关点云投影到与路面垂直的竖直平面XOZ上,形成相关点云的投影平面,在投影平面上离雷达最近的一段路面形成一条连续的直线,中间一段坡道为分段的直线,剩余的一段路面在投影平面上不做显示;针对前述所有投影后的点云数进行霍夫变换,找出形成长度大于0.5米的直线,从而找到为路面的直线,从而准确求出所有属于路面扫描点的相关点云。4. The method for identifying small obstacles on a slope based on multi-line laser radar according to claim 1, wherein: based on the projection dimension reduction method, the relevant point cloud identified with the obstacle on the slope road is projected to the road surface with the relevant point cloud. On the vertical vertical plane XOZ, the projection plane of the relevant point cloud is formed. On the projection plane, the road surface closest to the radar forms a continuous straight line. Do not display; perform Hough transform on all the aforementioned projected point cloud numbers to find a straight line with a length greater than 0.5 meters, so as to find the straight line that is the road surface, so as to accurately obtain all relevant point clouds belonging to the road scan points. 5.根据权利要求1所述的基于多线激光雷达的坡道小障碍物识别方法,其特征在于:对坡道路面上十米以内的范围内,在输入数据中对点云到临近点云的距离分布进行计算,得出点云对其临近点云的平均距离,处于这个平均距离的平均值范围内的点云即为障碍物扫描点,不符合的点云进行剔除。5. The method for recognizing small obstacles on a slope based on multi-line laser radar according to claim 1, characterized in that: within the range of ten meters on the slope road surface, in the input data, the point cloud to the adjacent point cloud Calculate the distance distribution of the point cloud to obtain the average distance of the point cloud to its adjacent point cloud. The point cloud within the average range of this average distance is the obstacle scanning point, and the point cloud that does not conform to it is eliminated. 6.根据权利要求1所述的基于多线激光雷达的坡道小障碍物识别方法,其特征在于:通过雷达的每条线扫描出的区域为圆锥面,采用DBCSAN聚类算法,通过计算各个点之间的欧式距离及其所在扫描半径内的密度值来判断这些点是属于核心点、边界点或者是噪声点。6. The method for identifying small obstacles on a ramp based on a multi-line laser radar according to claim 1, wherein the area scanned by each line of the radar is a conical surface, and the DBCSAN clustering algorithm is adopted. The Euclidean distance between points and the density value within the scanning radius are used to determine whether these points belong to core points, boundary points or noise points.
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