# 室内移动测图平台的多传感器联合标定Extrinsic Calibration of Multi LiDAR-Camera Robotic System for Indoor Mapping

DOI: 10.12677/GST.2019.74021, PDF, 下载: 465  浏览: 933  国家自然科学基金支持

Abstract: Multi LiDAR-camera is integrated on the indoor mapping robotic system for mission of high-precision positioning and three-dimensional spatial data acquisition. Accurate extrinsic calibration of sensors is the basis of effective utilization of multi-sensors data, and is also one of key issues of indoor mobile mapping research. This paper presents a convenient calibration method for multi-sensors. First, some control points are laid on the body of the robot to create the robot body coordinate system. Then, several identifiable targets are fixed in the effective field of view of LiDAR and camera. The coordinate value of targets in the robot body coordinate system is obtained by three-dimensional laser scanner. Finally, EPNP algorithm is used to calculate the extrinsic of camera based on the corresponding relationship between two-dimensional points and three-dimensional points, and RANSAC circle fitting is used to calibrate the 2D LiDAR. Experiments show that the camera reprojection error is less than 1 pixel and the calibration result of 2D LiDAR is better than 1 cm.

1. 引言

2. 传感器联合标定方法

Figure 1. Flow chart of extrinsic calibration for Indoor Mapping Robot

2.1. 坐标系定义及坐标系转换参数计算

Figure 2. Schematic diagram of sensor coordinate system

1) 相机坐标系：以相机的投影中心为坐标原点，X轴向右，Y轴向下，Z轴向右构成笛卡尔右手坐标系，使用 ${p}_{i}^{c}\left({x}_{i}^{c},{y}_{i}^{c},{z}_{i}^{c}\right)$ 表示相机坐标系下坐标。

2) 扫描仪坐标系：以扫描仪的激光发射中心为坐标原点，X轴向右，Y轴向前，Z轴向上构成笛卡尔右手坐标系，使用 ${p}_{i}^{l}\left({x}_{i}^{l},{y}_{i}^{l},{z}_{i}^{l}\right)$ 表示扫描仪坐标系下坐标。

3) 机身坐标系：为自定义坐标系，其中X轴向右，Y轴向前，Z轴向上构成笛卡尔右手坐标系，在文中使用 ${p}_{i}^{b}\left({x}_{i}^{b},{y}_{i}^{b},{z}_{i}^{b}\right)$ 表示该坐标系下坐标系。

${p}_{i}^{b}=R\left({A}_{x},{A}_{y},{A}_{z}\right)\left[\begin{array}{c}\begin{array}{c}{x}_{i}^{l}\\ {y}_{i}^{l}\\ {z}_{i}^{l}\end{array}\end{array}\right]+\left[\begin{array}{c}\begin{array}{c}{t}_{1}^{l}\\ {t}_{2}^{l}\\ {t}_{3}^{l}\end{array}\end{array}\right]$ (1)

$R=\left[\begin{array}{ccc}\mathrm{cos}{A}_{z}& -\mathrm{sin}{A}_{z}& 0\\ -\mathrm{sin}{A}_{z}& \mathrm{cos}{A}_{z}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{ccc}\mathrm{cos}{A}_{y}& 0& -\mathrm{sin}{A}_{y}\\ 0& 1& 0\\ -\mathrm{sin}{A}_{y}& 0& \mathrm{cos}{A}_{y}\end{array}\right]\left[\begin{array}{ccc}1& 0& 0\\ 0& \mathrm{cos}{A}_{x}& \mathrm{sin}{A}_{x}\\ 0& -\mathrm{sin}{A}_{x}& \mathrm{cos}{A}_{x}\end{array}\right]$ (2)

2.2. 相机外参数标定

${p}_{j}^{l}={\sum }_{i=1}^{4}{W}_{i,j}{c}_{i}^{pb}$ (3)

${p}_{j}^{c}={\sum }_{i=1}^{4}{W}_{i,j}{c}_{i}^{pc}$ (4)

${z}_{i}^{c}\left[\begin{array}{c}{u}_{i}\\ {v}_{i}\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_{u}& 0& {u}_{c}\\ 0& {f}_{v}& {v}_{v}\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_{i}^{c}\\ {y}_{i}^{c}\\ {z}_{i}^{c}\end{array}\right]$ (5)

${f}_{u}$${f}_{v}$ 为相机焦距， ${u}_{c}$${v}_{v}$ 为主点坐标。结合公式(4)，则公式(5)可以表示成：

${z}_{i}^{c}\left[\begin{array}{c}{u}_{i}\\ {v}_{i}\\ 1\end{array}\right]=\left[\begin{array}{ccc}{f}_{u}& 0& {u}_{x}\\ 0& {f}_{c}& {v}_{y}\\ 0& 0& 1\end{array}\right]{\sum }_{i=1}^{4}{W}_{i,j}\left[\begin{array}{c}{x}_{i}^{pc}\\ {y}_{i}^{pc}\\ {z}_{i}^{pc}\end{array}\right]$ (6)

$\left\{\begin{array}{l}{\sum }_{j=1}^{4}{W}_{i,j}{f}_{u}{x}_{i}^{pc}+{W}_{i,j}\left({u}_{c}-{u}_{i}\right){z}_{i}^{c}=0\\ {\sum }_{j=1}^{4}{W}_{i,j}{f}_{u}{x}_{i}^{pc}+{W}_{i,j}\left({u}_{c}-{u}_{i}\right){z}_{i}^{c}=0\end{array}$ (7)

2.3. 扫描仪外参数标定

Figure 3. Extrinsic calibration of 2D LiDAR

$|{Z}_{l}|=\sqrt{{R}^{2}-{r}^{2}}$ (8)

${x}^{2}+{y}^{2}+{z}^{2}-Ax-By-Cz+D=0$ (9)

$\left[\begin{array}{cccc}{x}_{1}& {y}_{1}& {z}_{1}& -1\\ ⋮& ⋮& ⋮& ⋮\\ {x}_{n}& {y}_{n}& {z}_{n}& -1\end{array}\right]\left[\begin{array}{c}A\\ B\\ C\\ D\end{array}\right]=\left[\begin{array}{c}{x}_{1}^{2}+{y}_{1}^{2}+{z}_{1}^{2}\\ ⋮\\ {x}_{n}^{2}+{y}_{n}^{2}+{z}_{n}^{2}\end{array}\right]$ (10)

$\left[\begin{array}{c}A\\ B\\ C\\ D\end{array}\right]={\left[\begin{array}{cccc}\sum {x}_{i}^{2}& \sum {x}_{i}{y}_{i}& \sum {x}_{i}{z}_{i}& -\sum {x}_{i}\\ \sum {x}_{i}{y}_{i}& \sum {x}_{1}^{2}& \sum {y}_{i}{z}_{i}& -\sum {y}_{i}\\ \sum {x}_{i}{z}_{i}& \sum {y}_{i}{z}_{i}& \sum {x}_{1}^{2}& -\sum {z}_{i}\\ -\sum {x}_{i}& -\sum {y}_{i}& -\sum {z}_{i}& n\end{array}\right]}^{-1}\left[\begin{array}{c}\sum {x}_{i}\left({x}_{i}^{2}+{y}_{i}^{2}+{z}_{i}^{2}\right)\\ \sum {y}_{i}\left({x}_{i}^{2}+{y}_{i}^{2}+{z}_{i}^{2}\right)\\ \sum {z}_{i}\left({x}_{i}^{2}+{y}_{i}^{2}+{z}_{i}^{2}\right)\\ \sum -\left({x}_{i}^{2}+{y}_{i}^{2}+{z}_{i}^{2}\right)\end{array}\right]$ (11)

3. 实验与结果分析

Table 1. Intrinsic parameters of camera

Figure 4. Experiment of camera extrinsic calibration, (a) Relationship between Pixel Error and Attitude solution accuracy; (b) Relationship between Pixel Error and Position solution accuracy; (c) Relationship between Pixel Error and Reprojection error; (d) Reprojection error of image control points

Figure 5. Experiment of 2D LiDAR extrinsic calibration, (a) Data interpretation of 2D LiDAR; (b) RANSAC circle fitting

Table 2. Coordinate of common points in 2D LiDAR extrinsic calibration experiment

Table 3. Experimental results of extrinsic calibration

4. 总结与分析

NOTES

*通讯作者。

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