﻿ 装车机器人激光雷达测量系统及其标定方法
 光电工程  2019, Vol. 46 Issue (7): 190002      DOI: 10.12086/oee.2019.190002

1. 河北科技大学电气工程学院，河北 石家庄 050018;
2. 河北科技大学机械工程学院，河北 石家庄 050018

Wang Chunmei1, Huang Fengshan2, Xue Ze2
1. School of Electrical Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China;
2. School of Mechanical Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, China
Abstract: To carry out the measurement of vehicle body position and dimension of loading robot before loading, an intelligent vehicle body measurement system based on two-dimensional LiDAR was provided, and the calibration method of this system was studied as a key point. The two-dimension LiDAR was driven by rotating the platform, and the three-dimensional information of car body measured was obtained by using the single two-dimensional laser radar. In allusion to the complexity of calibration method of LiDAR measurement system and the difficulty in making calibration pieces, a system parameter calibration method was proposed based on 321 coordinate system building method, and mathematical models of calibration was established, with the principle and procedure of calibration method in detail. Measurement system was set up in a laboratory to carry out calibration experiment and measurement experiment on simulation vehicle body, and the measurement experiment for real vehicle body was conducted outside. The experiment result shows that the maximum measurement error of vehicle body size and length of this measurement system was 26.4 mm; maximum angle measurement error was 0.18 degree, which fully meets the precision requirements of loading.

1 引言

2 系统组成 2.1 智能装车机器人整体系统

 图 1 智能装车机器人系统总体结构示意图 Fig. 1 Schematic diagram of the overall structure of the intelligent loading robot system
2.2 车体测量系统

 图 2 车体测量系统 Fig. 2 Body measurement system

3 系统标定 3.1 车体测量系统标定数学模型

 图 3 坐标转换关系模型 Fig. 3 Coordinate transformation relationship model

 $\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{y_1}}\\ {{z_1}}\\ 1 \end{array}} \right] = \left[ {\left[ {\begin{array}{*{20}{c}} {\cos \alpha }&{ - \sin \alpha }&0&0\\ {\sin \alpha }&{\cos \alpha }&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} 1&0&0&r\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{array}} \right]} \right]\left[ {\begin{array}{*{20}{c}} {{x_0}}\\ {{y_0}}\\ {{z_0}}\\ 1 \end{array}} \right]。$ (1)

 $\mathit{\boldsymbol{T}} = \left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{y_1}}\\ {{z_1}}\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 1&0&0&0\\ 0&{\cos {\theta _x}}&{ - \sin {\theta _x}}&0\\ 0&{\sin {\theta _x}}&{\cos {\theta _x}}&0\\ 0&0&0&1 \end{array}} \right]$
 $\cdot \left[ {\begin{array}{*{20}{c}} {\cos {\theta _z}}&{ - \sin {\theta _z}}&0&0\\ {\sin {\theta _z}}&{\cos {\theta _z}}&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{array}} \right]$
 $\cdot \left[ {\begin{array}{*{20}{c}} {\cos {\theta _y}}&0&{\sin {\theta _y}}&0\\ 0&1&0&0\\ { - \sin {\theta _y}}&0&{\cos {\theta _y}}&0\\ 0&0&0&1 \end{array}} \right] \cdot \left[ {\begin{array}{*{20}{c}} 1&0&0&{\Delta x}\\ 0&1&0&{\Delta y}\\ 0&0&1&{\Delta z}\\ 0&0&0&1 \end{array}} \right]。$

 $\begin{array}{l} \left[ {\begin{array}{*{20}{c}} {{x_2}}\\ {{y_2}}\\ {{z_2}}\\ 1 \end{array}} \right] = \mathit{\boldsymbol{T}}\left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{y_1}}\\ {{z_1}}\\ 1 \end{array}} \right]\\ = \mathit{\boldsymbol{T}}\left[ {\left[ {\begin{array}{*{20}{c}} {\cos \alpha }&{ - \sin \alpha }&0&0\\ {\sin \alpha }&{\cos \alpha }&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{array}} \right] \cdot \left[ {\begin{array}{*{20}{c}} 1&0&0&r\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&1 \end{array}} \right]} \right] \cdot \left[ {\begin{array}{*{20}{c}} {{x_0}}\\ {{y_0}}\\ {{z_0}}\\ 1 \end{array}} \right]。\end{array}$ (2)

3.2 标定参数求解

 特殊解 (x2, y2, z2) (x1, y1, z1) 第一组 (0, 0, 0) (x11, y11, z11) 第二组 (x21, 0, 0) (x12, y12, z12) 第三组 (0, y21, 0) (x13, y13, z13) 第四组 (0, 0, z21) (x14, y14, z14)
 ${\mathit{\boldsymbol{T}}^{ - 1}}\left[ {\begin{array}{*{20}{c}} {{x_2}}\\ {{y_2}}\\ {{z_2}}\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{a_1}}&{{a_2}}&{{a_3}}&{{a_4}}\\ {{a_5}}&{{a_6}}&{{a_7}}&{{a_8}}\\ {{a_9}}&{{a_{10}}}&{{a_{11}}}&{{a_{12}}}\\ 0&0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_2}}\\ {{y_2}}\\ {{z_2}}\\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{x_1}}\\ {{y_1}}\\ {{z_1}}\\ 1 \end{array}} \right]。$ (3)
3.3 标定方法

 图 4 标定板摆放位置示意图 Fig. 4 Calibration plate placement position

 图 5 扫描三个标定板 Fig. 5 Scan three calibration plates

 $- 0.009{x_1} + 0.017{y_1} + 0.998{z_1} - 2696.908 = 0，$ (4)

 $0.999{x_1} + 0.017{y_1} + 0.042{z_1} - 1875.577 = 0,$ (5)

 $- 0.017{x_1} + 0.999{y_1} + 0.028{z_1} - 1225.352 = 0。$ (6)

1) 联立式(4)~式(6)，解得三平面交点o2(x11, y11, z11)，即第一个特殊点，该点在装车坐标系下的坐标为(0, 0, 0)；

2) 联立式(4)、式(5)，解得直线o2x2在旋转中心坐标系下的直线方程。在该直线上任取一点，设该点为E(x12, y12, z12)，求E点到o2点的距离即x21，即该点在装车坐标系中的坐标为(x21, 0, 0)；

3) 此时已知装车坐标系的o2x2y2平面、坐标原点o2以及o2x2轴，以o2x2轴为法向量，过o2点建立y2o2z2平面。平面y2o2z2与平面x2o2y2交于o2y2轴，在该轴上任取一点FF点在装车坐标系中的坐标为(0, y21, 0)，在旋转中心坐标系中的坐标为(x13, y13, z13)；

4) 以o2y2轴为法向量，过o2点建立平面x2o2z2。平面x2o2z2与平面x2o2y2交于o2z2轴，在o2z2轴上任取一点GG点在装车坐标系中的坐标为(0, 0, z21)，在旋转中心坐标系中的坐标为(x14, y14, z14)；

5) 将o2EF以及G点在装车坐标系以及旋转中心坐标系中的坐标带入式(3)解得矩阵T-1，进而求解矩阵T，最终解得装车坐标系与雷达坐标系的转换关系。

4 实验 4.1 标定实验

 图 6 实验室搭建测量与标定系统 Fig. 6 Build a measurement and calibration system in the laboratory

 特殊解 (x2, y2, z2)/mm (x1, y1, z1)/mm o2 (0, 0, 0) (1745.17, 1180.29, 2693.93) E (1168.95, 0, 0) (1764.64, 11.68, 2714.34) F (0, 1728.22, 0) (17.27, 1151.21221, 2677.68) G (0, 0, 2667.77) (1771.02, 1134.13, 26.68)

 $\mathit{\boldsymbol{T}} = \left[ {\begin{array}{*{20}{c}} {0.017}&{ - 0.998}&{0.010}&{1745.167}\\ { - 0.999}&{ - 0.017}&{ - 0.017}&{1180.291}\\ {0.017}&{ - 0.009}&{ - 0.999}&{2693.927}\\ 0&0&0&1 \end{array}} \right]。$
4.2 模拟车体测量实验

 图 7 模拟车斗测量实验 Fig. 7 Measuring the simulated body

 图 8 车斗测量点云图 Fig. 8 Point cloud image measured on the body

 测量次数 车斗长/mm 车斗宽/mm 车斗高/mm A点坐标/mm ω/(°) 1 2024.8 1824.3 510.7 (2360.4, 1220.8, 4.7) 0.2 2 2015.9 1820.1 509.6 (2367.2, 1219.7, 3.9) 0.13 3 2020.1 1822.7 510.6 (2359.7, 1225.1, 5.9) 0.18 4 2022.6 1826.5 514.3 (2362.4, 1227.3, 3.5) 0.17 真实值 2009.5 1812.4 502.3 (2371.2, 1214.3, 0) 0.02 最大误差 15.3 14.1 12 两点相距16.8 0.18

4.3 真实车体测量实验

5 结论