﻿ 激光测距传感器光束矢向和零点位置标定方法<sup>*</sup>
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Calibration method for laser beam direction and zero point of laser displacement sensor
CAO Shuangqian, YUAN Peijiang, CHEN Dongdong, SHI Zhenyun
School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2017-07-05; Accepted: 2017-08-21; Published online: 2017-09-22 15:07
Foundation item: National Natural Science Foundation of China (61375085)
Corresponding author. YUAN Peijiang, E-mail:itr@buaa.edu.cn
Abstract: Laser displacement sensor is usually used in normal detection of aircraft panel. To solve the problem of the decrease of normal detection accuracy caused by machining and installing errors of laser displacement sensor, a calibration method based on math model and least square method was proposed and applied, which can calibrate the laser beam direction and zero point of laser displacement sensor. First, angle calibration theory was used to obtain the angle between laser beam and spindle feed direction. Then coordinate systems were built by a laser tracker. According to the measurements of laser displacement sensors when they detect the planes which have different angles with feed direction of the spindle, geometry math model was used to calculate the relative coordinates of all laser points. The space equations of laser beams were fitted by the least square method, so laser beam directions and zero points came out. Finally, calibration experiment was carried out in aviation drilling robot platform, and verification experiment was made according to the calibration result. The experimental results show that the method can precisely calibrate the laser beam direction and zero point of laser displacement sensor and the normal detection accuracy is 0.18°.
Key words: laser displacement sensor     laser beam spatial position calibration     least square method     automatic drilling     normal detection     robot

1 航空自动化制孔系统

 图 1 航空自动化制孔系统 Fig. 1 Aviation automatic drilling system

2 激光测距传感器标定理论 2.1 角度标定理论

 (1)

2.2 空间位置标定理论

2.2.1 直线方程标定

 图 2 激光束发射示意图 Fig. 2 Schematic of laser beam emission
 图 3 激光束投影图 Fig. 3 Projection of laser beam

AB激光测距传感器激光束所在的空间直线方程的单位向量分别为

 (2)

 (3)

 (4)

|AA'''|p、|B″B'''|p是激光束方向上|AA″|、|BB″|在ZT轴方向的投影，所以：

 (5)

 (6)

φ1φ2β1β2可以由式(7)、式(8)计算：

 (7)
 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

2.2.2 发射点标定

 (18)

zi0代入2.2.1节求出的空间直线方程中，即可计算出发射点在状态坐标系1{S1}下的坐标。

3 激光测距传感器标定步骤

3.1 角度标定步骤

 图 4 激光束与电主轴进给方向角度标定 Fig. 4 Calibration of angle between laser beam andfeed direction of spindle

3.2 空间位置标定步骤

 图 5 激光束空间位置标定 Fig. 5 Spatial position calibration of laser beam

4 标定结果

 图 6 激光束标定结果 Fig. 6 Calibration results of laser beam

 传感器 矢向vi 零点Oi0 A (-0.357 7, -0.353 8, 0.864 2) (9.598 4, 9.495 5, -23.193 3) B (0.359 0, -0.358 6, 0.861 7) (-61.075 2, 9.296 9, -23.029 8) C (0.382 8, 0.332 7, 0.861 8) (-61.465 5, -59.669 9, -22.912 6) D (-0.339 1, 0.371 0, 0.864 5) (8.738 2, -60.962 9, -23.044 0)

 编号 θ0/(°) Δθ/(°) 1 0.940 0 0.141 7 2 1.054 1 0.139 9 3 1.368 3 0.095 2 4 1.803 5 0.067 5 5 1.932 4 0.171 8 6 2.005 0 0.131 9 7 2.045 3 0.065 4 8 2.717 3 0.117 9 9 2.800 4 0.121 1 10 2.887 1 0.097 5 11 3.190 3 0.129 3 12 3.235 7 0.098 8 13 3.788 5 0.145 5 14 3.959 0 0.082 5 15 3.980 6 0.129 3 16 4.075 7 0.092 4 17 4.494 0 0.156 3 18 4.976 9 0.154 9 19 5.318 1 0.078 5 20 5.388 5 0.122 0

5 结论

1) 本文方法不依赖于工业机器人自身的坐标变换关系，根据几何数学模型建立不同状态下各激光点之间的坐标关系，运用最小二乘法拟合出激光束的空间方程，为激光束标定提供了新思路。

2) 进行了标定实验和验证实验，实验结果显示该方法标定出的激光测距传感器的光束矢向和零点位置具有很高的精度，可使制孔末端执行器的法向测量精度在0.18°内。

3) 在标定步骤中，需要调整制孔末端执行器电主轴进给方向与工件表面垂直，较为繁琐，会影响标定效率，这是本文方法的一个缺点；在下一步研究中，将致力于找到更加符合的数学模型，简化标定步骤。

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#### 文章信息

CAO Shuangqian, YUAN Peijiang, CHEN Dongdong, SHI Zhenyun

Calibration method for laser beam direction and zero point of laser displacement sensor

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(6): 1321-1327
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0450