基于标定及补偿提高串联机器人定位精度方法

范明争; 韩先国

doi:10.13700/j.bh.1001-5965.2016.0045

基于标定及补偿提高串联机器人定位精度方法

doi: 10.13700/j.bh.1001-5965.2016.0045

范明争,
韩先国^,

北京亚洲成人在线一二三四五六区机械工程及自动化学院, 北京 100083

基金项目:

国防基础科学研究计划 A0320132007

国家科技重大专项 2010ZX04007-052

详细信息

作者简介:
范明争,男,硕士研究生。主要研究方向:应用机器人的数字化装配

通讯作者:
韩先国,男,博士后,副教授,硕士生导师。主要研究方向:并联设备及柔性装配. E-mail:hanxianguo2003@163.com

中图分类号: TP242
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出版历程
- 收稿日期: 2016-01-13
- 录用日期: 2016-04-15
- 网络出版日期: 2017-01-20

Precision improvement method for serial robot localization based on a new calibration and compensation strategy

FAN Mingzheng,
HAN Xianguo^,

School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Funds:

National Defense Basic Scientific Research Program of China A0320132007

National Science and Technology Major Project 2010ZX04007-052

More Information

Corresponding author: E-mail:hanxianguo2003@163.com

摘要

摘要:
在使用串联机器人进行定位操作前，首先需要对机器人基坐标系与测量坐标系进行位姿关系的标定，针对具有隐藏机器人基坐标系以及机器人法兰坐标系的串联机构，本文提出一种等价变换思想并结合应用激光跟踪仪测得机器人末端靶标点的坐标数据建立标定矩阵方程，应用罗德里格矩阵变换将标定方程转化为三元二次矩阵方程形式，采用最小二乘法和牛顿迭代法求出数值解进而完成机器人基坐标系与测量坐标系标定的方法。然后应用这种方法进行标定试验得到了20组标定结果，通过比较标定结果偏差进而验证了这种方法的正确性。最后，本文验证了应用这种标定方法的标定结果并结合一种新的位姿补偿算法后，能极大地提高机器人末端的定位精度。
- 机器人 /
- 标定 /
- 等价变换法 /
- 补偿 /
- 定位精度
Abstract:
Before the localization operation, the serial robot position relationship between base coordinate system and measurement coordinate system needs to be demarcated. For the hidden robot base and flange coordinate systems of serial mechanism, a kind of equivalent transformation method is presented in this paper, which is combined with the application of the target-points coordinate measurement data at the end of the robot using laser tracker to establish the calibration matrix equation. Calibration equation can be transformed into the ternary quadratic matrix equation form by Rodrigo matrix. Then the matrix equation between the robot base and measurement coordinate systems can be solved by using least square method and Newton iteration method. This method is verified by calibration test and 20 groups of calibration results are obtained. The calibration results combined with a position compensation algorithm can greatly improve the localization precision of robot.
- robot /
- calibration /
- equivalent transformation method /
- compensation /
- localization precision

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图 1 标定模型

Figure 1. Calibration model

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图 2 等价变换法坐标系模型

Figure 2. Coordinate system model of equivalenttransformation method

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图 3 标定试验系统

Figure 3. System of calibration experiment

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图 4 标定结果

Figure 4. Records of calibration experiment

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图 5 新补偿算法原理

Figure 5. Principle of the new compensation algorithm

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表 1 标定试验记录

Table 1. Records of calibration experiment

序号	1	2	3	4	5	6
X/mm	787.08	1 034.80	781.15	920.70	845.21	1 260.31
Y/mm	652.11	421.65	789.07	716.23	624.32	779.90
Z/mm	1 397.13	1 510.33	1 421.27	1 300.67	1 336.91	1 256.55

A/(°)	-17.88	3.59	15.65	34.18	0.52	26.86
B/(°)	-34.95	-14.42	13.12	14.70	26.71	50.43
C/(°)	-131.82	-108.07	-77.79	-48.75	-122.20	-80.52
靶标点^PP₁/mm	-1 451.694 1	-1 532.075 4	-1 389.275 6	-1 388.278 1	-1 465.091 5	-1 104.085 2
	1 261.126 1	939.940 5	1 342.042 8	1 159.200 2	1 207.296 0	920.818 0
	870.637 0	1 016.827 0	975.633 1	864.795 4	882.391 6	836.600 1
靶标点^PP₂/mm	-1 481.243 6	-1 511.547 8	-1 356.844 6	-1 341.088 7	-1 492.635 2	-1 124.393 0
	1 176.577 6	874.397 1	1 337.026 3	1 197.063 4	1 173.368 3	946.855 1
	849.137 2	955.521 8	889.580 0	795.399 4	801.334 9	750.644 5
靶标点^PP₃/mm	-1 429.139 9	-1 466.628 8	-1 306.996 3	-1 288.543 3	-1 413.111 0	-1 046.697 3
	1 170.211 8	853.476 0	1 275.929 2	1 125.866 1	1 127.190 6	891.396 3
	928.905 5	1 037.245 2	943.469 3	831.433 4	827.094 3	747.072 6

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表 2 标定试验结果

Table 2. Results of calibration experiment

参数	X_r/mm	Y_r/mm	Z_r/mm	A_r/(°)	B_r/(°)	C_r/(°)
数值	2 614.63	1 173.67	490.06	55.31	-0.08	-0.21

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表 3 通用补偿算法补偿实验靶标数据记录

Table 3. Target data records in compensation experimentwith universal compensation algorithmmm

mm
靶标序号	初始靶标	目标靶标	补偿前	补偿后
靶标点1	-1 408.80	-1 455.28	-1 455.39	-1 455.30
	1 398.80	1 263.11	1 263.22	1 263.21
	1 027.63	848.95	849.21	848.94
靶标点2	-1 416.39	-1 463.87	-1 463.99	-1 463.87
	1 347.08	1 211.64	1 211.75	1 211.74
	1 081.34	902.76	903.00	902.74
靶标点	-1 416.51	-1 450.18	-1 450.29	-1 450.18
	1 400.22	1 262.90	1 263.00	1 263.00
	1 140.48	961.97	962.22	961.95

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表 4 通用补偿算法补偿前后靶标误差值

Table 4. Target error values before and afteruniversal compensation algorithmmm

mm
过程	靶标点1	靶标点2	靶标点3
补偿前	0.30	0.29	0.29
补偿后	0.10	0.10	0.10

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表 5 新补偿算法补偿实验靶标数据记录1

Table 5. Target data record 1 in compensation experiment with the new compensation algorithmmm

mm
靶标序号	初始靶标	目标靶标	补偿前	补偿后
靶标点1	-1 408.82	-1 455.28	-1 455.34	-1 455.30
	1 398.83	1 263.11	1 263.31	1 263.13
	1 027.55	848.95	849.28	848.95
靶标点2	-1 416.41	-1 463.87	-1 463.94	-1 463.88
	1 347.13	1 211.64	1 211.85	1 211.66
	1 081.25	902.76	903.07	902.75
靶标点3	-1 416.52	-1 450.18	-1 450.25	-1 450.18
	1 400.27	1 262.90	1 263.10	1 262.91
	1 140.39	961.97	962.29	961.97

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表 6 新补偿算法补偿前后靶标误差值

Table 6. Target error values before and after the new compensation algorithmmm

mm
过程	靶标点1	靶标点2	靶标点3
补偿前	0.39	0.38	0.39
补偿后	0.03	0.02	0.02

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表 7 新补偿算法补偿实验靶标数据记录2

Table 7. Target error values before and after the new compensation algorithmmm

mm
靶标序号	初始靶标	目标靶标	补偿前	补偿后
靶标点1	-1 630.62	-1 470.65	-1 470.99	-1 470.67
	631.62	385.45	385.36	385.43
	888.57	875.46	876.05	875.47
靶标点2	-1 632.82	-1 458.37	-1 458.74	-1 458.38
	681.02	434.08	433.99	434.06
	940.35	926.55	927.13	926.57
靶标点3	-1 648.09	-1 473.47	-1 473.83	-1 473.49
	611.25	364.67	364.57	364.65
	947.85	937.06	937.64	937.08

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表 8 补偿前后靶标误差值

Table 8. Target error values before and after compensation

mm
过程	靶标点1	靶标点2	靶标点3
补偿前	0.69	0.69	0.69
补偿后	0.03	0.03	0.03

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