一种基于激光位移测量的机械臂参数标定方法

邵鑫; 季力; 邹怀武; 解杨敏

doi:10.13700/j.bh.1001-5965.2021.0093

一种基于激光位移测量的机械臂参数标定方法

doi: 10.13700/j.bh.1001-5965.2021.0093

邵鑫¹,
季力¹,
邹怀武²,
解杨敏^1, ,

1.
上海大学机电工程与自动化学院, 上海 200444
2.
上海市空间飞行器机构重点实验室, 上海 201108

基金项目:

上海市自然科学基金 19ZR1455500

上海市科学技术委员会启明星计划 19QA1403500

上海市空间飞行器机构重点实验室开放课题 YYHT-F805201808013

详细信息

通讯作者:
解杨敏, E-mail: xieym@shu.edu.cn

中图分类号: TP241.2
计量
- 文章访问数: 401
- HTML全文浏览量: 62
- PDF下载量: 54
- 被引次数: 0
出版历程
- 收稿日期: 2021-02-24
- 录用日期: 2021-06-13
- 网络出版日期: 2021-07-12
- 整期出版日期: 2022-11-20

A parameter calibration method for manipulators based on laser displacement measurement

SHAO Xin¹,
JI Li¹,
ZOU Huaiwu²,
XIE Yangmin^{1
, ,}

1.
School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200444, China
2.
Shanghai Key Laboratory of Spacecraft Mechanism, Shanghai 201108, China

Funds:

Shanghai Natural Science Foundation 19ZR1455500

Shanghai Science and Technology Committee Rising-Star Program 19QA1403500

Open Project of Shanghai Key Laboratory of Spacecraft Mechanism YYHT-F805201808013

More Information

Corresponding author: XIE Yangmin, E-mail: xieym@shu.edu.cn

摘要

摘要:
针对传统机器人参数标定方法, 通常依赖昂贵设备, 技术实现成本高的问题, 提出一种新型低成本的基于激光位移测量的机器人标定系统, 利用安装于机械臂末端的激光位移计进行与外部参照物立方体的相对位置测量, 并设计实现了六自由度机械臂的运动学参数标定方法。基于单维度位移测量值, 采用平面度约束与平面角度约束共同构建误差函数, 并利用非线性优化方法求得最终的标定结果。在实验系统上进行标定方法的验证, 并与利用激光追踪仪标定的实验结果进行对比。实验数据表明：所提方法在操作简便、成本低廉的同时, 能够获得与使用昂贵的外部测量仪器近似的标定效果。
- 机械臂 /
- 运动学参数标定 /
- 激光位移测量 /
- 组合约束 /
- 非线性优化
Abstract:
The traditional method of robot parameter target usually requires an expensive equipment, and the technical realization cost is high, a novel low-cost calibration method for manipulators is proposed, which utilizes a laser displacement sensor installed on the end of the manipulator to measure the relative position of the manipulator end with respect to an external cubic reference. A kinematic parameter calibration is designed for a 6 degree of freedom manipulator. Based on single-dimensional measurements, the error function is constructed with combined consideration of plane flatness and plane angles, and further minimized with a nonlinear optimization method to obtain the final calibration results. The proposed method is testified on an experimental system and compared with the calibration by a laser tracker. Results show that this method has similar calibration accuracy to the methods using expensive external measurement devices and provides a handy and cheap solution to manipulator calibration.
- manipulators /
- kinematic parameter calibration /
- laser displacement measurement /
- combined constraints /
- nonlinear optimization

HTML全文

图 1 机械臂DH模型坐标系

Figure 1. DH model coordinate system of manipulators

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图 2 实验方案

Figure 2. Experimental scheme

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图 3 参数标定原理

Figure 3. Schematic diagram of parameter calibration

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图 4 激光位移传感器标定实验场景

Figure 4. Experimental scene of laser displacement sensor calibration

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图 5 标定板夹角求解实验场景

Figure 5. Experimental scene of calibration plate angle solution

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图 6 激光跟踪仪标定实验场景

Figure 6. Experimental scene of laser tracker calibration

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图 7 拟合平面结果

Figure 7. Graph of fitted plane

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图 8 基于跟踪仪标定后计算坐标和测量坐标对比

Figure 8. Comparison of calculated coordinates and measurement coordinates after tracker-based calibration

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图 9 标定误差对比

Figure 9. Comparison of calibration errors

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表 1 DH参数

Table 1. DH parameters

关节i	连杆长度a_i/mm	连杆偏角α_i/(°)	连杆距离d_i/mm	连杆夹角θ_i/(°)
1	0	90	184	θ₁
2	372	0	0	θ₂
3	382	0	0	θ₃
4	0	-90	0	θ₄
5	0	-90	280.4	θ₅
6	36	0	0	θ₆

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表 2 DH误差参数

Table 2. DH parameters with kinematic errors

关节i	连杆长度a_i/mm	连杆偏角α_i/(°)	连杆距离d_i/mm	连杆夹角θ_i/(°)
1	Δa₁	90+Δα₁	184+Δd₁	θ₁+Δθ₁
2	372+Δa₂	Δα₂	Δd₂	θ₂+Δθ₂
3	382+Δa₃	Δα₃	Δd₃	θ₃+Δθ₃
4	Δa₄	-90+Δα₄	Δd₄	θ₄+Δθ₄
5	Δa₅	-90+Δα₅	280.4+Δd₅	θ₅+Δθ₅
6	36+Δa₆	Δα₆	Δd₆	θ₆+Δθ₆

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表 3 权重μ取值

Table 3. Values of weight μ

μ	e₁/mm	e₂/(°)
0.01	1.04×10^-5	67.04
0.02	0.009 9	13.41
0.07	1.08	0.67
0.71	1.2	0.034

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表 4 DH参数变化值

Table 4. Values of DH parameter change

关节i	Δa_i/mm		Δα_i/(°)		Δd_i/mm		Δθ_i/(°)
关节i	粗标定	精标定	粗标定	精标定	粗标定	精标定	粗标定	精标定
1	-0.19	0.92	-4.52	0.45	-4.40	0.94	-3.35	-0.89
2	3.09	0.29	5.92	0.04	-2.41	0.92	-1.99	0
3	0.16	0.19	3.59	0.89	-2.46	0.59	-0.79	0.04
4	-10.24	0.07	1.78	0.62	-2.57	0.4	3.142 3	0.78
5	5.84	0.51	-2.56	0.06	-19.35	0	-2.11	0.4
6	0.95	0.18	5.13	0.33	1.35	0.05	-1.73	0.26

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表 5 标定实验误差值对比

Table 5. Comparison of error values of calibration experiment

实验类别	误差平均值/mm	最大值/ mm	最小值/ mm	方差/ mm²
跟踪仪标定前	3.67	6.37	1.24	1.34
跟踪仪标定后	1.01	3.19	0.11	0.36
位移计标定前	3.82	6.52	0.82	1.27
位移计标定后	1.08	3.45	0.01	0.39

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