Evaluation Method for Structural Strength of Directional Network of Workshop Measurement and Positioning System

Fig. 1. Schematic diagram of wMPS transmitter structure and mathematical model of single-station measurements. (a) Schematic diagram of the wMPS transmitter structure; (b) mathematical model of single-station measurements

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Fig. 2. Schematic diagram of wMPS multi-station measurements

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Fig. 3. Schematic diagram of wMPS directional network

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Fig. 4. Flowchart of simulating and solving DNSC

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Fig. 5. Geometric layout of four directional constraint points. (a)(d) Circular layout; (b)(e) semi-circular layout; (c)(f) scalloped layout

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Fig. 6. Effect of change in distance from the constraint point to transmitting station on DNSC. (a) DNSC of layout a; (b) DNSC of layout b; (c) DNSC of layout c

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Fig. 7. Impact of number of constraint points on DNSC. (a) DNSC of layout a; (b) DNSC of layout b; (c) DNSC of layout c

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Fig. 8. Change of DNSC when transmitting station moves along X-axis. (a) DNSC of layout a; (b) DNSC of layout b; (c) DNSC of layout c

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Fig. 9. Change of DNSC when transmitting station moves along Y-axis. (a) DNSC of layout a; (b) DNSC of layout b; (c) DNSC of layout c

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Fig. 10. Experimental scene and schematic diagram. (a) Experimental scenes; (b) schematic diagram of scene

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Fig. 11. Relative error of uncertainty of pose parameter

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Fig. 12. Distance of test point to laser planes under different directional networks. (a) Distance from test point to laser plane 1; (b) distance from test point to laser plane 2

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Table 1. Verification results of pose parameter uncertainty based on different scan angle uncertainties

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Table 1. Verification results of pose parameter uncertainty based on different scan angle uncertainties

$σ_{0}$ /″	$G_{α}$ /%	$G_{β}$ /%	$G_{Y}$ /%	$G_{t_{x}}$ /%	$G_{t_{y}}$ /%	$G_{t_{z}}$ /%
1	98.00	99.33	98.33	99.00	100.00	97.33
2	98.33	100.00	97.67	98.00	98.33	98.00
3	98.33	97.33	100.00	97.33	98.00	98.00
4	97.33	99.00	97.67	99.33	100.00	99.00
5	99.67	97.33	97.33	98.67	98.00	98.00
6	97.67	98.67	97.33	98.67	97.33	99.33

Table 2. Verification results of pose parameter uncertainty based on different constraint points number

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Table 2. Verification results of pose parameter uncertainty based on different constraint points number

Points number	$G_{α}$ /%	$G_{β}$ /%	$G_{Y}$ /%	$G_{t_{x}}$ /%	$G_{t_{y}}$ /%	$G_{t_{z}}$ /%
6	99.7	98.3	98.7	98.7	98.3	99.7
12	99.3	98.3	99.7	99.3	100.0	100.0
18	99.7	99.3	99.3	100.0	98.0	98.3
24	98.3	100.0	98.3	99.7	99.3	98.7
30	100.0	98.3	99.0	99.0	98.7	99.7
36	99.0	98.3	100.0	99.3	98.3	98.7
42	99.3	99.0	100.0	98.0	99.3	100.0
48	99.3	100.0	99.0	100.0	100.0	99.3

Table 3. DNSC for different constraint point layouts

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Table 3. DNSC for different constraint point layouts

Layout	${D_{N S C,}}_{α}$	${D_{N S C,}}_{β}$	${D_{N S C,}}_{γ}$	${D_{N S C,}}_{t_{x}}$ /（μm·arcsec^-1）	${D_{N S C,}}_{t_{y}}$ /（μm·arcsec^-1）	${D_{N S C,}}_{t_{z}}$ /（μm·arcsec^-1）
a	0.30	0.30	0.21	7.0	7.0	5.0
b	0.47	0.36	0.29	11.7	7.3	6.9
c	3.43	0.55	3.26	86.3	13.2	75.3
d	0.30	0.30	0.21	14.1	14.1	10.0
e	0.47	036	0.29	23.4	14.5	13.8
f	3.43	0.55	3.26	172.5	26.5	150.6

Table 4. DNSC for different directional networks

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Table 4. DNSC for different directional networks

Directional network	${D_{N S C,}}_{α}$	${D_{N S C,}}_{β}$	${D_{N S C,}}_{γ}$	${D_{N S C,}}_{t_{x}}$ /（μm·arcsec^-1）	${D_{N S C,}}_{t_{y}}$ /（μm·arcsec^-1）	${D_{N S C,}}_{t_{z}}$ /（μm·arcsec^-1）
1	1.29	1.38	1.86	47.6	35.2	53.7
2	1.93	2.83	3.11	109.8	61.2	111.2
3	2.64	3.13	3.25	125.1	120.6	162.4

Table 5. Average distance from test point to laser plane based on different directional networks
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Table 5. Average distance from test point to laser plane based on different directional networks
Laser plane DN 1 /mm DN 2 /mm DN 3 /mm
1 0.039 0.076 0.099
2 0.051 0.077 0.117

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Baoli Guo, Jiarui Lin, Mingxin Teng, Rao Zhang, Jigui Zhu. Evaluation Method for Structural Strength of Directional Network of Workshop Measurement and Positioning System[J]. Laser & Optoelectronics Progress, 2025, 62(3): 0312001

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Apr. 22, 2024

Accepted: May. 28, 2024

Published Online: Feb. 13, 2025

The Author Email:

DOI:10.3788/LOP241116

CSTR:32186.14.LOP241116

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Verification results of pose parameter uncertainty based on different scan angle uncertainties

Table 1. Verification results of pose parameter uncertainty based on different scan angle uncertainties

Table 2. Verification results of pose parameter uncertainty based on different constraint points number

Table 2. Verification results of pose parameter uncertainty based on different constraint points number

Table 3. DNSC for different constraint point layouts

Table 3. DNSC for different constraint point layouts

Table 4. DNSC for different directional networks

Table 4. DNSC for different directional networks

Table 5. Average distance from test point to laser plane based on different directional networks

Table 5. Average distance from test point to laser plane based on different directional networks