Calibration method for hand-eye system with rotation and translation couplings

Yuan Zhang; Zhicheng Qiu; Xianmin Zhang

doi:10.1364/AO.58.005375

Applied Optics
Vol. 58,
Issue 20,
pp. 5375-5387
(2019)
•https://doi.org/10.1364/AO.58.005375

Calibration method for hand-eye system with rotation and translation couplings

Yuan Zhang, Zhicheng Qiu, and Xianmin Zhang

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Yuan Zhang, Zhicheng Qiu, and Xianmin Zhang, "Calibration method for hand-eye system with rotation and translation couplings," Appl. Opt. 58, 5375-5387 (2019)

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Abstract

This paper develops a novel hand-eye calibration method for hand-eye systems with rotation and translation coupling terms. First, a nonlinear camera model with distortion terms and a model of a hand-eye system with rotation and translation coupling terms are established. Based on a non-linear optimization method and a reverse projection method, a decoupling calibration method for a lower-degree-of-freedom hand-eye system is proposed. Then the path planning for the calibration process is carried out. Based on the analysis of coupling constraints and hand-eye system motion constraints, three types of hand-eye calibration paths with high efficiency and easy operation are developed. In addition, the influence of key parameters on hand-eye calibration accuracy is analyzed. Finally, calibration experiments and parametric influence experiments are carried out. The results demonstrate that the proposed method is effective and practical for calibrating the hand-eye system.

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Equations (28)

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Parameter	Value
$M_{in}$	$[\begin{matrix} 1.036 \times 10^{4} & 0 & 1.215 \times 10^{3} \\ 0 & 1.036 \times 10^{4} & 1.050 \times 10^{3} \\ 0 & 0 & 1.000 \end{matrix}]$
$M_{ex}$	$[\begin{matrix} - 0.989 & 0.149 & 0.003 & 16.151 \\ - 0.149 & - 0.989 & - 0.003 & 6.796 \\ 0.002 & - 0.003 & 1.000 & 254.728 \\ 0 & 0 & 0 & 1.000 \end{matrix}]$
$({\tilde{k}}_{1}, {\tilde{k}}_{2})$	(0.041, 1.602)

Parameter	Mean Value	Maximum Error	Standard Deviation
$L$	397.799 mm	0.227 mm	0.120 mm
$γ$	1.553 rad	0.039 mrad	0.018 mrad
$ϕ$	6.121 mrad	1.688 mrad	0.546 mrad

Parameter	Mean Value	Maximum Error	Standard Deviation
$L$	397.618 mm	1.586 mm	0.974 mm
$γ$	1.553 rad	0.659 mrad	0.246 mrad

Parameter	Mean Value	Maximum Error	Standard Deviation
$E_{β}$	0.643 mrad	6.719 mrad	1.862 mrad

Num.	Mean Value (μm)	Maximum Error (μm)	Standard Deviation (μm)
1st	0.973	2.436	1.130
2nd	0.503	1.389	0.611
3rd	0.501	1.388	0.609
4th	0.512	1.402	0.622
5th	0.504	1.395	0.613
6th	0.500	1.384	0.607
7th	0.510	1.402	0.620
8th	0.500	1.385	0.608
9th	0.492	1.363	0.614
10th	0.498	1.381	0.609

Group	Number of Points	Mean Error (μm)	Maximum Error (μm)	Standard Deviation (μm)
1	3 Points	$8.620 \times 10^{- 12}$	$1.290 \times 10^{- 11}$	$1.278 \times 10^{- 11}$
2	4 Points	0.181	0.271	0.233
3	5 Points	0.263	0.489	0.357
4	8 Points	0.662	1.308	0.798
5	16 Points	0.741	1.638	0.961
6	27 Points	0.653	1.982	0.796
7	80 Points	0.749	2.292	0.912

Group	Number of Points	Error
Group	Number of Points	$Δ L$ (mm)	$Δ γ$ (mrad)	$Δ^{2} L$ (mm)	$Δ^{2} γ$ (mrad)
1	3 Points	1.360	−0.039	0.571	−0.120
2	4 Points	0.788	0.081	0.619	0.030
3	5 Points	0.169	0.051	−0.256	0.010
4	8 Points	0.425	0.041	0.031	0.032
5	16 Points	0.394	0.009	0.386	−0.004
6	27 Points	0.009	0.013	0.009	0.013
7	80 Points	0	0	—	—

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Applied Optics