Authors: Gumin Jin, Xingkai Yu, Yuqing Chen, Jianxun Li
For the classic method of hand-eye calibration, collecting data to cover all the pattern points at each moment is time-consuming, and the error of the camera pose would inevitably deteriorate the accuracy of the hand-eye estimation. In this paper, we aim to address this problem by directly building the hand-eye model on point alignment using 3D observation from a single marker rather than homogeneous pose alignment. Comprehensive experiments demonstrate the advantages of the proposed method over traditional pose-based methods in terms of accuracy, computational efficiency, and operational efficiency.
Figure: Visual representation of the hand-eye calibration of a single marker. (a) The eye-to-base case. (b) The eye-in-hand case.
MATLAB R2020a without any dependencies.
To run the single-marker calibration, call
[Rcf,tcf,pcf,Rit,tit,pit,rnticf,rntiit] = Alg(Ri,ti,ppi)
where
-
Ri(3x3xn): the rotation matrix of robot pose (n is the measurement number), -
ti(3xn): the translation vector of robot pose, -
ppi(3xnxm): the 3D observation of a marker (m is the marker number), -
Rcf(3x3): the rotation matrix of the hand-eye parameter of closed-form solution, -
tcf(3x1): the translation vector of the hand-eye parameter of closed-form solution (unit: mm), -
pcf(3mx1): the marker position of closed-form solution (unit: mm), -
rnticf(1x1): the runtime of closed-form solution (unit: seconds), -
Rit(3x3): the rotation matrix of the hand-eye parameter of iterative solution, -
tit(3x1): the translation vector of the hand-eye parameter of iterative solution (unit: mm), -
pit(3mx1): the marker position of iterative solution (unit: mm), -
rnticf(1x1): the runtime of closed-form solution of iterative solution (unit: seconds).
Demo mainSingle contains the calibration and evaluation of single-marker methods. run mainSingle.m, and the results for eye-in-hand calibration are as follows
Measurement number:30
Calibration results of the closed-form solution:
Euler angles(degree):-39.3942,-2.9623,-62.7325
translation (mm):-44.9947,6.2389,57.2844
marker position(mm):6.1064,-482.1404,10.277
RMSE(mm):1.7213
Runtime(s):0.0010371
--------------------------------------------------------------------
Calibration results of the iterative solution:
Euler angles(degree):-39.6224,-2.9328,-62.7816
translation (mm):-46.4082,7.5472,57.6744
marker position(mm):6.1807,-482.1297,10.2421
RMSE(mm):1.6757
Runtime(s):0.0014392
--------------------------------------------------------------------
Measurement number:50
Calibration results of the closed-form solution:
Euler angles(degree):-39.3794,-3.0738,-62.7562
translation (mm):-44.3712,7.3289,57.5741
marker position(mm):6.6562,-481.7926,9.1926
RMSE(mm):2.0093
Runtime(s):0.0045665
--------------------------------------------------------------------
Calibration results of the iterative solution:
Euler angles(degree):-39.6185,-3.049,-62.7731
translation (mm):-45.6604,8.666,57.8175
marker position(mm):6.5507,-481.832,9.0897
RMSE(mm):1.9666
Runtime(s):0.0059281
--------------------------------------------------------------------
Measurement number:70
Calibration results of the closed-form solution:
Euler angles(degree):-39.4001,-3.1151,-62.8463
translation (mm):-43.8228,7.8471,58.3511
marker position(mm):6.6675,-481.3842,8.3375
RMSE(mm):1.9946
Runtime(s):0.0008625
--------------------------------------------------------------------
Jin, G., Yu, X., Chen, Y., Li, J. (2023), General Hand-eye Parameter Estimation based on 3D Measurement of a Single-marker, submitted to IEEE Trans. Instrum. Meas.
A synced sequence of 3D camera observation and robot measurement can be downloaded from https://github.com/MatthewJin001/3Ddata.
Figure: Experimental configuration for the eye-in-hand calibration of a single marker.
Gumin Jin, Department of Automation, Shanghai Jiao Tong University, Shanghai, jingumin@sjtu.edu.cn