Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-24T05:56:56.478Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal robot-world and hand-eye calibration with rotation and translation coupling

Published online by Cambridge University Press:  27 January 2022

Xiao Wang  and
Hanwen Song Open the ORCID record for Hanwen Song [Opens in a new window]
Xiao Wang
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
Hanwen Song*
Affiliation:
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
*
*Corresponding author. E-mail: hwsong@tongji.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

A classic hand-eye system involves hand-eye calibration and robot-world and hand-eye calibration. Insofar as hand-eye calibration can solve only hand-eye transformation, this study aims to determine the robot-world and hand-eye transformations simultaneously based on the robot-world and hand-eye equation. According to whether the rotation part and the translation part of the equation are decoupled, the methods can be divided into separable solutions and simultaneous solutions. The separable solutions solve the rotation part before solving the translation part, so the estimated errors of the rotation will be transferred to the translation. In this study, a method was proposed for calculation with rotation and translation coupling; a closed-form solution based on Kronecker product and an iterative solution based on the Gauss–Newton algorithm were involved. The feasibility was further tested using simulated data and real data, and the superiority was verified by comparison with the results obtained by the available method. Finally, we improved a method that can solve the singularity problem caused by the parameterization of the rotation matrix, which can be widely used in the robot-world and hand-eye calibration. The results show that the prediction errors of rotation and translation based on the proposed method be reduced to $0.26^\circ$ and $1.67$ mm, respectively.

Keywords

hand-eye calibrationrobot-world calibrationLie algebraJacobiansingularity
Type
Research Article
Information
Robotica , Volume 40 , Issue 9 , September 2022 , pp. 2953 - 2968
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Huang, J., Zhou, K., Chen, W. and Song, H., “A pre-processing method for digital image correlation on rotating structures,” Mech. Syst. Signal Proc. 152(12), 107494 (2021). CrossRefGoogle Scholar
Ding, X. and Yang, F., “Study on hexapod robot manipulation using legs,” Robotica 34(2), 468–481 (2016).10.1017/S0263574714001799CrossRefGoogle Scholar
Peng, S., Ding, X., Yang, F. and Xu, K., “Motion planning and implementation for the self-recovery of an overturned multi-legged robot,” Robotica 35(5), 1107–1120 (2017).10.1017/S0263574715001009CrossRefGoogle Scholar
Wu, J., Sun, Y., Wang, M. and Liu, M., “Hand-Eye calibration: 4D procrustes analysis approach,” IEEE Trans. Instrum. Meas. 69(6), 2966–2981 (2020).Google Scholar
Pachtrachai, K., Vasconcelos, F., Dwyer, G., Hailes, S. and Stoyanov, D., “Hand-eye calibration with a remote centre of motion,” IEEE Rob. Autom. Lett. 4(4), 3121–3128 (2019).10.1109/LRA.2019.2924845CrossRefGoogle Scholar
Özgüner, O., Shkurti, T., Huang, S., Hao, R., Jackson, R. C., Newman, W. S. and Çavuşoğlu, M. C., “Camera-robot calibration for the Da Vinci robotic surgery system,” IEEE Trans. Autom. Sci. Eng. 17(4), 2154–2161 (2020).10.1109/TASE.2020.2986503CrossRefGoogle Scholar
Kansal, S. and Mukherjee, S., “Vision-Based kinematic analysis of the delta robot for object catching,” Robotica, 1–21 (2021). CrossRefGoogle Scholar
Ma, G., Jiang, Z., Li, H., Gao, J., Yu, Z., Chen, X., Liu, Y.-H. and Huang, Q., “Hand-eye servo and impedance control for manipulator arm to capture target satellite safely,” Robotica 33(4), 848–864 (2015).10.1017/S0263574714000587CrossRefGoogle Scholar
Ren, S., Yang, X., Song, Y., Qiao, H., Wu, L., Xu, J. and Chen, K., “A Simultaneous Hand-Eye Calibration Method for Hybrid Eye-in-Hand/Eye-to-Hand System,” 2017 IEEE 7th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER) (2017) pp. 568–573.Google Scholar
Wu, L., Wang, J., Qi, L., Wu, K., Ren, H. and Meng, M. Q.-H., “Simultaneous hand-eye, tool-flange, and robot-robot calibration for comanipulation by solving the AXB = YCZ problem,” IEEE Trans. Robot. 32(2), 413–428 (2016).CrossRefGoogle Scholar
Fu, Z., Pan, J., Spyrakos-Papastavridis, E., Chen, X. and Li, M., “A dual quaternion-based approach for coordinate calibration of dual robots in collaborative motion,” IEEE Robot. Autom. Lett. 5(3), 4086–4093 (2020).10.1109/LRA.2020.2988407CrossRefGoogle Scholar
Wang, G., Li, W.-L., Jiang, C., Zhu, D.-H., Xie, H., Liu, X.-J. and Ding, H., “Simultaneous calibration of multicoordinates for a dual-robot system by solving the axb = ycz problem,” IEEE Trans. Rob. 37(4), 1172–1185 (2021).10.1109/TRO.2020.3043688CrossRefGoogle Scholar
Su, J., “Convergence analysis for the uncalibrated robotic hand–eye coordination based on the unmodeled dynamics observer,” Robotica 28(4), 597–605 (2010).10.1017/S0263574709990270CrossRefGoogle Scholar
Shiu, Y. C. and Ahmad, S., “Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX = XB,” IEEE Trans. Robot. Autom. 5(1), 16–29 (1989).CrossRefGoogle Scholar
Zhuang, H., Roth, Z. S. and Sudhakar, R., “Simultaneous robot/world and tool/flange calibration by solving homogeneous transformation equations of the form AX = YB,” IEEE Trans. Robot. Autom. 10(4), 549–554 (1994).CrossRefGoogle Scholar
Wang, X., Huang, J. and Song, H., “Simultaneous robot–world and hand–eye calibration based on a pair of dual equations,” Measurement. 181(3), 109623 (2021).10.1016/j.measurement.2021.109623CrossRefGoogle Scholar
Tsai, R. Y. and Lenz, R. K., “A new technique for fully autonomous and efficient 3D robotics hand/eye calibration,” IEEE Trans. Rob. Autom. 5(3), 345–358 (1989).10.1109/70.34770CrossRefGoogle Scholar
Chou, J. C. K. and Kamel, M., “Finding the position and orientation of a sensor on a robot manipulator using quaternions,” Int. J. Robot. Res. 10(3), 240–254 (1991).10.1177/027836499101000305CrossRefGoogle Scholar
Horaud, R. and Dornaika, F., “Hand-eye calibration,” Int. J. Rob. Res. 14(3), 195–210 (1995).CrossRefGoogle Scholar
Malti, A. and Barreto, J. P., “Robust hand-eye calibration for computer aided medical endoscopy,” IEEE International Conference on Robotics and Automation, ICRA 2010, Anchorage(2010) pp. 5543–5549.Google Scholar
Park, F. C. and Martin, B. J., “Robot sensor calibration: Solving AX = XB on the Euclidean group,” IEEE Trans. Rob. Autom. 10(5), 717–721 (1994).CrossRefGoogle Scholar
Andreff, N., Horaud, R. and Espiau, B., “Robot hand-eye calibration using structure-from-motion,” Int. J. Rob. Res. 20(3), 228–248 (2001).10.1177/02783640122067372CrossRefGoogle Scholar
Chen, H., “A Screw Motion Approach to Uniqueness Analysis of Head-Eye Geometry,” Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, USA (IEEE Computer Society, 1991) pp. 145–151.Google Scholar
Zhao, Z. and Liu, Y., “A hand–eye calibration algorithm based on screw motions,” Robotica 27(2), 217–223 (2009).CrossRefGoogle Scholar
Daniilidis, K. and Bayro-Corrochano, E., “The Dual Quaternion Approach to Hand-Eye Calibration,” Proceedings of 13th International Conference on Pattern Recognition, vol. 1 (1996) pp. 318–322.10.1109/ICPR.1996.546041CrossRefGoogle Scholar
Daniilidis, K., “Hand-eye calibration using dual quaternions,” Int. J. Rob. Res. 18(3), 286–298 (1998).10.1177/02783649922066213CrossRefGoogle Scholar
Ma, Q., Li, H. and Chirikjian, G. S., “New Probabilistic Approaches to the AX = XB Hand-Eye Calibration without Correspondence,” 2016 IEEE International Conference on Robotics and Automation (ICRA) (2016) pp. 4365–4371.Google Scholar
Zhuang, H. and Shiu, Y. C., “A Noise Tolerant Algorithm For Wrist-mounted Robotic Sensor Calibration With Or Without Sensor Orientation Measurement,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (1992) pp. 1095–1100.Google Scholar
Strobl, K. H. and Hirzinger, G., “Optimal Hand-Eye Calibration,” 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (2006) pp. 4647–4653.Google Scholar
Heller, J., Havlena, M. and Pajdla, T., “Globally optimal hand-eye calibration using branch-and-bound,” IEEE Trans. Anal, Pattern. Mach. Intell. 38(5), 1027–1033 (2016).Google ScholarPubMed
Malti, A., “Hand-eye calibration with epipolar constraints: Application to endoscopy,” Robot. Auton. Syst. 61(2), 161–169 (2013).CrossRefGoogle Scholar
Koide, K. and Menegatti, E., “General hand–eye calibration based on reprojection error minimization,” IEEE Robot. Autom. Lett. 4(2), 1021–1028 (2019).CrossRefGoogle Scholar
Yang, G. and Zhao, L., “Optimal Hand–Eye Calibration of IMU and Camera,” 2017 Chinese Automation Congress (CAC) (2017) pp. 1023–1028.Google Scholar
Shah, M., “Solving the robot-world/hand-eye calibration problem using the Kronecker product,” J. Mech. Rob. 5(3), 031007 (2013).10.1115/1.4024473CrossRefGoogle Scholar
Ali, I., Olli, S., Gotchev, A. and Morales, E. R., “Methods for simultaneous robot-world-hand–eye calibration: A comparative study,” Sensors 19, 2837 (2019).10.3390/s19122837CrossRefGoogle ScholarPubMed
Li, A., Wang, L. and Wu, D., “Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product,” Int. J. Phys. Sci. 5(10), 1530–1536 (2010).Google Scholar
Li, H., Ma, Q., Wang, T. and Chirikjian, G. S., “Simultaneous hand-eye and robot-world calibration by solving the AX = YB problem without correspondence,” IEEE Robot. Autom. Lett. 1(1), 145–152 (2016).10.1109/LRA.2015.2506663CrossRefGoogle Scholar
Dornaika, F. and Horaud, R., “Simultaneous robot-world and hand-eye calibration,” IEEE Trans. Robot. Autom. 14(4), 617–622 (1998).10.1109/70.704233CrossRefGoogle Scholar
Tabb, A. and Ahmad Yousef, K. M., “Solving the robot-world hand-eye(s) calibration problem with iterative methods,” Mach. Vis. Appl. 28(5–6), 569–590 (2017).CrossRefGoogle Scholar
Zhao, Z. and Weng, Y., “A flexible method combining camera calibration and hand–eye calibration,” Robotica 31(5), 747–756 (2013).10.1017/S0263574713000040CrossRefGoogle Scholar
Heller, J., Henrion, D. and Pajdla, T., “Hand-Eye and Robot-World Calibration by Global Polynomial Optimization,” 2014 IEEE International Conference on Robotics and Automation (ICRA) (2014) pp. 3157–3164.Google Scholar
Zhao, Z., “Simultaneous robot-world and hand-eye calibration by the alternative linear programming,” Pattern Recognit. Lett. 127, 174–180 (2018).CrossRefGoogle Scholar
Wu, L. and Ren, H., “Finding the kinematic base frame of a robot by hand-eye calibration using 3D position Data,” IEEE Trans. Autom. Sci. Eng. 14(1), 314–324 (2017).CrossRefGoogle Scholar
Brewer, J., “Kronecker products and matrix calculus in system theory,” IEEE Trans. Circ. Syst. 25(9), 772–781 (1978).CrossRefGoogle Scholar
Murray, R., Li, Z. and Sastry, S., A Mathematical Introduction to Robot Manipulation, (1994). Google Scholar
Gorbatsevich, V., Onishchik, A. L. and Vinberg, E. B., Structure of Lie Groups and Lie Algebras, (1990).10.1007/978-3-642-74334-4CrossRefGoogle Scholar
Fu, Z., Dai, J., Kun, Y., Chen, X. and Lopez-Custodio, P., “Analysis of unified error model and simulated parameters calibration for robotic machining based on lie theory,” Rob. Comput. Integr. Manuf. 61, 101855 (2019). 10.1016/j.rcim.2019.101855CrossRefGoogle Scholar
Song, H., Du, Z., Wang, W. and Sun, L., “Singularity analysis for the existing closed-form solutions of the hand-eye calibration,” IEEE Access. 6, 75407–75421 (2018).CrossRefGoogle Scholar
Schmidt, J. and Niemann, H., “Data-selection for hand-eye calibration a vector quantization approach,” Int. J. Rob. Res. 27(9), 1027–1053 (2008).10.1177/0278364908095172CrossRefGoogle Scholar
Zhang, J., Shi, F. and Liu, Y., “Adaptive motion selection for online hand-eye calibration,” Robotica 25(5), 529–536 (2007).CrossRefGoogle Scholar
Bouguet, J. Y., Camera Calibration Toolbox for MATLAB.Google Scholar
Zhang, Z., “A flexible new technique for camera calibration,” IEEE Trans. Anal, Pattern. Mach. Intell. 22(11), 1330–1334 (2000).Google Scholar