A plane-based hand-eye calibration method for surgical robots_Journal of Biomedical Engineering

Authors：

ZENG Bowei ¹ , MENG Fanle ¹ , DING Hui ¹ , LIU Wenbo ² , WU Di ² ,  WANG Guangzhi ¹

1. Department of Biomedical Engineering, Tsinghua University, Beijing 100084, P.R.China;
2. Sino Precision Medical Technology (Beijing) Co., Ltd, Beijing 100062, P.R.China;

Corresponding author：

WANG Guangzhi, Email: wgz-dea@mail.tsinghua.edu.cn

Keywords：

surgical robot; hand-eye calibration; laser range finder; three orthogonal planes; nonlinear optimization

DOI：

10.7507/1001-5515.201605050

Video：

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In order to calibrate the hand-eye transformation of the surgical robot and laser range finder (LRF), a calibration algorithm based on a planar template was designed. A mathematical model of the planar template had been given and the approach to address the equations had been derived. Aiming at the problems of the measurement error in a practical system, we proposed a new algorithm for selecting coplanar data. This algorithm can effectively eliminate considerable measurement error data to improve the calibration accuracy. Furthermore, three orthogonal planes were used to improve the calibration accuracy, in which a nonlinear optimization for hand-eye calibration was used. With the purpose of verifying the calibration precision, we used the LRF to measure some fixed points in different directions and a cuboid’s surfaces. Experimental results indicated that the precision of a single planar template method was (1.37±0.24) mm, and that of the three orthogonal planes method was (0.37±0.05) mm. Moreover, the mean FRE of three-dimensional (3D) points was 0.24 mm and mean TRE was 0.26 mm. The maximum angle measurement error was 0.4 degree. Experimental results show that the method presented in this paper is effective with high accuracy and can meet the requirements of surgical robot precise location.

Citation： ZENG Bowei, MENG Fanle, DING Hui, LIU Wenbo, WU Di, WANG Guangzhi. A plane-based hand-eye calibration method for surgical robots. Journal of Biomedical Engineering, 2017, 34(2): 200-207. doi: 10.7507/1001-5515.201605050 Copy

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13.	Gan Z, Tang Q. Visual sensing and its applications: integration of laser sensors to industrial robots. Berlin, Germany: Springer Science & Business Media, 2011.
14.	卢科青, 王文, 陈子辰. 点激光测头激光束方向标定. 光学精密工程, 2010, 18(4): 880-886.
15.	王胜华, 都东, 张文增, 等. 机器人定点变位姿手-眼标定方法. 清华大学学报:自然科学版, 2007, 47(2): 165-168.
16.	Zhou A, Guo J, Shao W, et al. A segmental calibration method for a miniature serial-link coordinate measuring machine using a compound calibration artefact. Measurement Science and Technology, 2013, 24(6): 065001.
17.	吴聊, 杨向东, 蓝善清, 等. 基于平面模板的机器人 TCF 标定. 机器人, 2012, 34(1): 98-103.
18.	袁康正, 朱伟东, 陈磊, 等. 机器人末端位移传感器的安装位置标定方法. 浙江大学学报:工学版, 2015, 49(5): 829-834.
19.	Jolliffe I. Principal component analysis. New York, USA: Wiley Online Library, 2002.
20.	Transtrum M K, Sethna J P. Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization. arXiv preprint arXiv: 1201.5885, 2012.
21.	DENSO WAVE INCORPORATED. DENSO 机械臂操作指南[EB/OL]. (2011-02-11)[2016-05-19]. .

1. Marcus H J, Hughes-Hallett A, Cundy T P, et al. da Vinci robot-assisted keyhole neurosurgery: a cadaver study on feasibility and safety. Neurosurg Rev, 2015, 38(2): 367-371; discussion 371.
2. Šuligoj F, Jerbic B, Svaco M, et al. Medical applicability of a low-cost industrial robot arm guided with an optical tracking system// 2015 IEEE/RSJ International Conference o Intelligent Robots and Systems (IROS). Hamburg: IEEE, 2015: 3785-3790.
3. 颜国正, 陈雯雯. 肠道内窥镜机器人研究进展. 生物医学工程学杂志, 2015, 32(1): 214-217．.
4. Gonzalez-Martinez J, Vadera S, Mullin J, et al. Robot-assisted stereotactic laser ablation in medically intractable epilepsy: operative technique. Neurosurgery, 2014, 10(Suppl 2): 167-172; discussion 172-3.
5. von Langsdorff D, Paquis P, Fontaine D. In vivo measurement of the frame-based application accuracy of the Neuromate neurosurgical robot. J Neurosurg, 2015, 122(1): 191-194.
6. Cardinale F, Cossu M, Castana L, et al. Stereoelectroencephalography: surgical methodology, safety, and stereotactic application accuracy in 500 procedures. Neurosurgery, 2013, 72(3): 353-366; discussion 366.
7. Faria C, Erlhagen W, Rito M, et al. Review of robotic technology for stereotactic neurosurgery. IEEE Rev Biomed Eng, 2015, 8: 125-137.
8. Furlanetti L L, Monaco B A, Cordeiro J G, et al. Frame-based stereotactic neurosurgery in children under the age of seven: Freiburg University’s experience from 99 consecutive cases. Clinical Neurology and Neurosurgery, 2015, 130: 42-47.
9. Lü Y, Li C, Liu M, et al. MRI-guided stereotactic aspiration of brain abscesses by use of an optical tracking navigation system. Acta Radiol, 2014, 55(1): 121-128.
10. Shiu Y C, Ahmad S. Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the formAX=XB. IEEE Transactions on Robotics and Automation, 1989, 5(1): 16-29.
11. Tsai R Y, Lenz R K. A new technique for fully autonomous and efficient 3D robotics hand/eye calibration. IEEE Transactions on Robotics and Automation, 1989, 5(3): 345-358.
12. Wei G Q, Hirzinger G. Active self-calibration of hand-mounted laser range finders. IEEE Transactions on Robotics and Automation, 1998, 14(3): 493-497.
13. Gan Z, Tang Q. Visual sensing and its applications: integration of laser sensors to industrial robots. Berlin, Germany: Springer Science & Business Media, 2011.
14. 卢科青, 王文, 陈子辰. 点激光测头激光束方向标定. 光学精密工程, 2010, 18(4): 880-886.
15. 王胜华, 都东, 张文增, 等. 机器人定点变位姿手-眼标定方法. 清华大学学报:自然科学版, 2007, 47(2): 165-168.
16. Zhou A, Guo J, Shao W, et al. A segmental calibration method for a miniature serial-link coordinate measuring machine using a compound calibration artefact. Measurement Science and Technology, 2013, 24(6): 065001.
17. 吴聊, 杨向东, 蓝善清, 等. 基于平面模板的机器人 TCF 标定. 机器人, 2012, 34(1): 98-103.
18. 袁康正, 朱伟东, 陈磊, 等. 机器人末端位移传感器的安装位置标定方法. 浙江大学学报:工学版, 2015, 49(5): 829-834.
19. Jolliffe I. Principal component analysis. New York, USA: Wiley Online Library, 2002.
20. Transtrum M K, Sethna J P. Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization. arXiv preprint arXiv: 1201.5885, 2012.
21. DENSO WAVE INCORPORATED. DENSO 机械臂操作指南[EB/OL]. (2011-02-11)[2016-05-19]. .

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A plane-based hand-eye calibration method for surgical robots

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