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.
本文针对机械臂末端安装激光测距仪的手术机器人的手眼标定，设计了基于平面模板标定的方法，给出了平面模板的数学模型并推导了求解方法。针对实际系统中存在的测量误差，提出了一种新的关于单平面数据优选的算法，可有效地剔除测量误差大的数据，提高标定精度；在此基础上，进一步提出使用立体正交平面改进标定精度的方法，应用非线性优化方法提高手眼标定精度。为验证精度，使用激光测距仪从不同角度、位置对空间中的某些固定点和一个长方体的表面进行测量。结果表明，单平面方法标定的精度为（1.37±0.24）mm，使用立体正交平面得到的标定精度为（0.37±0.05）mm；测量三维空间点的平均 FRE 为 0.24 mm，平均 TRE 为 0.26 mm；角度的测量偏差最大为 0.4°。通过实验验证了本文方法的有效性，同时结果表明本方法的标定精度较高，能够满足手术机器人准确定位的需求。.
Keywords: hand-eye calibration; laser range finder; nonlinear optimization; surgical robot; three orthogonal planes.