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

Abstract

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.