Robust Hand-Eye Calibration of an Endoscopic Surgery Robot Using Dual Quaternions

This paper presents an approach for applying a dual quaternion hand– eye calibration algorithm on an endoscopic surgery robot. Special focus is on robustness, since the error of position and orientation data provided by the robot can be large depending on the movement actually executed. Another inherent problem to all hand–eye calibration methods is that non–parallel rotation axes must be used; otherwise, the calibration will fail. Thus we propose a method for increasing the numerical stability by selecting an optimal set of relative movements from the recorded sequence. Experimental evaluation shows the error in the estimated transformation when using well–suited and ill–suited data. Additionally, we show how a RANSAC approach can be used for eliminating the erroneous robot data from the selected movements.