Hand-eye calibration using dual quaternions in medical environment

Abstract

Nowadays medical interventions are often supported by localization systems using different measurement tools (MT). This requires to register the MT coordinate sytem to the world coordinate system used by the medical device. The hand-eye calibration is a well-known method from robotics to estimate the transformation between the gripper of a robot (hand) and a MT (eye) rigidly attached to the robot. Using a calibration tool (e.g. checker board) one can obtain the hand-eye transformation using known relative movements of the robot and the data from the MT. The approach can also be used for MT located elsewhere * using markers on the device. The position of the markers is not required to be known since they are rigid during the motions. Based on prior work using dual quaternions to represent transformations in the SE(3) we not only took into account movements between immediate neighbour positions Pi and Pj , but combined all positions to gain (P/2) submotions in every subset Σ p/n=3 (p/n) t without increasing the number of positions conducted during the calibration. We took into account the unity constraint for dual quaternions since only those represent rigid motions in space. We performed simulations that show the advantage of our algorithm. Additionally we gained experimental data which supported the outcome of the simulations. We can outline that our approach achieves more accurate results estimating the hand-eye transformation than the aforementioned algorithms.