Non-orthogonal tool/flange and robot/world calibration.

Background: For many robot-assisted medical applications, it is necessary to accurately compute the relation between the robot's coordinate system and the coordinate system of a localisation or tracking device. Today, this is typically carried out using hand-eye calibration methods like those proposed by Tsai/Lenz or Daniilidis.

Methods: We present a new method for simultaneous tool/flange and robot/world calibration by estimating a solution to the matrix equation AX = YB. It is computed using a least-squares approach. Because real robots and localisation are all afflicted by errors, our approach allows for non-orthogonal matrices, partially compensating for imperfect calibration of the robot or localisation device. We also introduce a new method where full robot/world and partial tool/flange calibration is possible by using localisation devices providing less than six degrees of freedom (DOFs). The methods are evaluated on simulation data and on real-world measurements from optical and magnetical tracking devices, volumetric ultrasound providing 3-DOF data, and a surface laser scanning device. We compare our methods with two classical approaches: the method by Tsai/Lenz and the method by Daniilidis.

Results: In all experiments, the new algorithms outperform the classical methods in terms of translational accuracy by up to 80% and perform similarly in terms of rotational accuracy. Additionally, the methods are shown to be stable: the number of calibration stations used has far less influence on calibration quality than for the classical methods.

Conclusion: Our work shows that the new method can be used for estimating the relationship between the robot's and the localisation device's coordinate systems. The new method can also be used for deficient systems providing only 3-DOF data, and it can be employed in real-time scenarios because of its speed.