Non-orthogonal Tool/Flange and Robot/World Calibration for Realistic Tracking Scenarios

This work presents a novel method for simultaneous tool/flange and robot/world calibration by estimating a solution to the common matrix equation AX=YB. This solution is computed using a least-squares approach. Since real robots and localisation are all afflicted by certain errors, our approach allows for non-orthogonal matrices, partially compensating for imperfect calibration of the robot or localisation device. Additionally, we also introduce a new method where full robot/world and partial tool/flange calibration is possible using localisation devices providing less than six degrees of freedom. The methods are evaluated on simulation data and on real-world measurements collected using optical and magnetical tracking devices (NDI's Polaris Spectra and Aurora systems), volumetric ultrasound (a modified GE Vivid7 Dimension station, providing 3-DOF data), and a surface laser scanning device (LAP GALAXY). We compare our methods to two classical approaches: the method by Tsai/Lenz and the Dual Quaternion method by Daniilidis. In all experiments, the new algorithms strongly outperform the classical methods in terms of translational accuracy (by as much as 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.