Simultaneous Hand-Eye and Robot-World Calibration by Solving the AX = YB Problem Without Correspondence

Calibration is often an important and necessary step in the use of image-guided systems. In the case of the AX = YB problem, the relative hand-eye (X) and robot-world (Y) transformations must be determined to provide accurate data for use in control. As an added difficulty, the exact correspondence between the streams of sensor data (A's and B's) is typically unknown due to asynchrony in sampling rates and processing time. One common scenario is a constant shift between the two data streams. Therefore, in this paper, we present a probabilistic method to simultaneously solve for X and Y without a priori knowledge of the correspondence between the streams of A's and B's. We begin by discussing probability density functions on SE(3) and then use Euclidean-group invariants to obtain an exact solution for X and Y. We then present a method to simultaneously recover X and Y and the correspondence between temporally shifted data sets using a correlation method. Following this, we show how to solve the problem in the case when the data are completely scrambled, corresponding to a complete loss of temporal information. Finally, we numerically simulated the proposed method with asynchronous data and noise added to the stream of B's to verify its efficiency and robustness.