The hand-eye calibration problem was first formulated decades ago and is widely applied in robotics, image guided therapy, etc. It is usually cast as the “AX = XB” problem where the matrices A, B, and X are rigid body transformations in SE(3). Many solvers have been proposed to recover X given data streams {Ai} and {Bi} with correspondence. However, exact correspondence might not be accessible in the real world due to the asynchronous sensors and missing data, etc. A probabilistic approach named “Batch method” was introduced in previous research of our lab, which doesn't require a prior knowledge of the correspondence between the two data streams {Ai} and {Bj}. Analogous to non-probabilistic approaches which require data selection to filter out ill-conditioned data pairs, the Batch method has restrictions on the data set {Ai} and {Bj} that can be used. We propose two new probabilistic approaches built on top of the Batch method by giving new definitions of the mean on SE(3), which alleviate the restrictions on the data set and significantly improve the calibration accuracy of X.
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