On the Covariance of $\boldsymbol X$ in $\boldsymbol A\boldsymbol X = \boldsymbol X\boldsymbol B$.

Hand–eye calibration, which consists in identifying the rigid-body transformation between a camera mounted on the robot end-effector and the end-effector itself, is a fundamental problem in robot vision. Mathematically, this problem can be formulated as: solve for $\boldsymbol {X}$ in $\boldsymbol {A}\boldsymbol {X}= \boldsymbol {X}\boldsymbol {B}$. In this paper, we provide a rigorous derivation of the covariance of the solution $\boldsymbol {X}$ , when $\boldsymbol {A}$ and $\boldsymbol {B}$ are randomly perturbed matrices. This fine-grained information is critical for applications that require a high degree of perception precision. Our approach consists in applying covariance propagation methods in $\boldsymbol {S}\boldsymbol {E}(3)$. Experiments involving synthetic and real calibration data confirm that our approach can predict the covariance of the hand–eye transformation with excellent precision. [ABSTRACT FROM AUTHOR]