On the Covariance of$oldsymbol X$in$oldsymbol Aoldsymbol X = oldsymbol Xoldsymbol B$

摘要

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$oldsymbol {X}$in$oldsymbol {A}oldsymbol {X}= oldsymbol {X}oldsymbol {B}$. In this paper, we provide a rigorous derivation of the covariance of the solution$oldsymbol {X}$, when$oldsymbol {A}$and$oldsymbol {B}$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$oldsymbol {S}oldsymbol {E}(3)$. Experiments involving synthetic and real calibration data confirm that our approach can predict the covariance of the hand–eye transformation with excellent precision.