On the covariance of X in AX = XB
This work addresses the need for precise uncertainty estimation in hand-eye calibration for robotics, though it is incremental as it builds on existing covariance propagation methods.
The paper tackles the problem of hand-eye calibration by rigorously deriving the covariance of the solution X in AX = XB when A and B are randomly perturbed, enabling high-precision perception. Experiments show the approach predicts the covariance with excellent precision on synthetic and real data.
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 X in AX = XB. In this paper, we provide a rigorous derivation of the covariance of the solution X, when A and 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 SE(3). Experiments involving synthetic and real calibration data confirm that our approach can predict the covariance of the hand-eye transformation with excellent precision.