Point Cloud Registration-Enabled Globally Optimal Hand-Eye Calibration

Hand-eye calibration crucial for robots relying on visual cues in their operational environments has seen decades of development. However, the existing methods still grapple with some open issues: closed-form solutions are overly sensitive to outliers, iterative solutions heavily rely on initial values leading to local optima, and calibration rigs are frequently required with limited applicability. To address these limitations, we introduce a novel method capable of achieving globally optimal hand-eye matrix solutions without dependence on specific calibration objects and initial values. Leveraging the progressive and adaptive variance minimization fine registration algorithm proposed here in conjunction with the four-point congruent sets coarse registration algorithm, this method ensures globally optimal registration of point cloud pairs. Through the point cloud pose consistency constraints, and by employing parameter space decomposition of edge vectors, a straightforward and effective method for solving the hand-eye matrix is derived. The solution of the hand-eye matrix becomes a straightforward closed-form solution, which is achieved through the optimal transformations and correspondences in point cloud registration for an optimal single-step solution. The method demonstrates robustness, high precision, and adaptability through experimental validations, establishing its superiority and effectiveness in hand-eye calibration.