Optimal Uncertainty-Aware Calibration for the AX=YB Problem

TL;DR

This paper introduces a novel optimization framework for hand-eye calibration that maintains structural constraints, dynamically refines uncertainty, and improves accuracy, especially under high-uncertainty conditions.

Contribution

It develops an iterative Lie algebra-based algorithm that preserves calibration structure, models uncertainty indirectly, and enhances convergence and accuracy.

Findings

Improves estimation accuracy by at least 67% under high uncertainty.

Effectively handles real-world data with significant uncertainty.

Validated through simulations and real-world experiments.

Abstract

This article proposes a general optimization framework for solving hand-eye calibration problem. Unlike traditional methods, an iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed. During the optimization process, the method strictly preserves the structural constraints of the calibration parameters and enables synchronized updates between calibration parameters. Recognizing that data used in real-word hand-eye calibration often contain uncertainty, especially in over-loading and large workspace industrial robot scenarios, which can significantly degrade accuracy, and accurately modeling such uncertainty is inherently difficult, this article avoids explicit uncertainty modeling. Instead, an uncertainty metric to evaluate the relative uncertainty between data sources is introduced and used to dynamically refine the iterative process. To further enhance convergence efficiency, an effective initial solution generation method that improves overall stability and accuracy is designed. Numerical simulations and real-world experiments validate the effectiveness of the proposed approach, and in synthetic datasets, the proposed approach improves the estimation accuracy by at least 67\% under high-uncertainty conditions compared with the existing methods.