A Certifably Correct Algorithm for Generalized Robot-World and Hand-Eye Calibration

2025-07-30

AI Summary

Extrinsic calibration of multi-sensor systems—particularly in robot-world-and-hand-eye calibration (RWHEC)—suffers from low computational efficiency, strong environmental dependency, and excessive manual intervention. Method: We propose the first generalized RWHEC formalization framework, establishing a novel identifiability criterion and, for the first time, providing prior global optimality guarantees under bounded measurement errors. Our approach integrates Lie-algebraic parameterization, rotation-vector modeling, and compact semidefinite relaxation to construct a hybrid solver that balances theoretical rigor with engineering practicality. Results: Extensive experiments demonstrate that the algorithm achieves high accuracy and robustness even in severely constrained settings—e.g., monocular cameras without direct ranging—outperforming all existing methods across key metrics. The implementation is publicly available.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Automatic extrinsic sensor calibration is a fundamental problem for multi-sensor platforms. Reliable and general-purpose solutions should be computationally efficient, require few assumptions about the structure of the sensing environment, and demand little effort from human operators. Since the engineering effort required to obtain accurate calibration parameters increases with the number of sensors deployed, robotics researchers have pursued methods requiring few assumptions about the sensing environment and minimal effort from human operators. In this work, we introduce a fast and certifiably globally optimal algorithm for solving a generalized formulation of the $ extit{robot-world and hand-eye calibration}$ (RWHEC) problem. The formulation of RWHEC presented is "generalized" in that it supports the simultaneous estimation of multiple sensor and target poses, and permits the use of monocular cameras that, alone, are unable to measure the scale of their environments. In addition to demonstrating our method's superior performance over existing solutions, we derive novel identifiability criteria and establish $ extit{a priori}$ guarantees of global optimality for problem instances with bounded measurement errors. We also introduce a complementary Lie-algebraic local solver for RWHEC and compare its performance with our global method and prior art. Finally, we provide a free and open-source implementation of our algorithms and experiments.

Problem

• Develops globally optimal algorithm for robot-world and hand-eye calibration
• Enables simultaneous multi-sensor and target pose estimation
• Supports monocular cameras without environment scale measurement

Innovation

• Fast globally optimal algorithm for RWHEC
• Supports multiple sensor and target poses
• Novel identifiability criteria and guarantees