Hand-Eye and Robot-World Calibration by Global Polynomial Optimization
This work addresses a fundamental problem in robotics and computer vision for engineers and researchers, offering a globally optimal method for calibration tasks.
The paper tackles hand-eye calibration, which relates camera measurements to a known coordinate system, by formulating it as multivariate polynomial optimization problems and solving them globally using convex LMI relaxations, achieving effective solutions validated on synthetic and real datasets.
The need to relate measurements made by a camera to a different known coordinate system arises in many engineering applications. Historically, it appeared for the first time in the connection with cameras mounted on robotic systems. This problem is commonly known as hand-eye calibration. In this paper, we present several formulations of hand-eye calibration that lead to multivariate polynomial optimization problems. We show that the method of convex linear matrix inequality (LMI) relaxations can be used to effectively solve these problems and to obtain globally optimal solutions. Further, we show that the same approach can be used for the simultaneous hand-eye and robot-world calibration. Finally, we validate the proposed solutions using both synthetic and real datasets.