# Solving the Robot-World Hand-Eye(s) Calibration Problem with Iterative Methods

## TL;DR

This paper introduces iterative methods for robot-world hand-eye calibration, improving accuracy over existing techniques by exploring various cost functions, parameterizations, and formulations, and extends to multi-camera setups.

## Contribution

It presents a new collection of iterative calibration methods with multiple parameterizations and formulations, outperforming state-of-the-art approaches and extending to multi-camera calibration.

## Key findings

- Methods achieve higher accuracy on real and simulated datasets.
- Comparison shows superior performance over seven existing methods.
- Extension to multi-camera calibration demonstrates versatility.

## Abstract

Robot-world, hand-eye calibration is the problem of determining the transformation between the robot end-effector and a camera, as well as the transformation between the robot base and the world coordinate system. This relationship has been modeled as $\mathbf{AX}=\mathbf{ZB}$, where $\mathbf{X}$ and $\mathbf{Z}$ are unknown homogeneous transformation matrices. The successful execution of many robot manipulation tasks depends on determining these matrices accurately, and we are particularly interested in the use of calibration for use in vision tasks. In this work, we describe a collection of methods consisting of two cost function classes, three different parameterizations of rotation components, and separable versus simultaneous formulations. We explore the behavior of this collection of methods on real datasets and simulated datasets, and compare to seven other state-of-the-art methods. Our collection of methods return greater accuracy on many metrics as compared to the state-of-the-art. The collection of methods is extended to the problem of robot-world hand-multiple-eye calibration, and results are shown with two and three cameras mounted on the same robot.