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

arXiv: https://arxiv.org/abs/1907.12425 · HTML: https://mlsanity.com/paper/1907.12425/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2019.

## Built on by (most cited first, 9 of 9)

- [Robotic Testbed for Rendezvous and Optical Navigation: Multi-Source Calibration and Machine Learning Use Cases](https://mlsanity.com/paper/2108.05529/) (2021)
- [Integrating Artificial Intelligence and Augmented Reality in Robotic Surgery: An Initial dVRK Study Using a Surgical Education Scenario](https://mlsanity.com/paper/2201.00383/) (2022)
- [Accurate calibration of multi-perspective cameras from a generalization of the hand-eye constraint](https://mlsanity.com/paper/2202.00886/) (2022)
- [RegHEC: Hand-Eye Calibration via Simultaneous Multi-view Point Clouds Registration of Arbitrary Object](https://mlsanity.com/paper/2304.14092/) (2023)
- [Multi-Camera Hand-Eye Calibration for Human-Robot Collaboration in Industrial Robotic Workcells](https://mlsanity.com/paper/2406.11392/) (2024)
- [HERO: Learning Humanoid End-Effector Control for Visual Whole-Body Open-Vocabulary Object Grasping](https://mlsanity.com/paper/2602.16705/) (2026)
- [Digital and Robotic Twinning for Validation of Proximity Operations and Formation Flying](https://mlsanity.com/paper/2507.20034/) (2025)
- [Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment](https://mlsanity.com/paper/2512.00659/) (2025)
- [Calousel: Extrinsic Calibration of Non-overlapping Multi-camera Systems from Pure Rotation](https://mlsanity.com/paper/2606.25646/) (2026)

## Abstract (arXiv)

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 AX=ZB, where X and 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.