# Hand-Eye Calibration

arXiv: https://arxiv.org/abs/2311.12655 · HTML: https://mlsanity.com/paper/2311.12655/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 33 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Built on by (most cited first, 8 of 8)

- [CtRNet-X: Camera-to-Robot Pose Estimation in Real-world Conditions Using a Single Camera](https://mlsanity.com/paper/2409.10441/) (2024)
- [Seamless Augmented Reality Integration in Arthroscopy: A Pipeline for Articular Reconstruction and Guidance](https://mlsanity.com/paper/2410.00386/) (2024)
- [CaLiV: LiDAR-to-Vehicle Calibration of Arbitrary Sensor Setups](https://mlsanity.com/paper/2504.01987/) (2025)
- [Kalib: Easy Hand-Eye Calibration with Reference Point Tracking](https://mlsanity.com/paper/2408.10562/) (2024)
- [CLAIM: Camera-LiDAR Alignment with Intensity and Monodepth](https://mlsanity.com/paper/2512.14001/) (2025)
- [Robot-Enabled Machine Learning-Based Diagnosis of Gastric Cancer Polyps Using Partial Surface Tactile Imaging](https://mlsanity.com/paper/2408.01554/) (2024)
- [ARC-Calib: Autonomous Markerless Camera-to-Robot Calibration via Exploratory Robot Motions](https://mlsanity.com/paper/2503.14701/) (2025)
- [Temporal and Rotational Calibration for Event-Centric Multi-Sensor Systems](https://mlsanity.com/paper/2508.12564/) (2025)

## Abstract (arXiv)

Whenever a sensor is mounted on a robot hand it is important to know the relationship between the sensor and the hand. The problem of determining this relationship is referred to as hand-eye calibration, which is important in at least two types of tasks: (i) map sensor centered measurements into the robot workspace and (ii) allow the robot to precisely move the sensor. In the past some solutions were proposed in the particular case of a camera. With almost no exception, all existing solutions attempt to solve the homogeneous matrix equation AX=XB. First we show that there are two possible formulations of the hand-eye calibration problem. One formulation is the classical one that we just mentioned. A second formulation takes the form of the following homogeneous matrix equation: MY=M'YB. The advantage of the latter is that the extrinsic and intrinsic camera parameters need not be made explicit. Indeed, this formulation directly uses the 3 by 4 perspective matrices (M and M') associated with two positions of the camera. Moreover, this formulation together with the classical one cover a wider range of camera-based sensors to be calibrated with respect to the robot hand. Second, we develop a common mathematical framework to solve for the hand-eye calibration problem using either of the two formulations. We present two methods, (i) a rotation then translation and (ii) a non-linear solver for rotation and translation. Third, we perform a stability analysis both for our two methods and for the classical linear method of Tsai and Lenz (1989). In the light of this comparison, the non-linear optimization method, that solves for rotation and translation simultaneously, seems to be the most robust one with respect to noise and to measurement errors.