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Generative Adversarial Networks for Solving Hand-Eye Calibration without Data Correspondence

Ilkwon Hong, Junhyoung Ha

TL;DR

This work reframes hand-eye calibration without data correspondence as a distribution-matching problem solvable by Generative Adversarial Networks (GANs). By constraining the generator to act as $G(A)=X^{-1}AX$ with $X\in SE(3)$, the method aligns the distributions of $\{B_j\}$ and $\{X^{-1}A_iX\}$ without requiring correspondences or explicit pdf models. The approach yields a mode-collapse-free, geometry-aware calibration procedure that leverages the full data distribution, demonstrated on synthetic data and a real hardware setup, with notable improvements in rotation accuracy and robustness to time offsets. The paper also discusses stabilization techniques (orthogonality-preserving updates, data normalization, multi-start optimization) and extends the framework to general parameter estimation problems beyond hand-eye calibration. Overall, the method offers a new GAN-based tool for unsupervised, distribution-level calibration on nonlinear manifolds, with practical impact for multi-sensor systems and online calibration scenarios.

Abstract

In this study, we rediscovered the framework of generative adversarial networks (GANs) as a solver for calibration problems without data correspondence. When data correspondence is not present or loosely established, the calibration problem becomes a parameter estimation problem that aligns the two data distributions. This procedure is conceptually identical to the underlying principle of GAN training in which networks are trained to match the generative distribution to the real data distribution. As a primary application, this idea is applied to the hand-eye calibration problem, demonstrating the proposed method's applicability and benefits in complicated calibration problems.

Generative Adversarial Networks for Solving Hand-Eye Calibration without Data Correspondence

TL;DR

This work reframes hand-eye calibration without data correspondence as a distribution-matching problem solvable by Generative Adversarial Networks (GANs). By constraining the generator to act as with , the method aligns the distributions of and without requiring correspondences or explicit pdf models. The approach yields a mode-collapse-free, geometry-aware calibration procedure that leverages the full data distribution, demonstrated on synthetic data and a real hardware setup, with notable improvements in rotation accuracy and robustness to time offsets. The paper also discusses stabilization techniques (orthogonality-preserving updates, data normalization, multi-start optimization) and extends the framework to general parameter estimation problems beyond hand-eye calibration. Overall, the method offers a new GAN-based tool for unsupervised, distribution-level calibration on nonlinear manifolds, with practical impact for multi-sensor systems and online calibration scenarios.

Abstract

In this study, we rediscovered the framework of generative adversarial networks (GANs) as a solver for calibration problems without data correspondence. When data correspondence is not present or loosely established, the calibration problem becomes a parameter estimation problem that aligns the two data distributions. This procedure is conceptually identical to the underlying principle of GAN training in which networks are trained to match the generative distribution to the real data distribution. As a primary application, this idea is applied to the hand-eye calibration problem, demonstrating the proposed method's applicability and benefits in complicated calibration problems.
Paper Structure (27 sections, 18 equations, 7 figures, 2 tables)

This paper contains 27 sections, 18 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Hand-Eye Calibration
  4. Under Exact Correspondence
  5. Under Loose Correspondence
  6. Without Correspondence
  7. Generative Adversarial Networks (GANs)
  8. Kullback–Leibler Divergence
  9. Hand-Eye Calibration without Data Correspondence
  10. Generative Adversarial Networks for Hand-Eye Calibration without Data Correspondence
  11. Method Outline
  12. Mode Collapse-Free Characteristic
  13. Implementation Details
  14. Orthogonality-Preserving Updates
  15. Reducing Solution Stochasticity
  16. ...and 12 more sections

Figures (7)

  • Figure 1: Proposed GAN-based method for hand-eye calibration without data correspondence.
  • Figure 2: Error comparison between proposed and existing methods in numerical simulations (a) using noiseless data and (b) using noise data.
  • Figure 3: Two system configurations constitute the $AX=XB$ loop in our experimental setup. An RGB-camera was attached to the end-effector of a Franka Emika Panda manipulator and captured a fixed checkerboard.
  • Figure 4: Error comparison for Exp. 1 between proposed and existing methods using experimental data without time offsets (left column) and with simulated time offsets (right column).
  • Figure 5: Error comparison for Exp. 2 between proposed and existing methods using experimental data without time offsets (left column) and with simulated time offsets (right column).
  • ...and 2 more figures