hand-eye calibration

Extrinsic calibration of multi-sensor systems—particularly in robot-world-and-hand-eye calibration (RWHEC)—suffers from low computational efficiency, strong environmental dependency, and excessive manual intervention. Method: We propose the first generalized RWHEC formalization framework, establishing a novel identifiability criterion and, for the first time, providing prior global optimality guarantees under bounded measurement errors. Our approach integrates Lie-algebraic parameterization, rotation-vector modeling, and compact semidefinite relaxation to construct a hybrid solver that balances theoretical rigor with engineering practicality. Results: Extensive experiments demonstrate that the algorithm achieves high accuracy and robustness even in severely constrained settings—e.g., monocular cameras without direct ranging—outperforming all existing methods across key metrics. The implementation is publicly available.

This work addresses the challenge of extrinsic calibration for non-overlapping multi-camera systems by proposing a novel method that requires only pure rotational motion and a single static calibration target. By introducing an implicit turntable coordinate frame and formulating a 3D reprojection error on the SE(3) manifold, the approach integrates observations of the same calibration board captured by different cameras at distinct time instances into a unified global nonlinear optimization framework. The method eliminates the need for large calibration patterns or complex motion estimation, thereby avoiding scale ambiguity and drift issues. High accuracy, strong robustness, and ease of deployment are demonstrated on both controlled rigs and real-world vehicle platforms, marking the first successful realization of high-precision extrinsic calibration for non-overlapping multi-camera setups using only pure rotation and a single static target.

This work addresses the observability of IMU-camera rotation extrinsics in visual-inertial odometry (VIO) under pure translational linear motion, identifying a fundamental limitation in existing observability theory. Method: Leveraging the Lie group–Lie algebra framework, we rigorously construct and analyze the system’s observability matrix, deriving theoretical conditions for extrinsic parameter identifiability; results are validated using both analytical proofs and real-world sensor data. Contribution/Results: We formally prove that linear translational motion renders at least one degree of freedom of the rotation extrinsics unobservable—a previously unrecognized deficiency in classical observability analysis. Experimental results confirm severe divergence in extrinsic estimation under such motion. Based on this insight, we propose a corrected observability criterion that explicitly accounts for motion-induced unobservability. This refined criterion effectively guides motion excitation design, significantly enhancing the robustness and reliability of online extrinsic calibration in practical VIO systems.

This work addresses the sensitivity of conventional 3D-to-2D methods to extrinsic calibration errors in estimating minute motions, which hinders high-precision six-degree-of-freedom (6-DOF) pose estimation. The authors propose a differential 6-DOF pose estimation approach that directly computes relative platform motion from inter-frame image displacements and known 3D control points, bypassing absolute pose estimation and supporting both monocular and multi-camera systems. Theoretical analysis demonstrates for the first time that translational extrinsic errors are entirely canceled out, while rotational errors introduce only bounded perturbations; the study further derives observability conditions, the Cramér–Rao lower bound, and an unbiased consistent estimator. Experiments show that under 0.5-pixel noise, the monocular system achieves 10.09 arcsec rotation RMSE and 3.70 mm translation RMSE in 0.34 ms, and the binocular system attains 10.58 arcsec and 3.91 mm in 0.27 ms—significantly outperforming existing PnP methods.

In robotic imitation learning, inaccurate camera extrinsic calibration—particularly due to local minima, poor generalization, and reliance on multiple markers or online interaction—remains a critical challenge. To address this, we propose an offline hand-eye calibration method requiring only a single fiducial marker. Our approach innovatively integrates vision foundation models (VFMs) with geometric constraints: first, leveraging VFMs to localize the marker, combined with point tracking, end-effector 3D trajectory estimation, and temporal PnP for coarse extrinsic initialization; then refining the solution via differentiable rendering optimization. The method is training-free, hardware-agnostic, and exhibits strong robustness and cross-platform generalizability. Evaluated on three heterogeneous robotic platforms, it significantly outperforms state-of-the-art approaches. Moreover, it simultaneously generates high-quality auxiliary annotations—including dense depth maps and part-level segmentation masks—without additional supervision.

本文提出P²Calib，利用目标板CAD模型中的图案先验和几何约束来提高LiDAR-相机外参标定的精度，解决了因激光雷达侧孔中心提取不准确导致的问题。

OmniCalib通过机器人自身运动和内置传感器，无需外部标定目标，实现人形机器人全身关节零点及相机外参的自标定。

本文提出了一种激光跟踪器辅助的手眼标定方法，用于配备摄像头的移动机器人，通过结合3D激光跟踪测量和2D摄像机观测来解决相机与机器人坐标系之间的校准问题。

This work addresses the limitations of conventional extrinsic calibration methods between inertial sensors and RGB-D cameras on unmanned aerial vehicles, which typically rely on calibration targets, specialized equipment, and initial parameter estimates. To overcome these constraints, the authors propose a target-free self-calibration approach that uniquely integrates deep learning-based ground segmentation with geometric constraints. By segmenting ground regions from depth data, estimating point cloud normals, and aligning them with the gravity direction derived from IMU measurements, the method achieves robust extrinsic calibration without requiring any initial guess. Experimental results demonstrate that the proposed technique attains calibration accuracy surpassing the MATLAB Camera Calibrator Toolbox and comparable to Kalibr, while entirely eliminating dependence on calibration targets—thereby significantly enhancing deployment flexibility and practical applicability in real-world scenarios.

本文提出一种基于重力先验的转换策略，通过解耦简化绝对位姿估计问题，并引入位姿精化算法提高精度，解决了机器人应用中绝对位姿估计的难题。