AnchorHEC: Targetless Hand-Eye Calibration of Wrist and Fixed Cameras

Markerless hand-eye calibration under continuous motion requires jointly resolving camera geometry and the time offset between images and joint states. We present SyncHeC (Synchronized Hand-Eye Calibration), a dense differentiable-rendering framework that estimates both from a single robot trajectory. Continuous-time forward kinematics makes latency differentiable, metric depth complements mask contours, and an offline planner combines spatial sensitivity with temporal excitation. Alternating updates support Eye-to-Hand, Eye-in-Hand, and multi-camera calibration. On a 7-DoF arm, one $6.5$,s motion yields $0.21$,cm translation error against a marker-board reference, $0.34$,cm touch-test error, and $2.7$,ms latency error relative to an $87$,ms reference with $95\%$ uncertainty of $\pm1.5$,ms. Against CM-Calib on matched recordings, translation and nominal latency errors improve by $3.7\times$ and $2.3\times$. Experiments span seven arms and four depth sensors. Compensating the recovered offset during policy training and deployment increases success by $8.1$ percentage points across six families and six tasks ($1{,}800$ matched pairs; paired $95\%$ confidence interval $[6.3,9.9]$ points).

This work presents an RGB-D imaging-based approach to marker-free hand-eye calibration using a novel implementation of the iterative closest point (ICP) algorithm with a robust point-to-plane (PTP) objective formulated on a Lie algebra. Its applicability is demonstrated through comprehensive experiments using three well known serial manipulators and two RGB-D cameras. With only three randomly chosen robot configurations, our approach achieves approximately 90% successful calibrations, demonstrating 2-3x higher convergence rates to the global optimum compared to both marker-based and marker-free baselines. We also report 2 orders of magnitude faster convergence time (0.8 +/- 0.4 s) for 9 robot configurations over other marker-free methods. Our method exhibits significantly improved accuracy (5 mm in task space) over classical approaches (7 mm in task space) whilst being marker-free. The benchmarking dataset and code are open sourced under Apache 2.0 License, and a ROS 2 integration with robot abstraction is provided to facilitate deployment.

This article proposes a general optimization framework for solving hand-eye calibration problem. Unlike traditional methods, an iterative algorithm based on Lie algebra that achieves approximately global optimal solutions is developed. During the optimization process, the method strictly preserves the structural constraints of the calibration parameters and enables synchronized updates between calibration parameters. Recognizing that data used in real-word hand-eye calibration often contain uncertainty, especially in over-loading and large workspace industrial robot scenarios, which can significantly degrade accuracy, and accurately modeling such uncertainty is inherently difficult, this article avoids explicit uncertainty modeling. Instead, an uncertainty metric to evaluate the relative uncertainty between data sources is introduced and used to dynamically refine the iterative process. To further enhance convergence efficiency, an effective initial solution generation method that improves overall stability and accuracy is designed. Numerical simulations and real-world experiments validate the effectiveness of the proposed approach, and in synthetic datasets, the proposed approach improves the estimation accuracy by at least 67% under high-uncertainty conditions compared with the existing methods.