MarUco: A Markerless 6D Pose Estimation Framework for Closed-Loop Control of Surgical Continuum Manipulators

Purpose: Marker-based tracking of surgical robots is occlusion-prone in cluttered operating rooms. We evaluate stereo differentiable rendering for marker-free, real-time robot pose tracking, potentially improving safety, reducing setup time, and enabling multi-robot interaction. Methods: We extend the markerless pose estimation framework roboreg to online dynamic tracking via (i) sequential optimisation that propagates pose estimates across frames with motion-adaptive hyperparameter tuning, and (ii) CUDA stream parallelisation of segmentation and optimisation, combined with CUDA-graph accelerated segmentation. We evaluate on 38 unobstructed and 5 occluded displacement sequences with static start/end ground-truth calibrations and dynamic marker-based reference tracking. Results: We achieve real-time 1080p tracking at 30 fps (up from 14 fps for vanilla roboreg), matching the camera frame rate. Accuracy reaches 1.7 cm / 0.6 deg against static ground truth and 1.2 cm mean 3D error over 27,460 frames against the marker-based reference (1.53 cm over 1,242 occluded frames). Our method outperforms FoundationPose by 11% in dynamic estimation (63% under occlusion) and 250% in static estimation, with 6x faster inference. Conclusions: Stereo differentiable rendering enables real-time, high-resolution marker-free surgical robot tracking, on par with marker-based approaches and surpassing foundation-model baselines.

Accurate six-degree-of-freedom (6-DOF) motion estimation is essential for robotic manipulation, autonomous systems, and structural displacement monitoring. Conventional 3D-2D methods estimate absolute camera poses independently at each time and recover platform motion through camera-to-platform extrinsics, making them sensitive to extrinsic calibration errors, especially for micromotion. We present a differential pose estimation method that directly recovers platform motion from inter-frame image displacements and known 3D control points. By differencing perspective projection equations, using a depth-invariance approximation, and modeling motion on SE(3), the method avoids independent absolute-pose estimation and supports both monocular and multi-camera systems. We prove that translational extrinsic errors cancel exactly, while rotational errors induce a bounded perturbation determined by calibration error, motion magnitude, and observation geometry. We also derive generic observability conditions, a Cramer-Rao lower bound, and a bias-eliminated consistent estimator, and characterize the validity limits of the approximations. Extensive synthetic and real-world experiments establish a new state of the art for 6-DOF platform micromotion estimation, outperforming representative PnP and generalized-PnP methods in accuracy, calibration robustness, and computational efficiency. With five control points and 0.5-pixel image noise, the monocular solver obtains a combined pitch-yaw rotation RMSE of 10.09 arcsec, a translation RMSE of 3.70 mm, and a runtime of 0.34 ms. The binocular solver achieves a rotation RMSE of 10.58 arcsec, a translation RMSE of 3.91 mm, and a runtime of 0.27 ms. Code will be released upon publication at https://github.com/zyoungszu/pami2026.

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.