Physically Constrained Kinematic Calibration for High-Precision Robotic Needle Guidance

Computed tomography (CT)-guided needle biopsies are critical for diagnosing a range of conditions, including lung cancer, but present challenges such as limited in-bore space, prolonged procedure times, and radiation exposure. Robotic assistance offers a promising solution by improving needle trajectory accuracy, reducing radiation exposure, and enabling real-time adjustments. In our previous work, we introduced a robotic platform designed for accurate needle insertion within the confined CT bore. However, its performance in clinical settings is restricted by limited dexterity and a constrained workspace. In this study, we present an 11-degree-of-freedom (DOF) robotic system that integrates a 6-DOF robotic base with an improved 5-DOF cable-driven end-effector, yielding a significantly expanded workspace and enhanced dexterity. To leverage the hyper-redundant degrees of freedom, we introduce a weighted inverse kinematics controller, along with a null-space control strategy to optimize maneuverability and dexterity. By using a task-oriented weight matrix as a hyperparameter, the system provides a two-stage priority scheme fit for both large-scale movement and fine in-bore adjustments. In clinically relevant simulated scenarios, the system demonstrates a consistent 97% reachability rate across various human models. In addition, the task-oriented weight-matrix policy is extensively explored in five representative subtasks seen during needle biopsy through both simulation and real-world experiments, demonstrating superior tracking accuracy and enhanced manipulability for CT-guided procedures.

Reliable estimation of surgical needle 3D position and orientation is essential for autonomous robotic suturing, yet existing methods operate almost exclusively under stereoscopic vision. In monocular endoscopic settings, common in transendoscopic and intraluminal procedures, depth ambiguity and rotational symmetry render needle pose estimation inherently ill-posed, producing a multimodal distribution over feasible configurations, rather than a single, well-grounded estimate. We present PinPoint, a probabilistic variational inference framework that treats this ambiguity directly, maintaining a distribution of pose hypotheses rather than suppressing it. PinPoint combines monocular image observations with robot-grasp constraints through analytical geometric likelihoods with closed-form Jacobians. This framework enables efficient Gauss-Newton preconditioning in a Stein Variational Newton inference, where second-order particle transport deterministically moves particles toward high-probability regions while kernel-based repulsion preserves diversity in the multimodal structure. On real needle-tracking sequences, PinPoint reduces mean translational error by 80% (down to 1.00 mm) and rotational error by 78% (down to 13.80°) relative to a particle-filter baseline, with substantially better-calibrated uncertainty. On induced-rotation sequences, where monocular ambiguity is most severe, PinPoint maintains a bimodal posterior 84% of the time, almost three times the rate of the particle filter baseline, correctly preserving the alternative hypothesis rather than committing prematurely to one mode. Suturing experiments in ex vivo tissue demonstrate stable tracking through intermittent occlusion, with average errors during occlusion of 1.34 mm in translation and 19.18° in rotation, even when the needle is fully embedded.

We present a Gaussian Splatting-based framework for hand-eye calibration of the da Vinci surgical robot. In a vision-guided robotic system, accurate estimation of the rigid transformation between the robot base and the camera frame is essential for reliable closed-loop control. For cable-driven surgical robots, this task faces unique challenges. The encoders of surgical instruments often produce inaccurate proprioceptive measurements due to cable stretch and backlash. Conventional hand-eye calibration approaches typically rely on known fiducial patterns and solve the AX = XB formulation. While effective, introducing additional markers into the operating room (OR) environment can violate sterility protocols and disrupt surgical workflows. In this study, we propose SurgCalib, an automatic, markerless framework that has the potential to be used in the OR. SurgCalib first initializes the pose of the surgical instrument using raw kinematic measurements and subsequently refines this pose through a two-phase optimization procedure under the RCM constraint within a Gaussian Splatting-based differentiable rendering pipeline. We evaluate the proposed method on the public dVRK benchmark, SurgPose. The results demonstrate average 2D tool-tip reprojection errors of 12.24 px (2.06 mm) and 11.33 px (1.9 mm), and 3D tool-tip Euclidean distance errors of 5.98 mm and 4.75 mm, for the left and right instruments, respectively.