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Automating surgical systems enhances precision and safety while reducing human involvement in high-risk environments. A major challenge in automating surgical procedures like suturing is accurately modeling the suture thread, a highly flexible and compliant component. Existing models either lack the accuracy needed for safety critical procedures or are too computationally intensive for real time execution. In this work, we introduce a novel approach for modeling suture thread dynamics using control barrier functions (CBFs), achieving both realism and computational efficiency. Thread like behavior, collision avoidance, stiffness, and damping are all modeled within a unified CBF and control Lyapunov function (CLF) framework. Our approach eliminates the need to calculate complex forces or solve differential equations, significantly reducing computational overhead while maintaining a realistic model suitable for both automation and virtual reality surgical training systems. The framework also allows visual cues to be provided based on the thread's interaction with the environment, enhancing user experience when performing suture or ligation tasks. The proposed model is tested on the MagnetoSuture system, a minimally invasive robotic surgical platform that uses magnetic fields to manipulate suture needles, offering a less invasive solution for surgical procedures., Comment: Accepted for 2025 IEEE International Conference on Robotics and Automation (ICRA). Supplementary video: https://www.youtube.com/watch?v=qO-nroi4Faw

Real-time visual localization of needles is necessary for various surgical applications, including surgical automation and visual feedback. In this study we investigate localization and autonomous robotic control of needles in the context of our magneto-suturing system. Our system holds the potential for surgical manipulation with the benefit of minimal invasiveness and reduced patient side effects. However, the non-linear magnetic fields produce unintuitive forces and demand delicate position-based control that exceeds the capabilities of direct human manipulation. This makes automatic needle localization a necessity. Our localization method combines neural network-based segmentation and classical techniques, and we are able to consistently locate our needle with 0.73 mm RMS error in clean environments and 2.72 mm RMS error in challenging environments with blood and occlusion. The average localization RMS error is 2.16 mm for all environments we used in the experiments. We combine this localization method with our closed-loop feedback control system to demonstrate the further applicability of localization to autonomous control. Our needle is able to follow a running suture path in (1) no blood, no tissue; (2) heavy blood, no tissue; (3) no blood, with tissue; and (4) heavy blood, with tissue environments. The tip position tracking error ranges from 2.6 mm to 3.7 mm RMS, opening the door towards autonomous suturing tasks.