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 (CLFs) 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.

Exerting forces and torques instantaneously on rigid magnetic bodies with no physical connection is an attractive feature of magnetic robotics. This demonstrates great potential for manipulating tools that are externally controlled through the use of magnetic fields in minimally invasive surgeries. The magnetic field can be controlled by the application of currents to electromagnets positioned around the surgical site, and the necessary currents for a specific desired manipulation can be derived from magnetic field models. However, the magnetic field generated by electromagnetic coils are highly nonlinear, especially in the vicinity of the magnetic field sources, which complicates the modeling process. While simple dipole models provide a good approximation for these fields far away from the electromagnets, these models tend to be highly inaccurate near the sources. Magnetic surgical applications benefit from models which accurately describe fields and gradients both near and far from the field source. Particularly, since forces and torques decay inversely proportionally with the cube of the distance to the coil, inaccurate modeling near the coil makes large regions near the coil unfit for applications requiring precisely predicted motion. Estimation errors near coils generate inaccuracies in field models that significantly reduce control performance for rigid magnetic bodies. In order to tackle this problem, we utilize Zernike basis functions to analytically represent the nonlinear magnetic field distribution more accurately. The accuracy of the controller is tested experimentally by driving a magnetic surgical suture needle with a length of 22 mm in the MagnetoSuture™ system along a lemniscate trajectory. The magnetic needle's tip position and the needle orientation, autonomously controlled by the proposed controller, shows RMS tracking error of 2.35 mm using typical dipole models and 1.71 mm for the Zernike fitting approach, a 27% improvement in tracking error. This suggests that the use of Zernike basis functions to capture the nonlinearities of the magnetic field may assist in implementing fast and precise autonomous control strategies for magnetic suture needles.

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 nonlinear 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.