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.

Abstract: Modeling human trajectories in crowded environments is challenging due to the complex nature of pedestrian behavior and interactions. This paper proposes a geometric graph neural network (GNN) architecture that integrates domain knowledge from psychological studies to model pedestrian interactions and predict future trajectories. Unlike prior studies using complete graphs, we define interaction neighborhoods using pedestrians' field of view, motion direction, and distance-based kernel functions to construct graph representations of crowds. Evaluations across multiple datasets demonstrate improved prediction accuracy through reduced average and final displacement error metrics. Our findings underscore the importance of integrating domain knowledge with data-driven approaches for effective modeling of human interactions in crowds.