Real-time simulation enabled navigation control of magnetic soft continuum robots in confined lumens

Magnetic soft continuum robots (MSCRs) have emerged as a promising technology for minimally invasive interventions, offering enhanced dexterity and remote-controlled navigation in confined lumens. Unlike conventional guidewires with pre-shaped tips, MSCRs feature a magnetic tip that actively bends under applied magnetic fields. Despite extensive studies in modeling and simulation, achieving real-time navigation control of MSCRs in confined lumens remains a significant challenge. The primary reasons are due to robot-lumen contact interactions and computational limitations in modeling MSCR nonlinear behavior under magnetic actuation. Existing approaches, such as Finite Element Method (FEM) simulations and energy-minimization techniques, suffer from high computational costs and oversimplified contact interactions, making them impractical for real-world applications. In this work, we develop a real-time simulation and navigation control framework that integrates hard-magnetic elastic rod theory, formulated within the Discrete Differential Geometry (DDG) framework, with an order-reduced contact handling strategy. Our approach captures large deformations and complex interactions while maintaining computational efficiency. Next, the navigation control problem is formulated as an inverse design task, where optimal magnetic fields are computed in real time by minimizing the constrained forces and enhancing navigation accuracy. We validate the proposed framework through comprehensive numerical simulations and experimental studies, demonstrating its robustness, efficiency, and accuracy. The results show that our method significantly reduces computational costs while maintaining high-fidelity modeling, making it feasible for real-time deployment in clinical settings.