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

TL;DR

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 is developed, making it feasible for real-time deployment in clinical settings.

Abstract

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.

Figures (12)

• Figure 1: Schematic of a magnetic soft continuum robot (MSCR) navigating through the confined lumen within the biological systems. (A) Anatomical illustration of luminal structures, including cerebral vessels, the aorta, and the colon. The MSCR demonstrates adaptability for operation within diverse pathways. (B) Composition of the MSCR. The magnetic tip (black), fabricated by embedding hard-magnetic particles (e.g. NdFeB) within polymer matrices (e.g. PDMS), deflects in response to an actuation magnetic field $\mathbf{B}_{a}$. (C) The MSCR is pushed at the proximal end with velocity $v_0$. By controlling the actuation magnetic fields $\mathbf{B}_{a}$, the MSCR is steered along the desired path (centerline $\mathbf{R}(S)$) through the confined lumen without the tip contact with the lumen wall.
• Figure 2: Simplified representation of the magnetic soft continuum robot (MSCR), characterized by a total length $L$, magnetic tip length $L_{m}$, and cross-sectional radius $r_0$. The centerline is modeled as a magneto-elastic rod (denoted as $s$), with a primary focus on its bending, stretching, and twisting behaviors.
• Figure 3: Discretization of the MSCR and confined lumen. The MSCR is discretized as a magneto-elastic rod with the centerline path $s$, and the confined lumen is approximated as a cylindrical tube with the centerline path $S$. (A) Discrete diagram of rod (labeled as $\{ \mathbf{x}_1, \cdots, \mathbf{x}_{N} \}$) and tube (labeled as $\{ \mathbf{p}_1, \cdots, \mathbf{p}_{M} \}$). (B) Discrete measurements for bending and twisting of the rod. (C) Contact model between rod and tube, where $\delta_j$ measures the minimal distance from rod node $\mathbf{x}_j$ to the tube path $S$.
• Figure 4: Demonstration of model-based control. (A) Magnetic field control prevents the rod tip from contacting the lumen, highlighting precise manipulation. (B) Control process: Step 1 — detect contact between the rod tip and the lumen; Step 2 — virtually relocate the rod tip to a contact-free region and compute the equivalent constraint force; Step 3 — determine the optimal magnetic field strength to minimize the constraint force and apply it to the current configuration.
• Figure 5: Description of the experiment platform. The lumen phantom is placed in the center of the Helmholtz coils. An advancer clamps the MSCR and then pushes it to navigate the phantom path under the actuating magnetic fields.