This paper introduces a learning-based modeling framework for a magnetically steerable soft suction device designed for endoscopic endonasal brain tumor resection. The device is miniaturized (4 mm outer diameter, 2 mm inner diameter, 40 mm length), 3D printed using biocompatible SIL 30 material, and integrates embedded Fiber Bragg Grating (FBG) sensors for real-time shape feedback. Shape reconstruction is represented using four Bezier control points, allowing for a compact and smooth representation of the device’s deformation. A data-driven model was trained on 5097 experimental samples to learn the mapping from magnetic field parameters (magnitude: 0–14 mT, frequency: 0.2–1.0 Hz, and vertical tip distances from the surface of the electromagnet coil table: 90–100 mm) to the resulting geometric configuration of the soft robot, represented by four Bezier control points that define its 3D shape. The model was implemented and compared using both Neural Network (NN) and Random Forest (RF) architectures. The RF model outperformed the NN across all metrics, achieving a mean root mean square error of 0.087 mm in control point prediction and a mean shape reconstruction error of 0.064 mm. Feature importance analysis further revealed that magnetic field components predominantly influence distal control points, while frequency and distance affect the base configuration. Unlike prior studies that apply general machine learning methods to soft robotic data, the proposed framework introduces a new modeling paradigm that links magnetic actuation inputs directly to geometric Bezier control points, creating an interpretable and low-dimensional representation of deformation. This conceptual integration of magnetic field characterization, embedded FBG sensing, and Bezier-based learning provides a unified modeling strategy that can be extended to other magnetically actuated continuum robots. This learning-based approach effectively models the complex nonlinear behavior of hyperelastic soft robots under magnetic actuation without relying on simplified physical assumptions. By enabling sub-millimeter shape prediction accuracy and real-time inference, this work establishes an advancement toward the intelligent control of magnetically actuated soft robotic tools in minimally invasive neurosurgery.
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