Physics-Based Reduced-Order Modeling of Magnetic Microparticle Swarms for Biomedical Control

Abstract

Magnetic particle swarms are governed by rich nonlinear collective dynamics that complicate predictive, feedback-based control in biomedical microrobotics. We develop a physics-based reduced-order ellipse model that describes the swarm morphology by its principal radii (r1, r2). At steady state, these radii depend explicitly on magnetic-field curvature, axial gradients, and actuation angular velocity through anisotropic stiffness terms. Model parameters are identified experimentally, yielding low validation errors (RMSE: 0.25 mm for r1 and 0.42 mm for r2) and revealing pronounced stiffness anisotropy (Sx/Sy ≈ 0.16). The resulting formulation provides compact, interpretable equations that enable tractable control design and feedback regulation of magnetic particle swarms.