A magneto-elastic model for soft magnetic concentric tube robots

Abstract This paper presents a numerical solution to a reduced-order analytical energy formulation of a soft, magnetically actuated concentric tube continuum robot. Unlike conventional concentric tube robots, which rely on pre-curved elastic energy storage and suffer from material stiffness constraints and snap through instability, our design uses softly magnetic rings adhered to braided sleeves to generate deformation directly from a strong, stationary background field. While high-field MRI systems provide a convenient actuation environment, the proposed design principle is broadly applicable to any application featuring a sufficiently strong background magnetic field (B $$\gtrsim $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>≳</mml:mo> </mml:math> 1T). We derive a complete magneto-elastic formulation that couples easy-plane magnetic torque with sleeve curvature to determine stable catheter configurations. The model captures mechanical hysteresis, bistability, and the nonlinear relationship between base rotation and tip pose. Experimental validation in the background field of a 7 T pre-clinical MRI scanner demonstrates strong agreement with simulated deformation, with an overall RMS error of $$4.4^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>.</mml:mo> <mml:msup> <mml:mn>4</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> . This framework provides a foundation for closed-loop control, systematic design optimization, and self-sensing capabilities in magnetically actuated soft continuum robots, enabling new classes of highly compliant robotic systems for constrained and sensitive environments.