Stability of Soft Magnetic Helical Microrobots

Nano/microrobotic swimmers have many possible biomedical applications such as drug delivery and micro-manipulation. This paper examines one of the most promising classes of these: rigid magnetic microrobots that are propelled through bulk fluid by rotation induced by a rotating magnetic field. Propulsion corresponds to steadily rotating and translating solutions of the dynamics of such microrobots that co-rotate with the magnetic field. To be observed in experiments and be amenable to steering control, such solutions must also be stable to perturbations. In this paper, we analytically derive a criterion for the stability of such steadily rotating solutions for a microrobot made of soft magnetic materials, which have a magnetization that depends on the applied field. This result generalizes previous stability criteria we obtained for microrobots with a permanent magnetization.