Control of magnetically-driven screws in a viscoelastic medium

Magnetically-driven screws operating in soft-tissue environments could be used to deploy localized therapy or achieve minimally invasive interventions. In this work, we characterize the closed-loop behavior of magnetic screws in an agar gel tissue phantom using a permanent magnet-based robotic system with an open-configuration. Our closed-loop control strategy capitalizes on an analytical calculation of the swimming speed of the screw in viscoelastic fluids and the magnetic point-dipole approximation of magnetic fields. The analytical solution is based on the Stokes/Oldroyd-B equations and its predictions are compared to experimental results at different actuation frequencies of the screw. Our measurements matches the theoretical prediction of the analytical model before the step-out frequency of the screw owing to the linearity of the analytical model. We demonstrate open-loop control in two-dimensional space, and point-to-point closed-loop motion control of the screw (length and diameter of 6 mm and 2 mm, respectively) with maximum positioning error of 1.8 mm.