On trajectory control of magnetized spherical solids driven by magnetic force through soft medium

Abstract

Manipulation of untethered millimeter-sized devices (bots) inside the human body has many medical applications. Most of the prior work focused on movement of such bots inside fluids, usually at low Reynolds numbers. Yet, many medical procedures are performed within soft tissues. Bot translation in soft materials differs dramatically from their motion in fluid. This paper focuses on trajectory control of small, untethered spheres driven magnetically in soft media commonly used to simulate tissues. While spherical bot shapes offer the advantage of potentially rapid change in the direction of motion, the main challenge in controlling trajectories through soft materials is their nonlinear and history dependent response forces associated with irreversible medium modification. This paper introduces control modules for manipulating spherical bots in soft media along elementary trajectories of circular and straight segments, from which more general trajectories may be assembled. The proposed control is based on a phenomenological model of soft media response forces. Numerical implementation of the proposed trajectory control along circular trajectories is shown to compare well with the results of experimental tests indicating that the accuracy on the order of the bot radius is readily achievable for trajectories whose radii of curvature is on the order of 10 bot radii.