Steering Control of Magnetic Helical Swimmers in Swirling Flows due to Confinement

Abstract

Artificial microswimmers are prospective robotic agents especially in biomedical applications. A rotating magnetic field can actuate a magnetized swimmer with a helical tail and enable propulsion. Such swimmers exhibit several modes of instability. Inside conduits, for example, hydrodynamic interactions with the boundaries lead to helical paths for pusher-mode swimmers; in this mode the helical tail pushes a rotating magnetic head. State-of-the-art in controlled navigation of micro-swimmers is based on aligning the swimmer orientation according to a reference path, thereby requiring both swimmer orientation and position to be known. Object-orientation is hard to track especially in in vivo scenarios which render orientation-based methods practically unfeasible. Here, we show that the kinematics for a confined swimmer can be linearized by assuming a low wobbling angle. This allows for a control law solely based on the swimmer position. The approach is demonstrated through experiments and two different numerical models: the first is based on the resistive force theory for a swimmer inside a swirling flow represented by a forced vortex and the second is a computational fluid dynamics model, which solves Stokes equations for a swimmer inside a circular channel. Helical pusher-mode trajectories are suppressed significantly for the straight path following problem. The error in real-life experiments remains comparable to those in the state-of-the-art methods.