2D Magnetic Actuation and Localization of a Surface Milli-Roller in Low Reynolds Numbers

Magnetic actuation of minimally invasive medical tetherless devices holds great promise in several biomedical applications. However, there are still several challenges in noninvasive localization, both in terms of sensing detectable signals of these devices and estimating their states. In this work, a magnetic milli-roller is actuated in a viscous fluid under the influence of a rotating magnetic field. A Lyapunov-based nonlinear state observer is designed and implemented to estimate the position of the roller using a 2D array of Hall-effect sensors. We show that the local stability of the state observer yields convergence to one of the local equilibria, for pre-defined levels of sensor noise, initial conditions, and modeling errors. Performance is quantified using redundant measurements of the fields and we investigate the influence of the number of magnetic field measurements on the observability of the system. Open-loop actuation and state estimation are demonstrated and experimental results show that the localization of a 5 mm diameter roller along sinusoidal, circular and square trajectories achieve a steady-state mean absolute position error of 2.3 \,\mathrm{m}\mathrm{m}, 1.67 \,\mathrm{m}\mathrm{m} and 1.73 \,\mathrm{m}\mathrm{m}, respectively.