Trajectory Generation for Millimeter Scale Ferromagnetic Swimmers: Theory and Experiments

Microrobots have the potential to impact many areas such as microsurgery, micromanipulation and minimally invasive sensing. Due to their small size, microrobots swim in a regime that is governed by low Reynolds number hydrodynamics. In this paper, we consider small scale artificial swimmers that are fabricated using ferromagnetic filaments and locomote in response to time varying external magnetic fields. We motivate the design of previously proposed control laws using tools from geometric mechanics and also demonstrate how new control laws can be synthesized to generate net translation in such swimmers. We further describe how to modify these control inputs to make the swimmers track rich trajectories in the workspace by investigating stability properties of their limit cycles in the orientation angles phase space. Following a systematic design optimization, we develop a principled approach to encode internal magnetization distributions in millimeter scale ferromagnetic filaments. We verify and demonstrate this procedure experimentally and finally show translation, trajectory tracking and turning in place locomotion in these optimal swimmers using a Helmholtz coils setup.