  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.
