Abstract
Controlling artificial devices that mimic the motion of real microorganisms, is attracting increasing interest, both from the mathematical point of view and applications. A model for a magnetically driven slender micro-swimmer, mimicking a sperm cell is presented, supported by two examples showing how to steer it. Using the well known Resistive Force Theory (RTF) approach to describe the hydrodynamic forces, the micro-swimmer can be described by a driftless affiine control system where the control is an external magnetic field. Moreover we discuss through at first an asymptotic analysis and them by numerical simulations how to realize different kind of paths.
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