Abstract
In this article, we present a simplified model of a flagellar magnetic micro-swimmer based on shape discretization and the simplification of the hydrodynamical interactions. We numerically solve the optimal control problem of finding the actuating magnetic fields that maximizes its horizontal propulsion speed over a fixed time. Depending on the chosen constraints on the control, the optimal trajectories of the swimmer can be planar or three-dimensional. Simulations show the periodicity of the optimal magnetic fields and the shape of the swimmer under optimal actuation. All the simulated magnetic fields out-perform the standard sinusoidal actuation method that is prevalent in the litterature and in experiments. Moreover, the non-planar actuation patterns leads to novel trajectories for flagellar low-Reynolds swimmers and perform significantly better than planar actuation.
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