Comparison of optimal actuation patterns for flagellar magnetic micro-swimmers

Abstract In this article, we present a simplified model of a flagellar micro-swimmer actuated by external magnetic fields that is based on shape discretization and an approximation of the hydrodynamical forces. We numerically solve the optimal control problem of finding the actuating magnetic fields that maximizes its horizontal propulsion speed over a fixed time under different constraints on the magnetic field amplitudes and compare the optimal solutions. All the simulated magnetic fields out-perform the standard sinusoidal actuation method that is prevalent in the literature and in experiments. Moreover, non-planar constraints on the control leads to novel optimal trajectories for flagellar low-Reynolds swimmers and perform significantly better than planar actuation.