Comparison of optimal actuation patterns for flagellar magnetic micro-swimmers

Yacine El Alaoui-Faris (1, 2) , Jean-Baptiste Pomet (1) , Stéphane Régnier (2, 3) , Laetitia Giraldi (4)

1 McTAO - Mathematics for Control, Transport and Applications
2 ISIR - Institut des Systèmes Intelligents et de Robotique
3 Interactions Multi-échelles
4 CALISTO - Stochastic Approaches for Complex Flows and Environment

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.

Mots clés: Magnetic micro-swimmers; Soft Robotics; Optimal control; Low-Reynolds Swimmers

Domaines: Automatique / Robotique

Yacine El Alaoui-Faris, Jean-Baptiste Pomet, Stéphane Régnier, Laetitia Giraldi. Comparison of optimal actuation patterns for flagellar magnetic micro-swimmers. 21st IFAC World Congress, IFAC, Jul 2020, Berlin / Virtual, Germany. pp.9125-9130, ⟨10.1016/j.ifacol.2020.12.2152⟩. ⟨hal-02507327v2⟩