Controllability of a bent 3-link magnetic microswimmer

Laetitia Giraldi (1) , Pierre Lissy (2) , Clément Moreau (1) , Jean-Baptiste Pomet (1)

1 McTAO - Mathematics for Control, Transport and Applications
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

— In this paper, we focus on a variant of a 3-link magnetic microswimmer which consists of three rigid magnetized segments connected by two torsional springs. In particular, we assume that one of the springs is twisted so that the swimmer is not aligned at rest. By acting on it with an external magnetic field, the swimmer twists and moves through the surrounding fluid. By considering the external magnetic field as a control function, we state a local partial controllability result around the equilibrium states. Then, we propose a constructive method to find the magnetic field that allows the swimmer to move along a prescribed trajectory. Finally, we show numerical simulations in which the swimmer moves along a prescribed path.

Domaines: Optimisation et contrôle [math.OC]

Laetitia Giraldi, Pierre Lissy, Clément Moreau, Jean-Baptiste Pomet. Controllability of a bent 3-link magnetic microswimmer. 2016. ⟨hal-01390138⟩