Section: New Results

Modelling and controllability of Magneto-elastic Micro-swimmers

Purcell magneto-elastic swimmer controlled by an external magnetic field

Participants : François Alouges [École Polytechnique] , Antonio Desimone [SISSA Trieste, Italy] , Laetitia Giraldi, Marta Zoppello [Univ. di Padova, Italy] .

We have studied the mechanism of propulsion of a Purcell swimmer whose segments are magnetized and react to an external magnetic field applied into the fluid. By an asymptotic analysis, we prove that it is possible to steer the swimmer along a chosen direction when the control functions are prescribed as an oscillating field. Moreover, there are obstructions that have to be overcome in order to get classical controllability result for this system. This is exposed in [7] (IFAC World Congress, Toulouse, July 2017).

Local Controllability of the Two-link Magneto-elastic Micro-swimmer

Participants : Laetitia Giraldi, Pierre Lissy [Univ. Paris Dauphine] , Clément Moreau, Jean-Baptiste Pomet.

For the smallest magneto-elastic micro-swimmer (2 links), we have been able to prove a strong local controllability result around its straight position of the swimmer. This is exposed in[6]. However, the latter result is weaker than the classical local controllability concept called STLC which means that a system could reach any position around its equilibrium with a small control (as small as the desired displacement of the system). Moreover, we prove in [5] that the 2-link magneto-elastic swimmer is indeed not STLC.