Section: New Results

Necessary conditions for local controllability, motivated by the Two-link Magneto-elastic Micro-swimmer

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

After proving in [66] a local controllability for the 2-link magneto-elastic swimmer around its straight configuration and noting that this property is weaker than Small-Time Locally Controllable (STLC), we investigated “full” STLC for this system, and were able to show that, except for very specific values of the lengths and magnetizations, this system is not STLC. This is published in [9]. This lead us to necessary condition for STLC for more general classes of systems. This is part of Clément Moreau's doctoral research and a publication is under preparation, for classes of control-affine systems with two controls that are not micro-swimmer models, but stem from the observations in [9] and [66].