Section: New Results

Sub-Riemannian Geometry and Micro-Swimmers and Extensions to Control in Hydrodynamics

Participants : Bernard Bonnard, Piernicola Bettiol [Univ. Bretagne Ouest] , Alice Nolot [Univ. de Bourgogne Franche Conté] , Jérémy Rouot.

We pursue our study concerning the 1-copepod swimmer using techniques from SR-geometry and numerical simulations, see [40] for previously obtained results. Following Takagi model, a 2d-swimmer is currently analyzed whose aim is to perform a 2d-motion where the copepod swimmer can change its orientation. Preliminary study concerning this problem was analysed during the internship of A. Lenc in relation with the motion planning of a car. Under the impulse of O. Cots and B. Wembe an extension of the project is the developments of the geometric optimal control techniques in hydrodynamics. In particular we studied a Zermelo navigation problem in a current with a vortex [25] (submitted to ESAIM-COCV). An interesting and new phenomenon detected in optimal control is the existence for the geodesic flow of a Reeb foliation.