The copepod model is a simplification of the 3-link Purcell swimmer and is relevant to analyze more complex micro-swimmers. The mathematical model is validated by observations performed by a team from Hawaii, showing the agreement between the predicted and observed motions. Sub-Riemannian geometry will be introduced, assuming that displacements are minimizing the expanded mechanical energy of the micro-swimmer. The objective is to maximize the efficiency of a stroke (the ratio between the displacement produced by a stroke and its length). Using the Maximum Principle in the framework of Sub-Riemannian geometry, this leads to analyze family of periodic controls producing strokes to determine the most efficient one. Finally a robotic copepod is presented whose aim is to validate the computations and very preliminary results are given.

TBA