We consider a system of self-propelled agents that move at constant speed
and control the curvature of their trajectories. This type of control
provides a good fit to fish or bird trajectories. Trajectory control aims to
attract the agents to one-another but is subject to noise. We aim at
deriving kinetic and hydrodynamic models under convenient scaling
assumptions. Because the particle velocities lie on a sphere, the model is
naturally posed on the tangent bundle to the sphere which is acted upon by
the orthogonal group. We derive the particle and kinetic models in this
geometrical setting and use equivariance by the orthogonal group to derive
expressions of the collision invariants and to ultimately formulate the
associated hydrodynamic model. This is a joint work with A. Diez (Kyoto) and
A. Frouvelle (Paris-Dauphine).
Jérémy Heleine, David Lafontaine
