Collisionless drone swarm dynamics through optical flow based control using general communication graphs

In this article, we address the problem of collision avoidance in optical flow driven drone swarms for small-enough drones with an underlying communication graph being not necessarily complete. To this end, we first recall how such a control translates into a singular Cucker–Smale model, for which global results of absence of collision are known only for finite time. Using this formalism, we hereby prove the existence of a security distance, i.e., a uniform-in-time minimal distance between all agents, which depends on the initial conditions and different parameters of the fleet. We show that this result remains valid for a wider class of settings than optical flow and further discuss whether this uniform bound still holds (or not) for the singular Cucker–Smale model with additional control terms, such as target following. Numerical experiments are provided for all considered models to illustrate our theoretical result.