Active stabilisation of patterned robotic swarms

Flocks of birds naturally order as a result of active forces which counteract destabilisation by random noise. Ordered patterns of drones or robotic agents are useful for many purposes such as surveying unknown territory, taking measurements of scientifically or economically important quantities over a large area, drone shows etc. Disruption of this pattern may occur due to many factors for e.g. atmospheric or ocean turbulence. Stabilising any given pattern in such a swarm is energy expensive and requires extensive computation and communication overheads. We propose an algorithm where one can achieve this is an energy efficient way. The strategy involves suppressing a class of fluctuations viz. non-affine displacements away from the given reference pattern while allowing affine deformations such as translations and rotations. The agents are not forced to sense, difficult to measure, environmental parameters such as local velocity of air or water in order to stabilise the swarm. Additionally, we show that by maintaining the structure/pattern of robotic swarms the statistics of the underlying flow field can be determined solely from "non-affine" forces. As the knowledge of these forces is a priori known, no extra measurement on the turbulent field is needed.