Pattern stabilisation in programmable active matter

Ordered patterns of drones or robotic agents are useful for many purposes such as surveying unknown territory, taking measurements of scientifically important quantities over a large area. Unlike birds, which naturally organise themselves to counteract destabilisation due to a turbulent environment, stabilising a patterned swarm of drones is energetically expensive and requires extensive computation and communication overheads. We propose an energy-efficient algorithm for creating stable, ordered, swarms of active robotic agents arranged in any given pattern. The strategy involves suppressing a class of fluctuations known as “non-affine” displacements, viz. those involving non-linear deformations of a reference pattern while allowing affine deformations. This is achieved using precisely calculated, fluctuating, thrust forces associated with vanishing average power input. A surprising outcome of our study is that once the shape of the swarm is maintained at a steady-state, the statistics of the underlying flow field is determined solely from that of the a-priori known forces needed to stabilize the swarm. Therefore, such techniques will be useful in studying the turbulent flow where direct measurement of flow velocities is difficult.