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We propose an algorithm for creating stable, ordered, swarms of activerobotic agents arranged in any given pattern. The strategy involves suppressinga class of fluctuations known as "non-affine" displacements, viz. thoseinvolving non-linear deformations of a reference pattern, while all (or most)affine deformations are allowed. We show that this can be achieved usingprecisely calculated, fluctuating, thrust forces associated with a vanishingaverage power input. A surprising outcome of our study is that once thestructure of the swarm is maintained at steady state, the statistics of theunderlying flow field is determined solely from the statistics of the forcesneeded to stabilize the swarm.

Pattern stabilisation in swarms of programmable active matter: a probe for turbulence at large length scales