We propose an 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 “nonaffine” displacements, viz., those involving nonlinear deformations of a reference pattern, while all (or most) affine deformations are allowed. We show that this can be achieved using precisely calculated, fluctuating, thrust forces associated with a vanishing average power input. A surprising outcome of our study is that once the structure of the swarm is maintained at steady state, the statistics of the underlying flow field is determined solely from the statistics of the forces needed to stabilize the swarm.

中文翻译：

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可编程活性物质群中的模式稳定：大长度尺度湍流的探测器

我们提出了一种算法，用于创建以任何给定模式排列的稳定、有序、活跃的机器人代理群。该策略涉及抑制一类称为“非仿射”位移的波动，即。，那些涉及参考图案的非线性变形，而允许所有（或大部分）仿射变形。我们表明，这可以使用与消失的平均功率输入相关的精确计算的、波动的推力来实现。我们研究的一个令人惊讶的结果是，一旦群体的结构保持在稳定状态，基础流场的统计数据就完全取决于稳定群体所需的力的统计数据。