Swarm robotics promises adaptability to unknown situations and robustness against failures. However, it still struggles with global tasks that require understanding the broader context in which the robots operate, such as identifying the shape of the arena in which the robots are embedded. Biological swarms, such as shoals of fish, flocks of birds, and colonies of insects, routinely solve global geometrical problems through the diffusion of local cues. This paradigm can be explicitly described by mathematical models that could be directly computed and exploited by a robotic swarm. Diffusion over a domain is mathematically encapsulated by the Laplacian, a linear operator that measures the local curvature of a function. Crucially the geometry of a domain can generally be reconstructed from the eigenspectrum of its Laplacian. Here we introduce spectral swarm robotics where robots diffuse information to their neighbors to emulate the Laplacian operator - enabling them to "hear" the spectrum of their arena. We reveal a universal scaling that links the optimal number of robots (a global parameter) with their optimal radius of interaction (a local parameter). We validate experimentally spectral swarm robotics under challenging conditions with the one-shot classification of arena shapes using a sparse swarm of Kilobots. Spectral methods can assist with challenging tasks where robots need to build an emergent consensus on their environment, such as adaptation to unknown terrains, division of labor, or quorum sensing. Spectral methods may extend beyond robotics to analyze and coordinate swarms of agents of various natures, such as traffic or crowds, and to better understand the long-range dynamics of natural systems emerging from short-range interactions.

翻译：群体机器人技术承诺能够适应未知情境并对故障具有鲁棒性。然而，它在处理需要理解机器人所处更广泛背景的全局任务时仍面临挑战，例如识别机器人所在竞技场的形状。生物群体，如鱼群、鸟群和昆虫群落，通常通过局部线索的扩散来解决全局几何问题。这一范式可以通过数学模型明确描述，并可直接被机器人群体计算和利用。在某个域上的扩散在数学上由拉普拉斯算子（Laplacian）描述，这是一个测量函数局部曲率的线性算子。关键在于，一个域的几何形状通常可以从其拉普拉斯算子的特征谱重建。在此，我们引入了频谱群体机器人技术，其中机器人向其邻居扩散信息以模拟拉普拉斯算子——从而使它们能够“听到”其竞技场的频谱。我们揭示了一个普适的缩放规律，将最优机器人数量（全局参数）与其最优交互半径（局部参数）联系起来。我们通过使用稀疏的Kilobot群体对竞技场形状进行一次性分类，在具有挑战性的条件下实验验证了频谱群体机器人技术。频谱方法可以辅助机器人需要对其环境建立涌现共识的复杂任务，例如适应未知地形、分工或群体感应。频谱方法的应用可能超越机器人领域，用于分析和协调各种性质的智能体群体，如交通或人群，并更好地理解由短程相互作用涌现的自然系统长程动力学。