用谱群机器人听取竞技场的形状
Hearing the shape of an arena with spectral swarm robotics
AI总结：
引入谱群机器人技术，通过机器人扩散信息模拟拉普拉斯算子以“听到”竞技场谱并识别其形状，揭示了最优机器人数量与交互半径的缩放规律，并用 Kilobots 实验验证。
摘要：
群机器人技术有望适应未知情况并具备抵抗故障的鲁棒性。然而，它在处理需要理解机器人所处更广泛环境的全局任务时仍然面临困难，例如识别机器人所在的竞技场形状。生物群（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，并由机器人群体直接计算和利用。在一个域上的扩散在数学上由 Laplacian（拉普拉斯算子）封装，这是一种测量函数局部曲率的线性算子。关键的是，域的几何形状通常可以从其 Laplacian 的特征谱中重建。在此，我们引入了谱群机器人技术，其中机器人将信息扩散给邻居以模拟 Laplacian 算子——使它们能够“听到”其竞技场的谱。我们揭示了一个普遍的缩放规律，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。我们在具有挑战性的条件下，通过使用稀疏的 Kilobots 群对竞技场形状进行一次性分类，在实验上验证了谱群机器人技术。谱方法可以辅助机器人需要就其环境建立涌现共识的挑战性任务，例如适应未知地形、劳动分工或群体感应。谱方法可能超越机器人领域，扩展到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交互产生的自然系统的长程动力学。
英文摘要：
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.
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