趋势形成与稀疏全局采样
Trend formation with sparse global sampling
- Tel Aviv University（特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出稀疏全局采样模型，证明少量随机采样即可驱动群体对齐，且采样越少加速有序化，并推导解析判据，实验验证于机器人集群。
AI中文摘要：
在没有中央控制器或密集全局通信的情况下实现全局协调，是生物群体和工程化集群共同面临的一个关键挑战。我们引入并分析了一个最小模型，在该模型中，有界区域内的自推进智能体周期性地将其运动方向重新定向到一小部分随机选择的同伴的质心，而不直接感知任何单个邻居的位置或朝向。我们表明，这种稀疏的非局部采样规则能够可靠地将初始无序的群体驱动到全局对齐的向列态，并且缩小采样子集——直至最少两个智能体——会加速而非阻碍有序化过程：由此产生的估计噪声，经过几何转向规则的过滤，本身就是对称性破缺的引擎。我们推导出一个解析判据，与模拟定量一致，该判据根据采样大小和采样频率预测这种有序化何时成功。我们在多达十五个差速驱动机器人的集群中实验验证了该机制。这些结果将稀疏随机采样确定为一种信息高效的集体协调途径，对理解动物群体和设计通信受限的机器人集群具有重要意义。
英文摘要：
Achieving global coordination without a central controller or dense global communication is a defining challenge for both biological collectives and engineered swarms. We introduce and analyze a minimal model in which self-propelled agents in a bounded domain periodically reorient their motions toward the centroid of a small, randomly chosen subset of their peers, with no direct sensing of any individual neighbor's position or heading. We show that this sparse, non-local sampling rule reliably drives an initially disordered population to a globally aligned, nematic state, and that shrinking the sampled subset -- down to the minimum of two agents -- accelerates ordering rather than impeding it: the resulting estimation noise, filtered through a geometric turning rule, is itself the engine of symmetry breaking. We derive an analytical criterion, in quantitative agreement with simulation, that predicts when this ordering succeeds as a function of the sampling size and sampling frequency. We confirm the mechanism experimentally in a swarm of up to fifteen differential-drive robots. These results identify sparse random sampling as an information-efficient route to collective coordination, with implications for understanding animal collectives and for designing communication-limited robotic swarms.
