标题： 群体中具有随机感知和动态的目标密度形成 显示英文标题

标题： Target-density formation in swarms with stochastic sensing and dynamics

摘要： 一个重要的目标是为群体研究创建预测、控制和设计群体的方法，这些方法通过涌现和稳定的模式形成来解决问题，而不需要持续干预，并且使用最少的参数和控制。 这样一个问题涉及群体通过局部感知、运动和相互作用在某个区域内共同产生所需的（目标）密度。 在此，我们采用统计物理的观点，开发并分析了一个模型，其中代理在联网的区域内进行随机行走，以减少群体密度与目标之间的误差，该误差基于群体代理对当前密度的局部、随机和不确定的测量。 通过结合平均场、小波动和有限数量分析，我们能够量化群体在感知不确定性、随机碰撞率、代理数量以及目标的空间变化的情况下，达到目标的接近程度和速度。 显示英文摘要

摘要： An important goal for swarming research is to create methods for predicting, controlling and designing swarms, which produce collective dynamics that solve a problem through emergent and stable pattern formation, without the need for constant intervention, and with a minimal number of parameters and controls. One such problem involves a swarm collectively producing a desired (target) density through local sensing, motion, and interactions in a domain. Here, we take a statistical physics perspective and develop and analyze a model wherein agents move in a stochastic walk over a networked domain, so as to reduce the error between the swarm density and the target, based on local, random, and uncertain measurements of the current density by the swarming agents. Using a combination of mean-field, small-fluctuation, and finite-number analysis, we are able to quantify how close and how fast a swarm comes to producing a target as a function of sensing uncertainty, stochastic collision rates, numbers of agents, and spatial variation of the target.