We introduce a distributed finite element algorithm that allows swarms of mobile robots to persistently monitor environmental quantities such as temperature or salinity. The robots deploy themselves into the environment, covering the domain and dividing it into nonoverlapping regions. Each robot estimates the environment over its own region using local measurements and communication with nearby robots. The algorithm ensures that each robot's estimate constitutes a piece of a global estimate that spans the entire domain, fuses the whole swarm's measurements, and accounts for the spatial correlation between measurement and estimation locations. By incorporating spatial correlation without requiring the transmission of measurements or measurement locations, the algorithm decouples its communication requirements from the spatial statistics of the environment and enables robots with fixed capabilities to monitor environments with different spatial correlation lengths. Analysis and simulation demonstrate that, as the number of robots increases, the memory and communication requirements of each individual robot decrease until reaching a minimum, after which the resolution of the environmental model increases. Additional robots, therefore, add computational resources to the swarm rather than introducing extra computational burdens.

中文翻译：

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使用有限元机器人进行分布式环境监测

我们引入了一种分布式有限元算法，该算法允许成群的移动机器人持续监测温度或盐度等环境量。机器人将自己部署到环境中，覆盖领域并将其划分为不重叠的区域。每个机器人使用本地测量和与附近机器人的通信来估计其自己区域的环境。该算法确保每个机器人的估计构成跨越整个域的全局估计的一部分，融合整个群体的测量，并说明测量和估计位置之间的空间相关性。通过在不需要传输测量或测量位置的情况下结合空间相关性，该算法将其通信需求与环境的空间统计数据分离，并使具有固定能力的机器人能够监控具有不同空间相关长度的环境。分析和仿真表明，随着机器人数量的增加，每个机器人的内存和通信需求减少，直到达到最小值，此后环境模型的分辨率增加。因此，额外的机器人为群增加了计算资源，而不是引入额外的计算负担。每个单独机器人的内存和通信需求减少，直到达到最小值，之后环境模型的分辨率增加。因此，额外的机器人为群增加了计算资源，而不是引入额外的计算负担。每个单独机器人的内存和通信需求减少，直到达到最小值，之后环境模型的分辨率增加。因此，额外的机器人为群增加了计算资源，而不是引入额外的计算负担。