Dynamic Visibility and Inverse Source Problems in Unknown Environments with Complicated Topology.

这一建议包含一个研究计划，系统地涵盖了一种新的震源发现问题，包括动态可见度、泊松方程、热方程和在复杂的非单连通区域中提出的波动方程。这些问题是由机器人路径规划应用所驱动的。假设数据的稀疏和顺序测量，PI和合作者提出了新的机器人路径算法，沿着该算法可以添加新的测量，以便有效地确定可信的源位置并到达特定的有利位置，使得可信的源位置处于视觉监视之下。PI进一步研究了通过机器人路径的可见性来部分获知区域中的障碍物的情况，考虑到被送到未知环境中的机器人应该发现信号源的位置并高效地将其放置在其视线下的情况。未知环境包含不可穿透的固体障碍物，应沿机器人的路径避开。在这种环境中，假设信号的特性，例如信号强度，满足某些数学方程。机器人从两个不同的传感器收集测量数据：一个距离传感器给出机器人到周围障碍物的距离，另一个传感器测量从尚未定位的信号源发出的信号强度。虽然测量可以在任何地方进行，但PI和合作者感兴趣的是让机器人用它的传感器进行很少的测量。这一考虑与有效的监视和反恐应用特别相关。目标是设计一种健壮的算法，确定机器人应该如何在环境中导航，以及它应该沿着路径的哪里进行测量，以便能够有效地实现发现信号源和监视信号源的目标。

This proposal contains a research program that systematically covers a novel source discovery problems involving dynamic visibility, the Poisson equation, the heat equation, and the wave equations posed in complicated, non-simply connected domains. These problems are motivated by robotic path planning applications. Assuming sparse and sequential measurements of data, the PI and collaborators propose new robotic path algorithms along which new measurements can be added in order to efficiently determine plausible source locations and to reach particular vantage points such that the plausible source locations are under visual surveillance. The PI further studies situations in which obstacles in the domains are partially known through the visibility along the robotic path.Consider the situation in which a robot, sent into an unknown environment, is supposed to discover the location of a signal source and place it under its line-of-sight in an efficient manner. The unknown environment contains non-penetrable solid obstacles and should be avoided along the robot's path. In this environment, the properties of the signal, such as the signal strength, are assumed to satisfy certain mathematical equations. The robot gathers measurements from two different sensors: a range sensor that gives distance from the robot to the surrounding obstacles, and a sensor that measures the signal strength that is being emitted from the yet-to-be-located source. While measurements can be taken anywhere, the PI and the collaborators are interested in having the robot take very few measurements with its sensors. This consideration is particularly relevant to efficient surveillance and anti-terrorism applications. The goal is to design an robust algorithm that determines how the robot should navigate through the environment and where along its path it should take measurements so that the ob jective of discovering signal sources and their surveillance can be achieved efficiently.