Problems in Distributed Sensing and Control

目前对分布式传感和控制的兴趣导致了图论思想在分析和综合各种期望的机器人团队和移动传感器群体行为(如蜂群、交会、达成共识)以及与分布式平均、搜索和救援、环境监测、安全等相关的各种传感和通信任务方面的应用迅速增加。虽然利用图论和系统理论的组合对这些问题的深入攻击已经进行了大约十年，但在未来几年可能会显著扩大。这方面的一个例子是，人们对一个名为结构可控性的旧概念重新产生了兴趣，并将其应用于涉及蜂拥而至的复杂社交网络和网络安全的新问题。另一个是人们对开发分布式计算程序的兴趣激增，这些程序用于解决基本的数值问题，如估计线性系统的参数，或求解可能是非线性的代数方程组。另一个是一些人最近的理论工作，重点是通过基于刚性的队形控制来协调移动机器人和移动传感器的网络。概括地说，这是我们建议工作的三个问题领域。该项目将通过至少两种不同的方式促进教学、培训和学习。首先，参与该项目的研究生将被要求参加并在技术会议上展示成果。其次，项目研究生将参与并参与一个关于这个主题的短期课程，我们设想在项目结束时组织和给予这个课程。在更多的技术术语中，该项目将在三个方面解决分布式传感和控制问题。首先，我们的任务是用图论的术语描述一个比目前正在追求的结构可控性概念要普遍得多的概念。第二，任务是开发分布式和异步算法来求解非线性函数方程组，包括在给定的自治代理网络上的仿缩，假设代理和时变网络之间的通信有限。第三个任务是探索各种算法，用于以分布式方式控制传感器和移动机器人的定向和无定向刚性编队。目标是解决对测量误差和代理之间的参数差异的鲁棒性问题，并试图找到一种方法来避免最近发现的无方向队形控制的基本鲁棒性问题。

Current interest in distributed sensing and control has led to a very rapid increase in the application of graph theoretic ideas to problems of analyzing and synthesizing a variety of desired robotic team and mobile sensor group behaviors such as swarming, rendezvousing, reaching a consensus, as well as well as a variety of sensing and communication tasks associated with distributed averaging, search and rescue, environmental monitoring, security, etc. While this in-depth assault on these problems using a combination of graph theory and system theory has been underway for about a decade, it is likely to significantly expand in the years to come. One example of this is the resurgence of interest in an old concept called structural controllability and its applications to new problems involving swarming, complex social networks and network security. Another is the explosion of interest in the development of distributed computational procedures for addressing basic numerical problems such as estimating parameters of a linear system, or solving a system of possibly nonlinear algebraic equations. Still another is the recent theoretical work by a number of individuals focused on the coordination of networks of mobile robots and mobile sensors by means of rigidity-based formation control. In broad terms these are the three problem areas within which we propose to work. This project will promoting teaching, training and learning in at least two different ways. First, graduate students involved in the project will be expected to attend and present there results at technical meetings. Second, project graduate students will contribute to and participate in a short course on the topic which we envision organizing and giving towards the end of the project. In more technical terms, this project will address distributed sensing and control on three fronts. First the task is to characterize in graph theoretic terms a significantly more general notion of structural controllability than the one currently being pursued. Second, task is to develop distributed and asynchronous algorithms for solving systems of nonlinear functional equations including para-contractions across a given network of autonomous agents assuming limited communication between agents and time-varying networks. The third task is to explore various algorithms for controlling both directed and undirected rigid formations of sensors and mobile robots in a distributed manner. The goal is to address the question of robustness to measurement errors and parameter discrepancies among agents and attempt to find a way to avoid the recently discovered fundamental robustness issue with undirected formation control.