Problems in Distributed Sensing and Control

Yale University, New Haven CT

Investigators

Abstract

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.