This thesis contributes in two ways. First it describes a new framework for the systematic design of collective behaviors and solves a key stability issue under this design framework. In this thesis we apply this framework to solve three tasks in the swarm robotics field: connectivity maintenance, formation control and target tracking. Second, in the process of solving one problem, the connectivity maintenance task, we design a decentralized power iteration algorithm. Given any connected graph, this generic algorithm allows each agent to estimate its corresponding component of the Fiedler eigenvector, the eigenvector corresponding to the second smallest eigenvalue of the graph Laplacian~\cite{mohar91}.The Fiedler eigenvector and eigenvalue have proved to be useful in many areas, including Google's pagerank system, graph segmentation algorithms and connectivity maintenance in mobile sensor networks. Given a group of mobile agents, this thesis describes a framework for the systematic design of collective behaviors. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Steps of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. In addition, the performance of this design framework can be optimized by increasing the convergence speed of the estimator through tuning the communication weights. We apply this framework to three different problems: $(1)$ estimation and control of graph connectivity, $(2)$ controlling the moment statistics describing the location and shape of a swarm, and $(3)$ cooperative target localization. For the first task, we design a decentralized power iteration algorithm allowing each agent to estimate its component of the Fiedler eigenvector of the graph. For the last two tasks, we derive small-gain conditions which, if satisfied, guarantee that the system falls into a stable equilibrium set, even in the presence of a changing network topology and the addition and deletion of robots. We validate our approach through computer simulation and physical experiments.

Last modified

• 09/19/2018

Creator

• Peng Yang

DOI

• https://doi.org/10.21985/N2V445

Subject

• Mechanical Engineering

Keyword

• Mechanical Engineering

Date created

• 2008-11-07

Resource type

• Dissertation

Rights statement

• In Copyright