Information Flow and Cooperative Control of VehicleFormations

J. Alex Fax, Control and Dynamical Systems, Thesis Defense, Caltech

Control of vehicle formations has emerged as a topic of significant interest to the research community. Examples of vehicle formations include satellite clusters, mobile robotics, and UAV formations. Typically, vehicles in a formation are decoupled dynamically, but are asked to perform a joint task. What enables them to perform the task is the flow of information between vehicles. We will distinguish between two types of information flow: sensed information, meaning the ability of a single vehicle to sense some information (e.g. relative position) about another vehicle in a way which involves no action on the part of the sensed vehicle, and transmitted information , which requires activity on the part of both vehicles. These information flow networks are generally incomplete (vehicles cannot all sense/transmit to each other) and are subject to change due to component failure and external effects.

In this talk, we merge tools from control theory and graph theory to model the information flow networks and their effects on formation stability and performance. The information flow is modeled as a directed graph, in which each vehicle is a node and each arc represents flow of information. For the case where only sensed information is available (and thus control is decentralized), the Laplacian matrix of the graph emerges as the object that is relevant from a controls perspective. Specifically, we derive a Nyquist-like criterion for formation stability in which the Nyquist plot must avoid encircling the negative inverse of the eigenvalues of the Laplacian. The Laplacian eigenvalues can in turn be related to structural properties of the network, enabling us to make qualitative statements about desirable properties of the sensed flow. These results suggest a paradigm for information flow design, in which the vehicles jointly realize a virtual dynamical system which uses the sensed information as an input and which converges to average properties of the formation. The transmitted information, which can be thought of as a decentralized virtual leader computation, can be designed to decouple stability of the information flow and local vehicle stability. This approach enjoys significant robustness to changes in the underlying graph. It also generates more direct vehicle trajectories and has good disturbance rejection properties.