A report presents the mathematical basis of a method of controlling multiple spacecraft flying in formation, subject to control constraints. The spacecraft are assumed to be equipped with relative-position-sensing, relative-velocity-sensing, and communication infrastructure, and with maneuvering actuators. The method involves a leader-following control scheme. A graph is used to represent the hierarchy of, and the data dependencies among, the leading and following spacecraft. Graph-theoretic concepts are shown to play a vital role in determining the basic properties of the leader-following control architecture; hence, changes in the hierarchy (represented by changes in the graph) translate directly to the required changes in control.
This work was done by Fred Hadaegh and Mehran Mesbahi of Caltech for NASA's Jet Propulsion Laboratory. To obtain a copy of the report, "Formation Flying Control of Multiple Spacecraft via Graphs, Matrix Inequalities, and Switching," access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp under the Mechanics category.