A report discusses the problem of controlling the maneuvers of multiple spacecraft flying in formation and, more specifically, making the entire formation rotate about a given axis and synchronizing the rotations of the individual spacecraft with the rotation of the formation. Such formation flying is contemplated for mission in which the spacecraft would serve as platforms for long-baseline-interferometer elements and the synchronized rotations would be needed for slewing of the interferometers. Starting from (1) a particle model of the dynamics of the spacecraft formation, (2) a rigid-body model of the spacecraft-attitude dynamics, and (3) an assumption that one spacecraft would serve as the reference for the positions and orientations of the other spacecraft, the report presents a mathematical derivation of control laws for formation flying in the absence of gravitation and disturbances. A simplified control law suitable for implementation is also derived. Results of a computer simulation for three spacecraft flying in a triangular formation are presented to show that the control laws are effective.

This work was done by Fred Y. Hadaegh and Kenneth Lau of Caltech and Paul K. C. Wang of the University of California for NASA’s Jet Propulsion Laboratory.