Optimal Maneuvers for Distributed Aperture Imaging Systems

Abstract

Interest in space-borne, distributed multi-aperture interferometric systems is driven by a need for continuously sustained imaging with high resolution. Amplitude interferometry systems measure the Fourier components of the image corresponding to the wave vectors (locations in the so-called u-v plane) that are proportional to the relative positions of the apertures. Imaging to specified resolution demands measurement of the Fourier components with adequate signal-to-noise ratio over the interior of a disk in the u-v plane (the resolution disk). In this paper we concentrate on the case in which interferometric measurements are made while the apertures are changing their relative positions. This work discusses heuristic maneuvers and strategies for a system of two space-borne telescopes to cover the frequency plane while optimizing a cost function that includes both a measure of image quality and propulsive effort.

The current study is motivated by previous research in which the optimization problem was formulated and the first-order necessary conditions (FONC) derived. The earlier work obtained short time horizon solutions to the FONC for various simple situations, but the complexity of the integro-differential equations for optimal maneuvering have heretofore prevented solution for an optimal maneuver for the entirety of the imaging process.

In place of a direct attack on the FONC, the present work investigates various heuristic approaches to minimizing the cost function in the discretized state and discretized time domains in a hexagonal coordinate system. Using three classes of coverage rules, experimentation with a variety of maneuver strategies involving two apertures has led to a number of time-optimal or fuel-optimal solutions based on the initial conditions of the spacecraft. This thesis shows that an optimal maneuver can be determined from the starting positions of the spacecraft and that a self-spiral class of motion seems to be the most beneficial for long term strategies. Future work may focus on strategies for interferometric systems with more than two apertures and with a finer mesh of the hexagonal coordinate system.