Design and optimal control of multi-spacecraft interferometric imaging systems.

Abstract

The objective of the proposed NASA Origins mission, Planet Imager, is the high-resolution imaging of exo-solar planets and similar high resolution astronomical imaging applications. The imaging is to be accomplished through the design of multi-spacecraft interferometric imaging systems (MSIIS). In this dissertation, we study the design of MSIIS. Assuming that the ultimate goal of imaging is the correct classification of the formed images, we formulate the design problem as minimization of some resource utilization of the system subject to the constraint that the probability of misclassification of any given image is below a pre-specified level. We model the process of image formation in an MSIIS and show that the Modulation Transfer function of and the noise corrupting the synthesized optical instrument are dependent on the trajectories of the constituent spacecraft. Assuming that the final goal of imaging is the correct classification of the formed image based on a given feature (a real valued function of the image variable), and a threshold on the feature, we find conditions on the noise corrupting the measurements such that the probability of misclassification is below some pre-specified level. These conditions translate into constraints on the trajectories of the constituent spacecraft. Thus, the design problem reduces to minimizing some resource utilization of the system, while satisfying the constraints placed on the system by the imaging requirements. We study the problem of designing minimum time maneuvers for MSIIS. We transform the time minimization problem into a painting problem. The painting problem involves painting a large disk with smaller paintbrushes (coverage disks). We show that spirals form the dominant set for the solution to the painting problem. We frame the time minimization in the subspace of spirals and obtain a bilinear program, the double pantograph problem, in the design parameters of the spiral, the spiraling rate and the angular rate. We show that the solution of this problem is given by the solution to two associated linear programs. We illustrate our results through a simulation where the banded appearance of a fictitious exo-solar planet at a distance of 8 parsecs is detected.