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Formation design of distributed telescopes in earth orbit with application to high-contrast imaging

This dissertation presents a new formation design that enables large distributed telescopes that must maintain alignment with inertial targets to be deployed in earth orbit. While previous approaches are infeasible for inter-spacecraft separations larger than a few hundred meters due to the large relative accelerations in earth orbit, the design proposed in this work allows separations within an order of magnitude of the orbit radius. This design is based on a two-phase operations concept that includes observation and reconfiguration phases. During observation phases, one spacecraft uses a quasi-continuous control system to ensure that the formation is aligned with the target. During this phase, control is only applied in the plane perpendicular to the line-of-sight to save propellant, allowing the separation to freely drift within a user-specified control window. During reconfiguration phases, one of the spacecraft performs a sequence of maneuvers that ensure that the formation is aligned with the target at the start of the next observation phase. Optimal absolute and relative orbits that minimize the delta-v cost of observation and reconfiguration phases are derived in closed-form including the effects of perturbations. To enable accurate control of the formation, a new methodology for deriving state transition matrices for spacecraft relative motion in perturbed orbits is proposed. This methodology is used to derive the first state transition matrices that capture the combined effects of earth oblateness and differential drag in orbits of arbitrary eccentricity for several state definitions based on relative orbital elements. Additionally, this dissertation presents a new real-time algorithm for globally optimal impulsive control of linear time-variant systems. A novel feature of this algorithm is accommodation of time-varying, norm-like cost functions, which enables inclusion of constraints such as asymmetric thruster configurations and time-varying attitude modes on spacecraft in the maneuver planning problem. These contributions are combined in the development of a stochastic model predictive control architecture that enables accurate and efficient control of the formation in the presence of sensing and actuation errors. The performance and value of the proposed formation design are demonstrated through analysis of a small-scale starshade formation deployed in earth orbit. Specifically, it is shown that a family of optical designs consisting of a small starshade and telescope separated by several hundred kilometers can provide sufficient contrast at inner working angles of hundreds of milliarcseconds to enable direct imaging of scientifically interesting targets and validation of the starshade optical performance. To further demonstrate the feasibility of a small starshade formation, high-fidelity simulations are conducted for two example mission profiles. In the first mission, the formation is deployed in a geosynchronous transfer orbit and images a single target for tens of hours to validate the optical performance of the starshade and image a bright exoplanet. In the second mission, the formation images a set of nearby sun-like stars to characterize the density of the surrounding debris disks. These missions are simulated using a navigation and control architecture with errors consistent with the performance of current commercially available sensors and actuators. The results of these simulations agree with the predicted behaviors of the orbit design and demonstrate that the delta-v costs of these mission profiles are within the capabilities of current propulsion systems for small satellites. Overall, the proposed formation design can be used to enable or improve the scientific return of a broad class of distributed telescope missions.