Modeling, Optimization, and Validation of the In-Space Facility Location Problem
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Shimane, Yuri
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Abstract
The last decade has seen an unprecedented level of new space activities, including in-space servicing, active debris removal, satellite mega constellations, in-situ monitoring of resident space objects, and lunar payload delivery services. Many of these activities require an in-space infrastructure in which multiple assets must be coordinated to fulfill their collective purpose. For terrestrial and in-space applications alike, one of the most fundamental and primary considerations in infrastructure design is the optimal placement and allocation of assets to demands.
This thesis is centered on in-space facility location problems (FLPs). The FLP provides a general framework to consider the placement and allocation of in-space assets for various applications, ranging from in-space servicing to cislunar space situational awareness. In-space FLPs require considerations of the underlying orbital mechanics and the associated nonlinear, potentially time-varying performance metrics. This thesis presents general considerations to determine whether a static or a time-expanded FLP formulation is appropriate for the application at hand; both a static and a time-expanded in-space problem are treated. With the time-expanded FLP, where the problem dimension becomes particularly large due to the time dependency of performance metrics and, consequently, of the allocation decisions, a customized Lagrangian relaxation algorithm together with a set of specialized heuristics is proposed. Overall, the in-space FLP formulations enable decision-makers to explore the variation of the optimal placement and allocation of assets to uncertain infrastructure parameters such as the frequency of demand or hardware performance.
In the context of cislunar infrastructures, libration point orbits (LPOs) provide relatively stable and geometrically diverse orbits for assets to be located. Motivated by the significantly lower number of existing missions in cislunar libration point orbits (LPOs), this thesis also provides orbital validation of LPOs in a high-fidelity ephemeris model (HFEM). The validation process consists of two steps: first, the nominal ballistic and quasi-ballistic design problem is considered through an optimal control approach. Then, station-keeping along the designed baseline in the presence of realistic uncertainties and operational constraints is studied. A targeting model predictive control scheme, suitable for both ballistic and quasi-ballistic baselines, is devised and demonstrated to provide satisfactory station-keeping performance, both in terms of cumulative cost and tracking deviation, over extended durations.
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Date
2025-07-28
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Text
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Dissertation