Optimization and Modeling of Multimodal Active Debris Removal Using a Time-Expanded Network

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Tepper, Julia Anne
Ho, Koki
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This thesis develops a framework to optimize the concept of operations of an active debris removal (ADR) mission targeting variable sizes and types of space debris. Given the challenging and costly nature of active debris removal, it is desirable to minimize the required ∆V and propellant of the mission while maximizing the reward from debris removed to determine the most optimal sequence and subset of debris to remove. Potentially damaging debris ranges in size and mass from very small microdebris to much larger debris. Removal of these different types of debris involves different mission requirements. This thesis investigates the feasibility and optimality of removing both types of debris in one mission to maximize potential reward. The optimization framework to design a mission to combine removal of both of these types of debris consists of a trajectory model to simulate orbital maneuvers throughout the mission as well as a mathematical formulation constructed as a Mixed-Integer Linear Problem. Orbital maneuvers between debris pairs are modeled as high-thrust two-impulse maneuvers, and the minimum ∆V for each maneuver at each time step between each pair of debris is determined. Next, the dynamic traveling salesperson problem is formulated as a Mixed-Integer Linear Problem. Solving a traveling salesperson problem with variable costs due to the dynamic nature of space debris is simplified by the use of a time-expanded network. The Mixed-Integer Linear Problem is then iteratively solved to optimize the mission for dual objectives. Using this formulation, an optimal mission scenario with a subset of targeted debris can efficiently and accurately be computed from a large set of potential debris for removal. Several case studies demonstrate the efficacy of this approach, examining missions to stabilize the debris environment by removing at least five pieces of debris over one year.
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