Uncertainty-Based Methodology for the Development of Space Domain Awareness Architectures in Three-Body Regimes
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Gilmartin, Matthew Lane
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Abstract
The past decade has seen a massive growth in interest in lunar space exploration. An increase in global competition has led a growing number of countries and non-governmental organizations towards lunar space exploration as a means to demonstrate their industrial and technological capabilities. This increase in cislunar space activity and resulting increase congestion and conjunction events poses a significant safety impact to spacecraft on or around the moon. This risk was demonstrated on October 18th 2021 when India’s Chandrayaan 2 orbiter was forced to maneuver to avoid a collision with NASA’s Lunar Reconnaissance Orbiter. In order to mitigate the safety impacts of increased congestion, enhanced space traffic management capabilities are needed in the cislunar regime. One foundational component of space traffic management is space domain awareness (SDA). Current SDA infrastructure, a network of earth-based and space-based sensors, was designed to track objects in near-earth orbits, and is not suitable for tracking objects in distant, non-Keplerian cislunar orbits. As a result, new infrastructure is needed to fill this capability gap.
The cislunar regime presents a number of challenges and constraints that complicate the SDA architecture design space. Unlike the near-earth regime, cislunar space is a three-body environment, violating many of the simplifying assumptions and models that are used in the near-earth domain. Furthermore, instability in cislunar dynamics means that state uncertainty plays a much more dominant role in system performance.
This research identified three technology gaps exposed by the transition to the cislunar regime, that impede the ability of designers to explore the design space and perform many-query analyses, such as design optimization. A new uncertainty-based methodology was then proposed to both address these gaps and enhance design space exploration.
The first technology gap identified was a reliance on three-body dynamics violate analytic two-body models of spacecraft motion, meaning that cislunar trajectories must be numerically integrated at much greater computational cost. A method was proposed that combines surrogate modeling techniques with and orbit family approach to develop an analytic parametric model of spacecraft motion. An experiment was carried out in order to interrogate the efficacy of this approach. Multiple surrogate models were generated using the approach, and each was compared to the state-of-the-art numerical integration approach. The surrogate modeling approach was found to greatly reduce the computational cost required to determine the initial state of an arbitrary periodic cislunar trajectory, while maintaining comparable accuracy to existing full-order methods. Of the surrogate model formulations tested, the interpolation methods were found to have the best combination of accuracy and speed for the proposed application.
The second technology gap identified was a reliance on Gaussian distributions in most tracking filter implementations. In non-linear domains such as the cislunar regime Gaussian distributions may deviate from a Gaussian shape when propagated through the system's non-linear dynamics. This creates convergence issues that limit the robustness of tracking schemes that rely on Gaussian characterizations of uncertainty. This in turn creates a need to characterize the realism of Gaussian uncertainty approximations of potentially non-Gaussian uncertainty distributions. The characterization of uncertainty realism was identified to be a computationally intensive process, limiting the breadth of potential design space exploration. To ameliorate this issue a surrogate modeling process was proposed for the development of models to characterize the realism of uncertainty estimates produced by tracking filters. An experiment was executed to evaluate the efficacy of this approach. The surrogate modeling process was found to greatly improve the computational cost of the full-order analysis. While the surrogate models were found to have non-negligible errors, these errors were on the same order of magnitude as the variability of the full-order model. Of the models tested, the model based on boosted decision trees was found to have the best balance of speed and accuracy. This massive increase in computational efficiency enables designers to evaluate much larger volumes of design cases using the same hardware.
The third identified technology gap was the exponential increases in the computational cost required to evaluate tracking uncertainty using full-order cislunar SDA simulations, as the number and diversity of systems in an SDA system increases. As a result of this ballooning computational cost, detailed uncertainty quantification can rapidly become intractable in a many-query analysis context, limiting the scope of design space exploration and uncertainty quantification. A surrogate modeling method was proposed to provide a volumetric assessment of tracking performance at reduce the computational cost compared to existing methods. As part of this proposed approach, changes in tracking uncertainty were evaluated with respect to the search volume. Changes in uncertainty were evaluated using a novel equivalent radius metric to estimate the rate of information gain of information gain for individual sensor systems which is then aggregated for the overall architecture. As part of this approach, field surrogates and reduced order models were investigated as potential techniques to improve the computational cost and quality of the generated surrogate models. An experiment was performed to investigate the efficacy of the proposed method in comparison to the existing methods. The generated surrogate models were found to significantly reduce the computational cost of the tracking analysis. Furthermore, this experiment found scalar surrogate models to provide the most accurate modeling of the full-order models. The field surrogates generally under-performed their scalar counterparts in terms of goodness-of-fit. Of the models tested, the scalar boosted decision tree model was found to have the best balance of speed and accuracy. In practice, this model offered was able to reduce the computational cost of evaluating SDA architecture tracking performance by several orders of magnitude, enabling designers to increase the breadth of design space exploration by similar orders of magnitude.
Finally, each of the developed modeling approaches were integrated into a unified methodology, named VENATOR, to evaluate \gls{SDA} architectures. A demonstration experiment was proposed, wherein the proposed VENATOR uncertainty-based methodology was compared to a state-of-the-art methodology using equivalent full-order analyses. The experiment was broken into two phases. In the first phase, both frameworks were used to evaluate the same architecture. Next, in the second phase, the VENATOR uncertainty-based methodology was used to evaluate a simple optimization problem. The first phase of this analysis found the VENATOR uncertainty-based methodology to offer an improvement in computational cost of over three orders of magnitude. During the second phase, a simple optimization was run using the VENATOR uncertainty-based methodology, evaluating over 82,000 cases in a total of 1.6 days. A short design space exploration was carried out, identifying the Pareto front of non-dominated cases, to demonstrate the utility of this approach. Using the run time of the state-of-the-art system when evaluating a single architecture, it was estimated that using this reference methodology would have taken over 14 years to evaluate the same number of cases using the same hardware. This massive increase in computational efficiency allows designers to greatly increase the breadth of design space exploration, enabling them to examine far larger case loads, reducing design risk and increasing design knowledge. For this reason, the uncertainty-based methodology was deemed to be a significant improvement over the state-of-the-art methodologies.
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Date
2024-04-29
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Dissertation