Monday, April 08, 2024 08:00AM

Ph.D. Defense


Matthew Gilmartin

(Advisor: Prof. Dimitri N. Mavris)




Uncertainty-Based Methodology for the Development of Space Domain Awareness Architectures in Three-Body Regimes


Thursday, April 8th 

8:00 a.m.
Collaborative Visualization Environment (CoVE)
Weber Space Science and Technology Building (SST II)






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 gaps in existing design methods, exposed by the transition to the cislunar regime, that impede the ability of designers to explore the design space and perform many-query analyses like optimization. A new uncertainty-based methodology was then proposed to address these gaps and enhance design space exploration.



Firstly, 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 improve on the run time required to evaluate shooting methods, but compared less favorably to propagation alone.



Second, reliance of most tracking filters on Gaussian distributions creates convergence issues in non-linear domains such as the cislunar regime. This creates a need to characterize the realism of Gaussian uncertainty approximations of non-Gaussian uncertainty distributions. 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 on 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.



Third, full-order cislunar SDA simulations suffer from exponential increases in computational cost as the number and diversity of systems in an SDA system increases. As a result, the computational cost of computing the detailed uncertainty produced by an SDA architecture is generally intractable in a many-query analysis context. A method wherein a reduced order model is developed to estimate the rate of information gain of information gain for individual sensor systems which is then aggregated for the overall architecture. Once again an experiments was performed to investigate the efficacy of the proposed method in comparison to the existing methods. 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 accuracy.



Finally, each of the developed modeling approaches were integrated into a unified approach to evaluate SDA architectures. A demonstration experiment was proposed, wherein the proposed uncertainty-based methodology was compared to a state-of-the-art methodology using equivalent full-order analyses. The experiment was broken into two phases, first both frameworks were used to evaluate the same architecture, next the uncertainty-based methodology was used to evaluate a simple optimization problem. The first phase of this analysis found the 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, evaluating over 82,000 cases in a total of 1.6 days. A short design space exploration was carried out 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 10 years to evaluate the same number of cases using the same hardware. For this reason, the uncertainty-based methodology was deemed to be a significant improvement over the state-of-the-art methodologies.



·         Prof. Dimitri Mavris – School of Aerospace Engineering (advisor)

·         Prof. John Christian – School of Aerospace Engineering

·         Prof. Brian Gunter – School of Mechanical Engineering

·         Dr. Greg Badura – Research Scientist, Georgia Tech Research Institute

·         Dr. Alicia Sudol – Research Engineer, Lockheed Martin