After graduating with my BS in Aeronautical and Astronautical Engineering from Purdue in May 2016, I entered grad school as a member of Professor Jim Longuski’s Advanced Astrodynamics Concepts research group at Purdue. I completed my non-thesis MS in Aeronautics and Astronautics in May 2017, and finally I graduated with my PhD in May 2022. You can find my dissertation here, and the GitHub repository for much of the code that I developed here.

The main focus of my graduate studies was to investigate how machine learning techniques could compare to existing numerical optimization techniques for spacecraft trajectory design, particularly with applications to the missed thrust problem for low-thrust spacecraft. Ultimately, I found using a neural network could provide high quality initial guesses for a numerical optimizer to quickly find the best solution, but I would be cautious trying to use a neural network without additional oversight and error checking.

As I started out with my research, I became interested in machine learning and wanted to see if I could incorporate that into my work, since at the time there was very little research that applied machine learning techniques to spacecraft trajectory problems. I also came across the missed-thrust problem, which requires a tremendous amount of computations to sufficiently characterize a trajectory. With a problem and potential solution in mind, I began to investigate how I could use machine learning to improve upon existing techniques for missed-thrust trajectory design.

I go into more detail in my dissertation, and if you want to learn more about my work I suggest you at least skim the parts that you are interested in. That being said, below I discuss at a high level what my research entailed.

Mass is the name of the game when it comes to spacecraft, since the fuel required to move objects around increases exponentially as the object mass increases. This relationship is captured by the Tsiolkovsky rocket equation, which states that the change in velocity achieved during a propulsive maneuver is proportional to the logarithm of the fraction of mass before the maneuver (wet mass) relative to the mass after the maneuver (dry mass). Conversely, this can be rearranged to show that the required mass for a maneuver is exponentially proportional to the change in velocity achieved. The equation also shows that the efficiency of the the rocket engine, represented by the exhaust velocity term, is inversely exponentially proportional to the change in velocity. Therefore, it is paramount both to minimize the dry mass and maximize the engine efficiency when considering spacecraft design.

Traditionally, rockets use high-thrust engines which have moderate efficiencies with relatively high thrust-to-weight ratios. A newer class of rocket engine can achieve much higher efficiencies, therefore decreasing the required propellant required for a given maneuver. The drawback of these engines is that the thrust-to-weight ratios are generally quite low, and therefore this class of engine is referred to a low-thrust engine, and spacecraft that use these engines are called low-thrust spacecraft. Because the thrust-to-weight ratios are so low, the engines must be active for a much longer time.

While maneuvers with high-thrust engines are often on the order of seconds to minutes, maneuvers with low-thrust engines can be on the order of days to weeks (or longer!). Because the burn times are so long, spacecraft reliability starts to become a factor. If the spacecraft experiences an outage while it is in the middle of a maneuver, it can get very far off track from its intended trajectory and require an entirely new mission design strategy to get it back to where it needs to be. The study of how outages can affect low-thrust spacecraft and how trajectories can be designed to be more resilient to these outages is called the missed-thrust problem.