Novel methods for high-fidelity low-thrust spacecraft trajectory optimization and mission design

Low-thrust propulsion has emerged as a key technology for spaceflight. It provides higher efficiency and substantial propellant savings over chemical propulsion, allowing for the deployment of heavier payloads to orbit for a given spacecraft mass. Although enabling, this technology presents challenges for mission design. For example, low-thrust engines must operate over much longer periods of time to perform a maneuver, and designing trajectories that minimize a given cost metric and meet the mission constraints requires solving optimal control problems. In the context of spacecraft trajectories, these problems are known to exhibit highly nonlinear behavior and extreme sensitivity to initial conditions, resulting in poor convergence properties that can make it impossible to obtain a solution, particularly when considering realistic mission scenarios. This dissertation includes the development of an optimization framework for designing optimal low-thrust trajectories in high-fidelity dynamical models. This optimization framework is based on the formalism of indirect methods, which introduces adjoints to the state variables to encode the conditions of optimality. The trajectory design challenges associated with low-thrust trajectory optimization are addressed through the development of advanced homotopy continuation techniques, which embed a complex problem within a parametrized family of simpler sub-problems. We employ state-of-the-art numerical tools, such as the advanced numerical integrators and automatic differentiation methods implemented in the Julia language. The methods developed and presented in this dissertation enable robust convergence and a considerable decrease in the computational effort required for obtaining the solution, thus overcoming the limitations of standard optimization techniques and allowing for the exploration of complex design spaces, rapid prototyping, and accurate trade studies. The methods are applied to the design and optimization of time-optimal and fuel-optimal Earth-centered trajectories, transfers to periodic and quasi-periodic orbit near Sun-Earth L2 point, and interplanetary transfers to Mars. These applications demonstrate the framework’s capability to handle complex dynamical regimes and stringent mission constraints. Overall, this work advances the state of the art in low-thrust trajectory optimization by providing a high-fidelity, computationally efficient, and extensible approach for the formulation and solution of realistic space mission design problems.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Pascarella, Alex

Contributors dc:contributor

• Woollands, Robyn
• Prussing, John
• Raginsky, Maxim
• Wilson, Roby

• Astrodynamics
• Optimization
• Optimal Control
• Indirect Methods
• Spacecraft Trajectories
• Low-thrust
• Homotopy

Statement dc:rights

• Copyright 2025 Alex Pascarella

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/129874

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F129874