Using Numerical Optimization Techniques and General Perturbation Equations to Find Optimal Near-Earth Orbit Transfers

Open Access
Williams, Patrick
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
Committee Members:
  • Dr David B Spencer, Thesis Advisor
  • Low-thrust
  • Optimization
  • Molniya Orbits
  • Evolutionary Comuptation
  • Satellite Toolkit
With recent developments in low-thrust optimization techniques, several methods of trajectory optimization can be implemented across various transfers. Much recent work has focused on performing methods of optimal control on low-thrust, near-Earth orbit transfers, achieving maximum efficiency in both energy use and time-of-flight. However, the use of optimal control relies on the exploitation of a satellites’ equation of state, which becomes problematic if optimization is to be performed through a “black box” venue, where state equations cannot be manipulated. This situation is particularly evident when attempting to perform trajectory optimization through a commercial off-the-shelf satellite mission modeling software package. Thus, a robust optimization method must be chosen to produce competitive results comparable to optimal control in these types of situations. However, the formulation of an objective function, as well as which type of optimization method to chose is important, since some formulations or algorithms may lead to better or faster convergence when compared to others. To address this issue, several non-linear constrained numerical optimization methods, including classical algorithms and evolutionary strategies, are implemented on simple low-thrust trajectories modeled using Satellite Toolkit’s Astrogator®, to determine what methods perform better when applied to these transfers. Once a suitable algorithm is selected, an appropriate objective function and problem formulation based on general perturbation equations is created, which can construct a time-varying thrust vector without manipulating a satellite’s equation of state. The objective function is then optimized within the selected algorithm in an attempt to obtain an optimal LEO to Molniya trajectory which can produce results on par with those found using a method of optimal control. Initial testing has shown that when an evolutionary strategy is applied to the objective function created in these studies, the resulting optimal trajectories are in fact competitive with those found using optimal control.