A Study of Heuristic Optimizers in Spacecraft Trajectory Problems
Open Access
- Author:
- Steratore, Benjamin
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- April 02, 2021
- Committee Members:
- Robert Graham Melton, Thesis Advisor/Co-Advisor
Amy Ruth Pritchett, Program Head/Chair
Puneet Singla, Committee Member
Daning Huang, Committee Member - Keywords:
- Heuristic
Trajectory Optimization
Optimization
Particle Swarm Optimization
Gray Wolf Optimization
Ant Colony Optimization
Spacecraft - Abstract:
- This thesis expands upon the work done by Pontani and Conway on Particle Swarm Optimization’s (PSO) application in common spacecraft trajectory problems. The heuristics studied here are PSO, Grey Wolf Optimization (GWO), and an Ant Colony Optimizer (ACO) modified for continuous domains. They are tested on the percentage of times they converge to a known solution. The optimization problems tested are a simple two-impulse circular-to-circular orbit transfer, a circular-to-circular orbit finite thrust problem, and a Lyapunov orbit problem. The simple two-impulse transfer’s solution is known to be the Hohmann transfer, this provides an indication of the algorithm’s ability to solve simple problems. The finite thrust problem is defined to solve for four coefficients in a polynomial that determines the thrust pointing angle and the time of thrust for both thrusting arcs and a change in eccentric anomaly over the single interior coasting arc, using a total of eleven unknowns. The Lyapunov problem is given various Jacobi constants in the Earth-Moon circular restricted three body problem, and is defined to find the initial ’x’ position, distance from the center of mass in the synodic frame along the line made by the Earth and Moon, and the period of orbit. Each heuristic is trained when needed on a separate training set of data, and tested for its ability to converge to the known solutions and the time per iteration. PSO is a good benchmark for comparison that did not need training and is able to acquire the solutions with which the others were trained and with which all of them were tested. One noteworthy assumption in this method is that PSO is capable of acquiring accurate training and testing solutions for the trials. Another important caveat is that this thesis does not claim to have found the best way of training these algorithms. There are very likely other variables and functions that will increase the success rate of ACO and GWO, and yet more training methods. Since PSO is a reliable optimizer it is used to solve for the unknowns in training ACO and GWO using Penn States ‘Roar’ supercomputer (formerly the Institute for Computational and Data Sciences Advanced CyberInfrastructure, or ICDS-ACI), however this is very time consuming and not many full trials were done. For this reason, it cannot be confidently claimed that the results of the training are truly optimized. Despite this uncertainty, these trained algorithms did very well. All three converged over 99 percent of the time to the Hohmann transfer solution for the impulsive transfer. GWO relied too heavily on quick convergence to offer much use in the Lyapunov problem. ACO however, is able to out-compete PSO for the majority of Jacobi constants. The largest success is GWO and ACO’s performance in the finite thrust problem. GWO is best for the final radius being two to five times more than the initial, ACO is best for six to nine times, and PSO is best only for ten times. Hopefully, this work will contribute to spacecraft automation. This thesis offers some tools and methods to develop automated trajectory correction for long range missions, station keeping for unstable quasi-periodic orbits, and a few potential planar L1-to-Moon cycler orbits that were accidentally generated in solutions of the Lyapunov problem.