## Graduate College Dissertations and Theses

2015

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Mechanical Engineering

Darren Hitt

Chris Danforth

#### Abstract

Satellite formation missions allow for scientific measurement opportunities that are only otherwise possible with the use of unrealistically large satellites. This work applies the Evolutionary Algorithm (EA), Differential Evolution (DE), to a 4-satellite mission design that borrows heavily from the mission specifications for Phase 1 of NASA's Magnetospheric Multi-Scale Mission (MMS). This mission specifies goals for formation "quality" and size over the arc when scientific measurements are to be taken known as the Region of Interest (ROI). To apply DE to this problem a novel definition of fitness is developed and tailored to trajectory problems of the parameter scales of this mission. This method uses numerical integration of evolved initial conditions for trajectory determination. This approach allows for the inclusion of gravitational perturbations without altering the method. Here, the J2 oblateness correction is considered but other inclusions such as solar radiation pressure and other gravitational bodies are readily possible by amending the governing equations of integration which are stored outside of the method and called only during evaluation. A set of three launch conditions is evaluated using this method. Due to computational limitation, the design is restricted to only single-impulse maneuvers at launch and the ROI is initially restricted but then expanded through a process known here as "staging". The ROIs of tests are expanded until they fail to meet performance criteria; no result was able to stage to the full MMS specified $\pm20^\circ$ ROI but this is a result of the single-impulse restriction. The number of orbits a launch condition is able to meet performance criteria is also investigated. Revolutions considered and the ROIs therein contained are staged to investigate if the method is able to handle this additional problem space. Evidence of suitable formation trajectories found by this method is here presented.

en

112 p.

COinS