Automated detection of invariant manifold intersections using grid based approach

Aurich, Joshua Daniel

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https://hdl.handle.net/2142/97385 Copy

Description

Title

Automated detection of invariant manifold intersections using grid based approach

Author(s)

Aurich, Joshua Daniel

Issue Date

2017-04-24

Director of Research (if dissertation) or Advisor (if thesis)

Coverstone, Victoria L.

Department of Study

Aerospace Engineering

Discipline

Aerospace Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• Low energy
• Trajectory
• Poincare surface of section
• Poincare
• Compute unified device architecture (CUDA)
• Automated detection
• Spacecraft trajectory
• Periodic orbit
• Invariant manifold
• Manifold intersection

Abstract

When designing spacecraft trajectories, there exist cases where a trade-off between time-of-flight and fuel become crucial to the mission design scenario, especially for unmanned missions where longer time-of-flight solutions can be considered. One effective way to produce longer time of flight solutions is to leverage the natural dynamics of the system, which lends towards low energy trajectories. The dynamical structures of such systems provide global transport in multi-body regimes, and therefore avenues to low-cost solutions in a minimum fuel or Delta-V sense. Trajectories using the natural dynamics are termed low-energy (LE), and typically include either impulsive or low-thrust control to navigate from one global transport to the next. The multi-body model studied in this thesis is the circular restricted three-body problem (CR3BP) and the dynamical structure of interest are the invariant manifolds of the Euler-Lagrange points. The construction of LE trajectories in the CR3BP is most often accomplished by manually finding homoclinic and/or heteroclinic intersections of invariant manifolds located on specific Poincare surfaces of section. Historically, these patch-points are chosen by hand and used to seed either differential correction, at most yielding a feasible solution, or a control transcription with nonlinear programming to hopefully yield a locally optimal solution. Manual selection of these patch-points is a severe limitation of the current LE trajectory optimization approach and greatly reduces the chance to identify a globally optimal solution. The focus of this thesis is to present an automated solution which removes the bottleneck of characterization and analysis of these intersections of invariant manifolds. This thesis will demonstrate the application of the functionality to autonomously detect and characterize intersections of invariant manifolds, as well as explore the effects of different parameters on performance and generated solutions.

Graduation Semester

2017-05

Type of Resource

text

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http://hdl.handle.net/2142/97385

Copyright and License Information

Copyright 2017 Joshua Aurich

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