Path optimization using sub-Riemannian manifolds with applications to astrodynamics
Name
722474695-MIT.pdf
Description
Full printable version
Size
6.32 MB
Format
Adobe PDF
Checksum (MD5)
80f9d76be4dab4c3b8fde736fa0f5210
Author(s)
Whiting, James K. (James Kalani), 1980-
Advisor(s)
Olivier deWeck, Manuel Martinez-Sanchez and Ray Sedwick.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
Abstract
Differential geometry provides mechanisms for finding shortest paths in metric spaces. This work describes a procedure for creating a metric space from a path optimization problem description so that the formalism of differential geometry can be applied to find the optimal paths. Most path optimization problems will generate a sub-Riemannian manifold. This work describes an algorithm which approximates a sub-Riemannian manifold as a Riemannian manifold using a penalty metric so that Riemannian geodesic solvers can be used to find the solutions to the path optimization problem. This new method for solving path optimization problems shows promise to be faster than other methods, in part because it can easily run on parallel processing units. It also provides some geometrical insights into path optimization problems which could provide a new way to categorize path optimization problems. Some simple path optimization problems are described to provide an understandable example of how the method works and an application to astrodynamics is also given.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 131).
Subjects
Aeronautics and Astronautics.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
M.I.T. theses are protected by
copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
permission. See provided URL for inquiries about permission.
copyright. They may be viewed from this source for any purpose, but
reproduction or distribution in any format is prohibited without written
permission. See provided URL for inquiries about permission.
Persistent DSpace Link
