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Pierre F.J. Lermusiaux. Wei, Quantum Jichi Massachusetts Institute of Technology. Department of Mechanical Engineering. Massachusetts Institute of Technology. Department of Mechanical Engineering 2015-09-17T19:09:30Z 2015-09-17T19:09:30Z 2015 2015 http://hdl.handle.net/1721.1/98749 920897616 Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2015. Cataloged from PDF version of thesis. Includes bibliographical references (pages 53-54). Path-planning has many applications, ranging from self-driving cars to flying drones, and to our daily commute to work. Path-planning for autonomous underwater vehicles presents an interesting problem: the ocean flow is dynamic and unsteady. Additionally, we may not have perfect knowledge of the ocean flow. Our goal is to develop a rigorous and computationally efficient methodology to perform path-planning in uncertain flow fields. We obtain new stochastic Dynamically Orthogonal (DO) Level Set equations to account for uncertainty in the flow field. We first review existing path-planning work: time-optimal path planning using the level set method, and energy-optimal path planning using stochastic DO level set equations. We build on these methods by treating the velocity field as a stochastic variable and deriving new stochastic DO level set equations. We use the new DO equations to simulate a simple canonical flow, the stochastic highway. We verify that our results are correct by comparing to corresponding Monte Carlo results. We explore novel methods of visualizing the results of the equations. Finally we apply our methodology to an idealized ocean simulation using Double-Gyre flows. by Quantum Jichi Wei. S.B. 54 pages eng Massachusetts Institute of Technology 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. http://dspace.mit.edu/handle/1721.1/7582 Mechanical Engineering. Time-optimal path planning in uncertain flow fields using stochastic dynamically orthogonal level set equations Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="a9d958df-ad64-4c44-b0ea-83ea66818343"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Time-optimal path planning in uncertain flow fields using stochastic dynamically orthogonal level set equations</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2015</PublicationDate> <Authors> <Author> <DisplayName>Wei, Quantum Jichi</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Mechanical Engineering.</Keyword> <Abstract>Path-planning has many applications, ranging from self-driving cars to flying drones, and to our daily commute to work. Path-planning for autonomous underwater vehicles presents an interesting problem: the ocean flow is dynamic and unsteady. Additionally, we may not have perfect knowledge of the ocean flow. Our goal is to develop a rigorous and computationally efficient methodology to perform path-planning in uncertain flow fields. We obtain new stochastic Dynamically Orthogonal (DO) Level Set equations to account for uncertainty in the flow field. We first review existing path-planning work: time-optimal path planning using the level set method, and energy-optimal path planning using stochastic DO level set equations. We build on these methods by treating the velocity field as a stochastic variable and deriving new stochastic DO level set equations. We use the new DO equations to simulate a simple canonical flow, the stochastic highway. We verify that our results are correct by comparing to corresponding Monte Carlo results. We explore novel methods of visualizing the results of the equations. Finally we apply our methodology to an idealized ocean simulation using Double-Gyre flows.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>