Path-planning has many applications, ranging from self-driving cars to flying drones,\r\nand to our daily commute to work. Path-planning for autonomous underwater vehicles\r\npresents an interesting problem: the ocean flow is dynamic and unsteady. Additionally,\r\nwe may not have perfect knowledge of the ocean flow. Our goal is to develop\r\na rigorous and computationally efficient methodology to perform path-planning in\r\nuncertain flow fields. We obtain new stochastic Dynamically Orthogonal (DO) Level\r\nSet equations to account for uncertainty in the flow field. We first review existing\r\npath-planning work: time-optimal path planning using the level set method, and\r\nenergy-optimal path planning using stochastic DO level set equations. We build on\r\nthese methods by treating the velocity field as a stochastic variable and deriving new\r\nstochastic DO level set equations. We use the new DO equations to simulate a simple\r\ncanonical flow, the stochastic highway. We verify that our results are correct by comparing\r\nto corresponding Monte Carlo results. We explore novel methods of visualizing\r\nthe results of the equations. Finally we apply our methodology to an idealized ocean\r\nsimulation using Double-Gyre flows. <\/p>","protected":false},"excerpt":{"rendered":"
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 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,5,43],"tags":[],"class_list":["post-3997","post","type-post","status-publish","format-standard","hentry","category-meche-theses","category-publications","category-bachelors-theses"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3997","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3997"}],"version-history":[{"count":1,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3997\/revisions"}],"predecessor-version":[{"id":3998,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3997\/revisions\/3998"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3997"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3997"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3997"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}