{"id":3845,"date":"2015-10-26T10:25:13","date_gmt":"2015-10-26T14:25:13","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=3845"},"modified":"2015-10-26T10:30:26","modified_gmt":"2015-10-26T14:30:26","slug":"optimal-path-planning-in-dynamic-environments","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=3845","title":{"rendered":"Optimal Path Planning in Dynamic Environments"},"content":{"rendered":"A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts are derived. Their solution provides the distribution of time-optimal reachability fronts and corresponding distribution of time-optimal paths. An optimization is then performed on the vehicle&#8217;s energy-time joint distribution to select the energy-optimal paths for each arrival time, among all stochastic time-optimal paths for that arrival time. The accuracy and efficiency of the DO level-set equations for solving the governing stochastic level-set reachability fronts are quantitatively assessed, including comparisons with independent semi-analytical solutions. The stochastic DO level-set equations is then extended to account for uncertainties in the flow field. Time-optimal planning is completed in a wind-driven barotropic quasi-geostrophic stochastic double-gyre ocean circulation (these stochastic flow fields are simulated using our DO Navier Stokes equations). Energy-optimal missions are studied in wind-driven barotropic quasi-geostrophic double-gyre circulations, and in realistic data-assimilative re-analyses of multiscale coastal ocean flows. The latter re-analyses are obtained from multi-resolution 2-way nested primitive-equation simulations of tidal-to-mesoscale dynamics in the Middle Atlantic Bight and Shelbreak Front region. The effects of tidal currents, strong wind events, coastal jets, and shelfbreak fronts on the energy-optimal paths are illustrated and quantified. Results showcase the opportunities for longer-duration missions that intelligently utilize the ocean environment to save energy, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.","protected":false},"excerpt":{"rendered":"<p>A stochastic optimization methodology is formulated for computing energy-optimal paths from among time-optimal paths of autonomous vehicles navigating in a dynamic flow field. To set up the energy optimization, the relative vehicle speed and headings are considered to be stochastic, and new stochastic Dynamically Orthogonal (DO) level-set equations that govern their stochastic time-optimal reachability fronts [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[168,7],"tags":[],"class_list":["post-3845","post","type-post","status-publish","format-standard","hentry","category-fall-2015","category-seminars"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3845","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=3845"}],"version-history":[{"count":1,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3845\/revisions"}],"predecessor-version":[{"id":3846,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/3845\/revisions\/3846"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3845"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3845"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3845"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}