{"id":4291,"date":"2018-01-01T14:42:00","date_gmt":"2018-01-01T19:42:00","guid":{"rendered":"http:\/\/mseas.mit.edu\/?p=4291"},"modified":"2021-07-06T12:52:43","modified_gmt":"2021-07-06T16:52:43","slug":"stochastic-time-optimal-path-planning-in-uncertain-strong-and-dynamic-flows","status":"publish","type":"post","link":"https:\/\/mseas.mit.edu\/?p=4291","title":{"rendered":"Stochastic Time-Optimal Path-Planning in Uncertain, Strong, and Dynamic Flows"},"content":{"rendered":"Accounting for uncertainty in optimal path planning is essential for many applications. We present and apply stochastic\nlevel-set partial differential equations that govern the stochastic time-optimal reachability fronts and time-optimal paths for\nvehicles navigating in uncertain, strong, and dynamic flow fields. To solve these equations efficiently, we obtain and employ\ntheir dynamically orthogonal reduced-order projections, maintaining accuracy while achieving several orders of magnitude in\ncomputational speed-up when compared to classic Monte Carlo methods. We utilize the new equations to complete stochastic\nreachability and time-optimal path planning in three test cases: (i) a canonical stochastic steady-front with uncertain flow strength,\n(ii) a stochastic barotropic quasi-geostrophic double-gyre circulation, and (iii) a stochastic flow past a circular island. For all the\nthree test cases, we analyze the results with a focus on studying the effect of flow uncertainty on the reachability fronts and\ntime-optimal paths, and their probabilistic properties. With the first test case, we demonstrate the approach and verify the accuracy\nof our solutions by comparing them with the Monte Carlo solutions.With the second, we show that different flow field realizations\ncan result in paths with high spatial dissimilarity but with similar arrival times. With the third, we provide an example where\ntime-optimal path variability can be very high and sensitive to uncertainty in eddy shedding direction downstream of the island.\n\nKeywords:\nStochastic Path Planning, Level Set Equations, Dynamically Orthogonal, Ocean Modeling, AUV, Uncertainty Quantification","protected":false},"excerpt":{"rendered":"<p>Accounting for uncertainty in optimal path planning is essential for many applications. We present and apply stochastic level-set partial differential equations that govern the stochastic time-optimal reachability fronts and time-optimal paths for vehicles navigating in uncertain, strong, and dynamic flow fields. To solve these equations efficiently, we obtain and employ their dynamically orthogonal reduced-order projections, [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31,183,33,35,5,63,64],"tags":[],"class_list":["post-4291","post","type-post","status-publish","format-standard","hentry","category-uncertainty-quantification-and-reduced-order-modeling","category-science-of-autonomy","category-uncertainty-quantification-and-predictions","category-optimal-path-planning","category-publications","category-papers-in-refereed-journals-optimal-path-planning","category-papers-in-refereed-journals-uncertainty-quantification-and-predictions"],"_links":{"self":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/4291","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=4291"}],"version-history":[{"count":3,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/4291\/revisions"}],"predecessor-version":[{"id":4331,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=\/wp\/v2\/posts\/4291\/revisions\/4331"}],"wp:attachment":[{"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mseas.mit.edu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}