Stochastic time-optimal path-planning in uncertain, strong, and dynamic flows
Name
Lermusiaux_stochastic_time_optimal.pdf
Description
Submitted version
Size
13.47 MB
Format
Adobe PDF
Checksum (MD5)
1300106ec920d94adead8f4fcc4f5c10
Author(s)
Subramani, Deepak N
Wei, Quantum J
Lermusiaux, Pierre FJ
Date Issued
2018
Journal
Computer Methods in Applied Mechanics and Engineering
Publisher
Elsevier BV
Version
Original manuscript
Abstract
© 2018 Elsevier B.V. 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, maintaining accuracy while achieving several orders of magnitude in computational speed-up when compared to classic Monte Carlo methods. We utilize the new equations to complete stochastic reachability and time-optimal path planning in three test cases: (i) a canonical stochastic steady-front with uncertain flow strength, (ii) a stochastic barotropic quasi-geostrophic double-gyre circulation, and (iii) a stochastic flow past a circular island. For all the three test cases, we analyze the results with a focus on studying the effect of flow uncertainty on the reachability fronts and time-optimal paths, and their probabilistic properties. With the first test case, we demonstrate the approach and verify the accuracy of our solutions by comparing them with the Monte Carlo solutions. With the second, we show that different flow field realizations can result in paths with high spatial dissimilarity but with similar arrival times. With the third, we provide an example where time-optimal path variability can be very high and sensitive to uncertainty in eddy shedding direction downstream of the island.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.CMA.2018.01.004
