Risk-optimal path planning in stochastic dynamic environments

• Published in: Computer methods in applied mechanics and engineering 2019-08, Vol.353 (C), p.391-415
• Main Authors: Subramani, Deepak N., Lermusiaux, Pierre F.J.
• Format: Article
• Language: English
• Subjects: AUV; Coastal environments; Decision theory; Differential equations; Dynamically orthogonal; Flow distribution; Level set equations; Mathematical analysis; Ocean modeling; Oceans; Path planning; Planning; Product design; Risk analysis; Stochastic path planning; Uncertainty quantification; Urban environments
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.04.033

We combine decision theory with fundamental stochastic time-optimal path planning to develop partial-differential-equations-based schemes for risk-optimal path planning in uncertain, strong and dynamic flows. The path planning proceeds in three steps: (i) predict the probability distribution of environmental flows, (ii) compute the distribution of exact time-optimal paths for the above flow distribution by solving stochastic dynamically orthogonal level set equations, and (iii) compute the risk of being suboptimal given the uncertain time-optimal path predictions and determine the plan that minimizes the risk. We showcase our theory and schemes by planning risk-optimal paths of unmanned and/or autonomous vehicles in illustrative idealized canonical flow scenarios commonly encountered in the coastal oceans and urban environments. The step-by-step procedure for computing the risk-optimal paths is presented and the key properties of the risk-optimal paths are analyzed. •Combined decision theory and time-optimal S-PDEs in uncertain, dynamic, strong flows.•Risk of being suboptimal given the uncertain time-optimal path predictions minimized.•Multiple error and cost metrics used for rigorous risk evaluation and minimization.•Applied planning in stochastic front, double-gyre QG flow and flow exiting a strait.