Time and Risk Optimal Path Planning for Surface Vehicle via Level Set in Dynamic Environment

Many oceanographic vehicles, especially those used for long-distance missions and with limited operating speeds, are sensitive to external field influences, such as ocean currents. A feasible, safe, and optimal path is critical for autonomous operation due to the dynamic and intermittent environment of the vehicle and physical constraints. This article develops a path planning algorithm on the basis of the level set method. Specifically, we utilize the second-order alternating evolution method to solve the Hamilton–Jacobi equation with time parameter. In addition, the flow field information is mapped to the level set equation, and the basemap and ocean current information are updated in real time. Meanwhile, to optimize the evolution of the accessible boundary, a second-order polygon is constructed through Newton's mean difference interpolation method. Finally, we can plan the optimal path under the current environment via the accessible boundary information and the path backtracking equation. The goal is to compute the path for the surface vehicle so as to minimize the travel time in the presence of ocean currents. Numerical examples confirm the efficiency of the approach.