Time-Optimal Path Planning in an Evolving Ocean Wave Field Based on Reachability Theory

We consider the navigation of surface vessels in an evolving ocean wave field, where the detrimental extreme waves are treated as moving and deforming obstacles. We propose a new time-optimal path planning algorithm with avoidance of such obstacles based on the reachability theory. In our framework, the mathematical optimization problem is boiled down to: 1) forward propagation of reachable set described by a variational inequation (VI), which is numerically solved through the level set method combined with a prediction-correction scheme and 2) a backtracking procedure to find the optimal path. The new path planner is tested in a number of cases including one with realistic ocean waves. We demonstrate that our algorithm can provide correct paths avoiding high waves and achieve multiple optimal (equivalent in time) paths when available. Finally, the framework can be straightforwardly extended to other problems involving collision avoidance with moving and deforming obstacles.