Energy-Risk Optimal Path Planning for Surface Vehicle via Parameterized Level Set in Dynamic Flow Marine Environment

A considerable proportion of ocean vehicles, particularly those with constrained operational capabilities, are vulnerable to external factors such as wind patterns and ocean currents. It is therefore imperative that a safe and viable route be identified for a ship to operate autonomously. The proposed methodology delineates a systematic approach for the mapping of environmental pathways on electronic charts, underpinned by parameter-level set equations. In order to address the shortcomings of the traditional level set method, namely its lack of smoothness and slow convergence, a new approach was devised. This approach is predicated on the premise that the impact of non-uniform dynamic wind and wave flows is accounted for by incorporating a matrix expansion processing method of wind field data slices into the boundary evolution part of the level set equation. Secondly, in order to optimise the real-time evolution of the reachable boundary, a curve parameter formula expressed by implicit function on Euclidean space is designed. In conclusion, the perturbation energy functional is constructed in order to solve the gradient descending flow and to ensure the robustness of the ship evolution curve in the presence of disturbance. The validity of the proposed methodology is substantiated by numerical exemplification.