Research on Locating and Searching for Missing Submersibles Based on Differential Equations and SAR-A* Algorithm

Abstract

In recent years, the application of submersibles has become increasingly widespread. The current focus of research is on real-time and accurate positioning of submersibles to cope with potential emergencies. This paper aims to establish a trajectory model for faulty submersibles. Firstly, a differential equation model for submersible dynamics is established, numerical solutions are obtained and fitted to determine the exponential relationship between velocity and time, resulting in a theoretical formula for submersible displacement. Subsequently, based on the trajectory, a probability model for the presence of targets is established using a two-dimensional Gaussian distribution. The SAR-A* algorithm is employed for regional search, combined with a greedy algorithm to obtain initial deployment points for search and rescue, thus deriving the search and rescue trajectory. This study provides theoretical support for locating and rescuing missing submersibles and is expected to play an important role in future submersible applications.