Hybrid Search method for Zermelo's navigation problem

TL;DR

This paper introduces a Hybrid Search algorithm that combines Zermelo's navigation problem with a heuristic-based approach to efficiently find optimal routes for vessels, incorporating obstacle avoidance in both Euclidean and spherical spaces.

Contribution

The paper presents a novel hybrid algorithm integrating Zermelo's problem with a heuristic method, applicable to real-world navigation scenarios including obstacle avoidance.

Findings

Effective in synthetic vector fields

Demonstrates improved efficiency in real ocean data

Handles both Euclidean and spherical spaces

Abstract

In this paper, we present a novel algorithm called the Hybrid Search algorithm that integrates the Zermelo's Navigation Initial Value Problem with the Ferraro-Mart\'in de Diego-Almagro algorithm to find the optimal route for a vessel to reach its destination. Our algorithm is designed to work in both Euclidean and spherical spaces and utilizes a heuristic that allows the vessel to move forward while remaining within a predetermined search cone centred around the destination. This approach not only improves efficiency but also includes obstacle avoidance, making it well-suited for real-world applications. We evaluate the performance of the Hybrid Search algorithm on synthetic vector fields and real ocean currents data, demonstrating its effectiveness and performance.