Hybrid Search Method for Zermelo’s Navigation Problem

Published in Computational and Applied Mathematics, 2024

Abstract

In this paper, we present a novel algorithm called the Hybrid Search algorithm to tackle the Zermelo’s navigation problem. This method can be regarded as an extension of the recent Ferraro–Martín de Diego-Sato algorithm to allow for further exploration in search for the global optimum, in situations of complex vector fields where many locally optimal trajectories exist. 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 centered 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, demonstrating its effectiveness and performance.

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Authors & Affiliations

  • Daniel Precioso
    IE University

  • Robert Milson
    Dalhousie University

  • Louis Bu
    Dalhousie University

  • Yvonne Menchions
    Dalhousie University

  • David Gómez-Ullate
    IE University