Hybrid search method for Zermelo’s navigation problem

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...

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Bibliographic Details
Published in:Computational & applied mathematics Vol. 43; no. 4
Main Authors: Precioso, Daniel, Milson, Robert, Bu, Louis, Menchions, Yvonne, Gómez-Ullate, David
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2024
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
49M15 Newton-type methods
Weather routing
70-08 Computational methods for problems pertaining to mechanics of particles and systems
70-10 Mathematical modeling or simulation for problems pertaining to mechanics of particles and systems
Time optimal trajectories
70Q05 Control of mechanical systems
49Mxx Numerical methods in optimal control
Optimization
65K10 Numerical optimization and variational techniques
Zermelo navigation problem
65L10 Numerical solution of boundary value problems involving ordinary differential equations
ISSN:2238-3603, 1807-0302
Online Access:Get full text
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Summary: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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-024-02756-w