{"title":"Bearing-only solution for Fermat–Weber location problem: Generalized algorithms","authors":"Nhat-Minh Le-Phan , Phuoc Doan Nguyen , Hyo-Sung Ahn , Minh Hoang Trinh","doi":"10.1016/j.automatica.2025.112242","DOIUrl":null,"url":null,"abstract":"<div><div>This paper presents novel algorithms for the Fermat–Weber Location Problem, guiding an autonomous agent to the point that minimizes the weighted sum of Euclidean distances to some beacons using only bearing measurements. The current results address only the simple scenario where the beacons are stationary and the agent is modeled by a single integrator. In this paper, we present a number of bearing-only algorithms that let the agent follow the Fermat–Weber point of a group of stationary or moving beacons. Exponential and finite-time stability of the Fermat–Weber point are also established. The theoretical results are rigorously proven using Lyapunov theory and supported with simulation examples.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"176 ","pages":"Article 112242"},"PeriodicalIF":5.9000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109825001347","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/11 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents novel algorithms for the Fermat–Weber Location Problem, guiding an autonomous agent to the point that minimizes the weighted sum of Euclidean distances to some beacons using only bearing measurements. The current results address only the simple scenario where the beacons are stationary and the agent is modeled by a single integrator. In this paper, we present a number of bearing-only algorithms that let the agent follow the Fermat–Weber point of a group of stationary or moving beacons. Exponential and finite-time stability of the Fermat–Weber point are also established. The theoretical results are rigorously proven using Lyapunov theory and supported with simulation examples.
期刊介绍：
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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