Bearing-only solution for Fermat–Weber location problem: Generalized algorithms
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 stat...
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| Published in | Automatica (Oxford) Vol. 176; p. 112242 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2025
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| Online Access | Get full text |
| ISSN | 0005-1098 |
| DOI | 10.1016/j.automatica.2025.112242 |
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| 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. |
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| AbstractList | 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. |
| ArticleNumber | 112242 |
| Author | Ahn, Hyo-Sung Le-Phan, Nhat-Minh Nguyen, Phuoc Doan Trinh, Minh Hoang |
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| Cites_doi | 10.1111/j.1467-9787.1962.tb00902.x 10.1016/j.automatica.2019.108650 10.1016/j.conengprac.2016.03.013 10.1109/TAC.2015.2459191 10.2514/1.G004820 10.2514/1.G003003 10.1109/TAC.2019.2903290 10.1109/ICCAIS59597.2023.10382274 10.1109/TRO.2022.3218268 10.1007/s10957-014-0586-7 10.1002/rnc.6904 10.1016/j.oceaneng.2016.07.028 10.1109/9.317122 10.1016/j.automatica.2015.06.017 10.1007/BF01592245 10.1007/BF01584648 |
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| Keywords | Bearing-only algorithm Fermat–Weber location problem Moving beacons Single-integrator agent Time-varying velocity |
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| References | Kuhn (b4) 1973; 4 Trinh, Lee, Ahn (b18) 2015; 59 Sabet, Fathi, Daniali (b14) 2016; 123 Le-Phan, Nguyen, Ahn, Trinh (b6) 2024 Li, Ning, He, Lee, Zhao (b8) 2023; 39 Shevitz, Paden (b15) 1994; 39 Brimberg (b2) 1995; 71 Parayil, Ratnoo (b10) 2018; 41 Plastria (b11) 2011; vol. 155 Beck, Sabach (b1) 2015; 164 Zhao, Li, Ding (b19) 2019; 64 Trinh, Ko, Pham, Oh, Ahn (b17) 2016; 51 Khalil (b3) 2002 Lin, Miao, Wang, Wu, He, Fierro (b9) 2023; 33 Roy, Baldi, Fridman (b13) 2020; 111 Suresh, Ratnoo (b16) 2020; 43 Zhao, Zelazo (b20) 2016; 61 Rockafellar (b12) 1970 (pp. 628–633). Le-Phan, N.-M., Trinh, M. H., & Nguyen, P. D. (2023). Dimensional Lifting, Finite-Time Convergence, and Bearing-Only Algorithms for the Fermat-Weber Location Problem. In Kuhn, Kuenne (b5) 1962; 4 Shevitz (10.1016/j.automatica.2025.112242_b15) 1994; 39 Plastria (10.1016/j.automatica.2025.112242_b11) 2011; vol. 155 Trinh (10.1016/j.automatica.2025.112242_b17) 2016; 51 Zhao (10.1016/j.automatica.2025.112242_b19) 2019; 64 Kuhn (10.1016/j.automatica.2025.112242_b4) 1973; 4 Suresh (10.1016/j.automatica.2025.112242_b16) 2020; 43 10.1016/j.automatica.2025.112242_b7 Lin (10.1016/j.automatica.2025.112242_b9) 2023; 33 Kuhn (10.1016/j.automatica.2025.112242_b5) 1962; 4 Li (10.1016/j.automatica.2025.112242_b8) 2023; 39 Sabet (10.1016/j.automatica.2025.112242_b14) 2016; 123 Le-Phan (10.1016/j.automatica.2025.112242_b6) 2024 Brimberg (10.1016/j.automatica.2025.112242_b2) 1995; 71 Rockafellar (10.1016/j.automatica.2025.112242_b12) 1970 Khalil (10.1016/j.automatica.2025.112242_b3) 2002 Trinh (10.1016/j.automatica.2025.112242_b18) 2015; 59 Zhao (10.1016/j.automatica.2025.112242_b20) 2016; 61 Roy (10.1016/j.automatica.2025.112242_b13) 2020; 111 Parayil (10.1016/j.automatica.2025.112242_b10) 2018; 41 Beck (10.1016/j.automatica.2025.112242_b1) 2015; 164 |
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| SubjectTerms | Bearing-only algorithm Fermat–Weber location problem Moving beacons Single-integrator agent Time-varying velocity |
| Title | Bearing-only solution for Fermat–Weber location problem: Generalized algorithms |
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