1. Modelling, simulation and mathe-matical analysis of drone swarms viaentropy methods
- Author
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Negulescu, Claudia, Maupoux, Axel, Lehman, Etienne, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,[MATH]Mathematics [math] ,[NLIN.NLIN-AO]Nonlinear Sciences [physics]/Adaptation and Self-Organizing Systems [nlin.AO] - Abstract
The mathematical modelling and analysis of the collective behaviour of a cloud of N interacting particles or agents has attracted a lot of interest in the last years in several communities, such as biologists, physicists, mathematicians, computer scientists etc. This is motivated not only by fundamental reasons, such as the understanding of the natural phenomena occurring around us, but also by the wide applications of this field in several domains, such as collective robotics, unmanned areal vehicles, ...Several mathematical models appeared in literature in the last years, such as for ex. the Viscek model, the Kuramoto model, the Cucker-Smale model etc, each one being specifically adapted for a particular situation, and several mathematical and numerical studies have been performed, the literature being constantly growing. The basic models have been fully understood today, what is still open in our opinion is the design of more realistic models, permitting to get closer to reality, and the corresponding mathematical and numerical analysis. In fact, a truly good model must on one hand recreate the real-life behaviour one is investigating, and on the other hand it must be simple enough to enable a detailed mathematical and numerical study. So in our particular case of a drone swarm, all the specificities mentionned in Section 3.2 shall be step by step included in a realistic drone model and efficient, multi-scale numerical schemes designed to be proposed to the industrials
- Published
- 2023