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On a Three Dimensional Vision Based Collision Avoidance Model

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Abstract

This paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enable a group of vehicles to converge to a common destination point avoiding collisions with each other and with moving obstacles in their environment. The interaction rules lead the agents to adapt their velocity vectors through a modification of the relative bearing angle and the relative elevation. Moreover the model satisfies the limited field of view constraints resulting from individual perception sensitivity. From the proposed individual based model, a mean-field kinetic model is derived. Simulations are performed to show the effectiveness of the proposed model.

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Acknowledgements

The authors thank anonymous referees and highly appreciate their valuable comments and suggestions, which significantly contributed to improve the quality of the justification of the model in Sect. 2.2.

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Authors and Affiliations

  1. Ecole Nationale de L’aviation Civile, Laboratoire ENAC, Équipe OPTIM, 7 Avenue Douard-Belin, BP 54005, Toulouse, France

    Céline Parzani

  2. Université de Toulouse III & IUF, UMR5219, Institut de Mathématiques de Toulouse, 118, Route de Narbonne, 31062, Toulouse Cedex, France

    Francis Filbet

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  1. Céline Parzani
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  2. Francis Filbet
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Correspondence to Francis Filbet.

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Parzani, C., Filbet, F. On a Three Dimensional Vision Based Collision Avoidance Model. J Stat Phys 168, 680–706 (2017). https://doi.org/10.1007/s10955-017-1825-8

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  • DOI: https://doi.org/10.1007/s10955-017-1825-8

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