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A Simple Mathematical Model to Steering Oceanic Debris to a Targeted Region

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Advanced Research in Technologies, Information, Innovation and Sustainability (ARTIIS 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1937))

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Abstract

In this article, a simplified mathematical model is presented to depict the process of collecting ocean debris. The responsible autonomous vehicles for transporting the trash are represented as passive particles, while the ocean current is simulated by the movement of point vortices on a sphere. To ensure the autonomy of the vehicles, a system of piecewise constant controls is employed, using a limited number of predetermined switching points that determine their trajectories. Each control incurs an energy cost that is aimed to be minimized. This minimization is achieved by solving a nonlinear optimization problem on the spherical surface. The initial findings indicate the existence of multiple possible trajectories for autonomous vehicles.

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Acknowledgements

Carlos Balsa is grateful to the Foundation for Science and Technology (FCT, Portugal) for financial support through national funds FCT/MCTES (PIDDAC) to CeDRI (UIDB/05757/2020 and UIDP/05757/2020) and SusTEC (LA/P/0007/2021).

M. Victoria Otero-Espinar is partially supported by the Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación (Spain), grant PID2020-115155GB-I00.

Sílvio Gama is partially supported by (i) CMUP, member of LASI, which is financed by national funds through FCT - Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UIDB/00144/2020, and (ii) project SNAP NORTE-01-0145- FEDER-000085, co-financed by the European Regional Development Fund (ERDF) through the North Portugal Regional Operational Programme (NORTE2020) under Portugal 2020 Partnership Agreement.

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Authors and Affiliations

  1. Research Centre in Digitalization and Intelligent Robotics (CeDRI) and Laboratório para a Sustentabilidade e Tecnologia em Regiões de Montanha (SusTEC), Instituto Politécnico de Bragança, 5300-253, Bragança, Portugal

    Carlos Balsa

  2. Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela and Galician Center for Mathematical Research and Technology (CITMAga), 15782, Santiago de Compostela, Spain

    M. Victoria Otero-Espinar

  3. Centro de Matemática da Universidade do Porto, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre s/n, 4169-007, Porto, Portugal

    Sílvio Gama

Authors
  1. Carlos Balsa
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  2. M. Victoria Otero-Espinar
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  3. Sílvio Gama
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Corresponding author

Correspondence to Carlos Balsa .

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Editors and Affiliations

  1. Universidad Estatal Peninsula de Santa Elena Campus Matriz, La Libertad, Ecuador

    Teresa Guarda

  2. Algoritmi Research Centre, University of Minho, Guimarães, Portugal

    Filipe Portela

  3. Universidad a Distancia de Madrid, Madrid, Spain

    Jose Maria Diaz-Nafria

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Balsa, C., Otero-Espinar, M.V., Gama, S. (2024). A Simple Mathematical Model to Steering Oceanic Debris to a Targeted Region. In: Guarda, T., Portela, F., Diaz-Nafria, J.M. (eds) Advanced Research in Technologies, Information, Innovation and Sustainability. ARTIIS 2023. Communications in Computer and Information Science, vol 1937. Springer, Cham. https://doi.org/10.1007/978-3-031-48930-3_5

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  • DOI: https://doi.org/10.1007/978-3-031-48930-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-48929-7

  • Online ISBN: 978-3-031-48930-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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