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Dynamic region visit routing problem for vehicles with minimum turning radius

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Abstract

In this paper we address the problem of planning optimized routes among dynamically selected target regions for vehicles with a turning radius motion constraint, hereinafter called dynamic Dubins traveling salesman problem with neighborhoods (DDTSPN). Initially, we present a heuristic to solve a simpler version of this problem, called off-line step, where only previously given targets are concerned. We further extend this approach for the more complex case of dynamic scenarios, called on-line step, addressing the inclusion of new targets during the execution of the initial route, whilst minimizing the impact on the total traveled distance. Formal analyzes of our techniques are provided, presenting upper bounds for the total length of the final tour. Results with statistical investigation over a large number of trials in a simulated environment are also provided. Finally, to demonstrate the applicability of our technique in solving the DDTSPN at real-world scenarios, we also report on results of an experiment performed with a real car-like robot.

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Notes

  1. For these classes of vehicles, the Dubins model is an approximation due to discontinuities of the angular velocity’s first derivative, but it is generally acceptable.

  2. This is not a restriction of the method, just a convenience to keep reasoning, implementation, and results visualization simple. The methodology proposed in this paper covers continuous, convex regions in general.

  3. Cases where nodes die or disappear were omitted, but the methodology is trivially extensible to deal with the decreasing of \(N\). This was intentionally left out, especially to avoid cluttered definitions.

  4. Available at http://www.tsp.gatech.edu/concorde/index.html.

  5. A video of the execution is available at https://youtu.be/aIUZN1vmesU.

  6. A method is called zealous if the vehicle cannot wait, or should remain in constant motion if there are still unserved demands in the environment (Ausiello et al. 2008) (a scenario closer to the problem addressed here).

  7. A video of the execution is available at https://youtu.be/YUrxqUg7euw.

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Acknowledgements

This work was developed with support of Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) and Fundação Centro de Análise, Pesquisa e Inovação Tecnológica (FUCAPI).

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Authors and Affiliations

  1. Department of Computer Science, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

    Douglas G. Macharet & Mario F. M. Campos

  2. Department of Electronic Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil

    Armando Alves Neto

  3. Fundação Centro de Análise, Pesquisa e Inovação Tecnológica, Manaus, AM, Brazil

    Vila F. da Camara Neto

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  1. Douglas G. Macharet
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  2. Armando Alves Neto
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  3. Vila F. da Camara Neto
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  4. Mario F. M. Campos
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Correspondence to Douglas G. Macharet.

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Macharet, D.G., Alves Neto, A., da Camara Neto, V.F. et al. Dynamic region visit routing problem for vehicles with minimum turning radius. J Heuristics 24, 83–109 (2018). https://doi.org/10.1007/s10732-017-9359-4

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  • DOI: https://doi.org/10.1007/s10732-017-9359-4

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