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Multi-agent path planning with nonlinear restrictions

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Abstract

This paper presents a novel simplified mathematical modeling that can solve a path planning problem comprising three agents in a triangular formation. The problem is modeled to optimize the trajectories of the agents and to minimize the distances traveled. The trajectories are obtained in a way that deviates them from fixed obstacles whose dimensions are known. Furthermore, geometry and orientation constraints of the formation of the multi-agent are imposed. Heuristics methods such as the Genetic Algorithm, Differential Evolution and Particle Swarm Optimization are applied to solve the non-linear algebraic equations which represent the system. Comparisons are presented among the results of the different methods highlighting the processing time and the convergence to the global minimum solution. The results prove that all the algorithms can be applied to the path planning problem with constraints. The Particle Swarm Optimization method presents the lowest processing time for all simulated cases. However, the Differential Evolution method is more robust than the others when searching for the global minimum solution.

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Acknowledgements

This work was financially supported by CAPES in the Master´s in Mechanical Engineering program at EESC - USP.

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Authors and Affiliations

  1. Aeronautical Engineering Department, University of São Paulo, João Dagnone Avenue, 1100 - Jardim Santa Angelina, São Carlos, São Paulo, 13563-120, Brazil

    Juliana Veiga C. F. de Lima & Eduardo Morgado Belo

  2. Mechanical Engineering Department, Federal University of Triângulo Mineiro, Randolfo Borges Júnior Avenue, 1400 - Univerdecidade, Uberaba, Minas Gerais, 38064-200, Brazil

    Vinícius Abrão da Silva Marques

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  1. Juliana Veiga C. F. de Lima
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  2. Eduardo Morgado Belo
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  3. Vinícius Abrão da Silva Marques
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Correspondence to Vinícius Abrão da Silva Marques.

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de Lima, J.V.C.F., Belo, E.M. & Marques, V.A. Multi-agent path planning with nonlinear restrictions. Evol. Intel. 14, 191–201 (2021). https://doi.org/10.1007/s12065-020-00534-1

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