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Waves In Isotropic Totalistic Cellular Automata: Application To Real-Time Robot Navigation

Author

Listed:
  • C. CALVO

    (Instituto de Matematica Interdiciplinar, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid, 28040, Spain)

  • J. A. VILLACORTA-ATIENZA

    (Instituto de Matematica Interdiciplinar, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid, 28040, Spain)

  • V. I. MIRONOV

    (#x2020;N. I. Lobachevsky State University, Gagarin Av. 23, Nizhny Novgorod, 603950, Russia)

  • V. GALLEGO

    (Instituto de Matematica Interdiciplinar, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid, 28040, Spain)

  • V. A. MAKAROV

    (Instituto de Matematica Interdiciplinar, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid, 28040, Spain†N. I. Lobachevsky State University, Gagarin Av. 23, Nizhny Novgorod, 603950, Russia)

Abstract

Totalistic cellular automata (CA) are an efficient tool for simulating numerous wave phenomena in discrete media. However, their inherent anisotropy often leads to a significant deviation of the model results from experimental data. Here, we propose a computationally efficient isotropic CA with the standard Moore neighborhood. Our model exploits a single postulate: the information transfer in an isotropic medium occurs at constant rate. To fulfill this requirement, we introduce in each cell a local counter keeping track of the distance run by the wave from its source. This allows maintaining the wave velocity constant in all possible directions even in the presence of nonconductive local areas (obstacles) with complex spatial geometry. Then, we illustrate the model on the problem of real-time building of cognitive maps used for navigation of a mobile robot. The isotropic property of the CA helps obtaining “smooth” trajectories and hence natural robot movement. The accuracy and flexibility of the approach are proved experimentally by driving the robot to a target avoiding collisions with obstacles.

Suggested Citation

  • C. Calvo & J. A. Villacorta-Atienza & V. I. Mironov & V. Gallego & V. A. Makarov, 2016. "Waves In Isotropic Totalistic Cellular Automata: Application To Real-Time Robot Navigation," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(04n05), pages 1-18, June.
    • Handle: RePEc:wsi:acsxxx:v:19:y:2016:i:04n05:n:s0219525916500120
    DOI: 10.1142/S0219525916500120
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    References listed on IDEAS

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    1. Ortigoza, Gerardo M., 2015. "Unstructured triangular cellular automata for modeling geographic spread," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 520-536.
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