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Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map

Author

Listed:
  • Lazaros Moysis

    (Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece)

  • Karthikeyan Rajagopal

    (Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India)

  • Aleksandra V. Tutueva

    (Youth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, 197376 St Petersburg, Russia)

  • Christos Volos

    (Laboratory of Nonlinear Systems—Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece)

  • Beteley Teka

    (Department of Electronics Engineering, Defence University College of Engineering, Bishoftu 1041, Ethiopia)

  • Denis N. Butusov

    (Youth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, 197376 St Petersburg, Russia)

Abstract

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.

Suggested Citation

  • Lazaros Moysis & Karthikeyan Rajagopal & Aleksandra V. Tutueva & Christos Volos & Beteley Teka & Denis N. Butusov, 2021. "Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map," Mathematics, MDPI, vol. 9(15), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1821-:d:606893
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    References listed on IDEAS

    as
    1. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Nasr, Salah & Mekki, Hassen & Bouallegue, Kais, 2019. "A multi-scroll chaotic system for a higher coverage path planning of a mobile robot using flatness controller," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 366-375.
    3. Wong, Kwok-Wo & Kwok, Bernie Sin-Hung & Yuen, Ching-Hung, 2009. "An efficient diffusion approach for chaos-based image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2652-2663.
    4. Luiz S. Martins-Filho & Elbert E. N. Macau, 2007. "Patrol Mobile Robots and Chaotic Trajectories," Mathematical Problems in Engineering, Hindawi, vol. 2007, pages 1-13, June.
    5. Xuan Huang & Lingfeng Liu & Xiangjun Li & Minrong Yu & Zijie Wu, 2019. "A New Pseudorandom Bit Generator Based on Mixing Three-Dimensional Chen Chaotic System with a Chaotic Tactics," Complexity, Hindawi, vol. 2019, pages 1-9, June.
    6. Caihong Li & Yong Song & Fengying Wang & Zhenying Liang & Baoyan Zhu, 2015. "Chaotic Path Planner of Autonomous Mobile Robots Based on the Standard Map for Surveillance Missions," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, August.
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    Cited by:

    1. Othman Abdullah Almatroud & Viet-Thanh Pham, 2023. "Building Fixed Point-Free Maps with Memristor," Mathematics, MDPI, vol. 11(6), pages 1-11, March.

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