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Chaotic Path-Planning Algorithm Based on Courbage–Nekorkin Artificial Neuron Model

Author

Listed:
  • Dmitriy Kvitko

    (Computer-Aided Design Department, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia)

  • Vyacheslav Rybin

    (Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia)

  • Oleg Bayazitov

    (Computer-Aided Design Department, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia)

  • Artur Karimov

    (Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia)

  • Timur Karimov

    (Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia)

  • Denis Butusov

    (Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia)

Abstract

Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm based on the chaotic behavior of the Courbage–Nekorkin neuron model with a coverage control parameter. Our study aims to reduce the number of iterations required to cover the chosen investigated area, which is a typical efficiency criterion for this class of algorithms. To achieve this goal, we implemented a pseudorandom bit generator (PRBG) based on a Courbage–Nekorkin chaotic map, which demonstrates chaotic behavior and successfully passes all statistical tests for randomness. The proposed PRBG generates a bit sequence that can be used to move the tracked robot in four or eight directions in an operation area of arbitrary size. Several statistical metrics were applied to evaluate the algorithm’s performance, including the percentage of coverage of the study area and the uniformity of coverage. The performance of several competing path-planning algorithms was analyzed using the chosen metrics when exploring two test areas of the sizes 50 × 50 cells and 100 × 100 cells, respectively, in four and eight directions. The experimental results indicate that the proposed algorithm is superior compared to known chaotic path-planning methods, providing more rapid and uniform coverage with the possibility of controlling the covered area using tunable parameters. In addition, this study revealed the high dependence of the coverage rate on the starting point. To investigate how the coverage rate depends on the choice of chaotic map, we implemented six different PRBGs using various chaotic maps. The obtained results can be efficiently used for solving path-planning tasks in both real-life and virtual (e.g., video games) applications.

Suggested Citation

  • Dmitriy Kvitko & Vyacheslav Rybin & Oleg Bayazitov & Artur Karimov & Timur Karimov & Denis Butusov, 2024. "Chaotic Path-Planning Algorithm Based on Courbage–Nekorkin Artificial Neuron Model," Mathematics, MDPI, vol. 12(6), pages 1-20, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:892-:d:1358981
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    References listed on IDEAS

    as
    1. Sun, Fuyan & Liu, Shutang, 2009. "Cryptographic pseudo-random sequence from the spatial chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2216-2219.
    2. Jianfang Lian & Wentao Yu & Kui Xiao & Weirong Liu, 2020. "Cubic Spline Interpolation-Based Robot Path Planning Using a Chaotic Adaptive Particle Swarm Optimization Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-20, February.
    3. Zhao, Liang & Liao, Xiaofeng & Xiao, Di & Xiang, Tao & Zhou, Qing & Duan, Shukai, 2009. "True random number generation from mobile telephone photo based on chaotic cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1692-1699.
    4. Seadawy, Aly R. & Ali, Safdar & Rizvi, Syed T.R., 2022. "On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Al-Raeei, Marwan, 2021. "Applying fractional quantum mechanics to systems with electrical screening effects," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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