procyberВестник кибернетикиProceedings in Cybernetics1999-7604Бюджетное учреждение высшего образования Ханты-Мансийского автономного округа – Югры «Сургутский государственный университет»10.35266/1999-7604-2026-2-10procyber-771Research ArticleФИЗИКО-МАТЕМАТИЧЕСКИЕ НАУКИPhysics and MathematicsНейросетевое оценивание состояния и оптимизационный синтез распределенного управления роем мобильных роботов в условиях неопределенностиNeural state estimation and optimization synthesis of flocking control for mobile robots swarm under uncertaintyhttps://orcid.org/0000-0002-7028-9407КондратьевС. Е.KondratevS. E.

аспирант

Postgraduate

razthepsycho@yandex.ruhttps://orcid.org/0009-0002-3274-0444КазюраН. В.KazyuraN. V.

магистр

Master

https://orcid.org/0000-0003-2887-3703МещеряковВ. Н.MeshcheryakovV. N.

доктор технических наук, профессор

Doctor of Sciences (Engineering), Professor

Липецкий государственный технический университет, ЛипецкРоссияLipetsk State Technical University, LipetskRussian Federation20260409202625292101Copyright © Кондратьев С.Е., Казюра Н.В., Мещеряков В.Н., 20262026Кондратьев С.Е., Казюра Н.В., Мещеряков В.Н.Kondratev S.E., Kazyura N.V., Meshcheryakov V.N.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.vestcyber.ru/jour/article/view/771

Рассмотрена задача распределенного управления группой мобильных роботов, осуществляющих коллективное движение в трехмерной среде с препятствиями при ограниченном обмене информацией между агентами. Актуальность обусловлена необходимостью координации роя в условиях эпизодической доступности данных о состоянии соседей. Целью исследования является разработка распределенного регулятора, реализующего правила коллективного движения и обеспечивающего безопасность перемещения при неполной наблюдаемости. Предложен метод, объединяющий обучаемый оценщик состояния на основе полносвязной нейронной сети, аппроксимирующей фильтр частиц с одновременной оценкой неопределенности, и оптимизационный регулятор на основе функций барьерного управления и функций управления Ляпунова. По результатам моделирования установлено, что нейросетевой оценщик обеспечивает точность, сопоставимую с классическими методами фильтрации, при вычислительных затратах на один-два порядка ниже. Взвешенный центроид, учитывающий надежность оценок, уменьшает ошибку координации. Результаты применимы при проектировании систем управления многороботными группами.

The paper addresses the flocking control problem for groups of mobile robots collectively moving in a three-dimensional environment with obstacles under limited communication between agents. The research relevance lies in the need for swarm coordination given intermittent interaction between an agent and those inside its communication range, i.e. neighbors. In this article, the goal is to create a flocking controller that adheres to collective motion principles while maintaining safety in conditions of limited visibility. The authors propose a method that integrates a learned state estimator based on a fully connected neural network, approximating the particle filter with simultaneous uncertainty evaluation, and an optimization regulator with a control barrier function and a control-Lyapunov function. The simulation reveals that the neural network estimator ensures accuracy comparable to traditional filtration techniques at a computational cost one to two orders of magnitude lower. In addition, the weighted centroid, which considers estimation reliability, reduces the possibility of coordination errors. Results can be applied in designing multi-robot group control systems.

распределенное управлениерой мобильных роботовоценивание состояниянейронные сетифункции барьерного управленияфункции управления Ляпуноваколлективное движениефильтр частицоценка неопределенностиflocking controlmobile robots swarmstate estimationneural networkscontrol barrier functioncontrol-Lyapunov functioncollective motionparticle filteruncertainty evaluationReferencesBartolomei L., Teixeira L., Chli M. Fast multi-UAV decentralized exploration of forests // IEEE Robotics and Automation Letters. 2023. Vol. 8, no. 9. P. 5576–5583. https://doi.org/10.1109/LRA.2023.3296037.Bartolomei L., Teixeira L., Chli M. Fast multi-UAV decentralized exploration of forests // IEEE Robotics and Automation Letters. 2023. Vol. 8, no. 9. P. 5576–5583. https://doi.org/10.1109/LRA.2023.3296037.Ali Z. A., Alkhammash E. H., Hasan R. State-of-the-art flocking strategies for the collective motion of multi-robots // Machines. 2024. Vol. 12, no. 10. https://doi.org/10.3390/machines12100739.Ali Z. A., Alkhammash E. H., Hasan R. State-of-the-art flocking strategies for the collective motion of multi-robots // Machines. 2024. Vol. 12, no. 10. https://doi.org/10.3390/machines12100739.Kim J., Kim S., Ju C. et al. Unmanned aerial vehicles in agriculture: A review of perspective of platform, control, and applications // IEEE Access. 2019. Vol. 7. P. 105100–105115. https://doi.org/10.1109/ACCESS.2019.2932119.Kim J., Kim S., Ju C. et al. Unmanned aerial vehicles in agriculture: A review of perspective of platform, control, and applications // IEEE Access. 2019. Vol. 7. P. 105100–105115. https://doi.org/10.1109/ACCESS.2019.2932119.Shao X., Zhang J., Zhang W. Distributed cooperative surrounding control for mobile robots with uncertainties and aperiodic sampling // IEEE Transactions on Intelligent Transportation Systems. 2022. Vol. 23, no. 10. P. 18951–18961. https://doi.org/10.1109/TITS.2022.3189201.Shao X., Zhang J., Zhang W. Distributed cooperative surrounding control for mobile robots with uncertainties and aperiodic sampling // IEEE Transactions on Intelligent Transportation Systems. 2022. Vol. 23, no. 10. P. 18951–18961. https://doi.org/10.1109/TITS.2022.3189201.Brunacci V., De Angelis A., Costante G. et al. Development and analysis of a UWB relative localization system // IEEE Transactions on Instrumentation and Measurement. 2023. Vol. 72. P. 1–12. https://doi.org/10.1109/TIM.2023.3265107.Brunacci V., De Angelis A., Costante G. et al. Development and analysis of a UWB relative localization system // IEEE Transactions on Instrumentation and Measurement. 2023. Vol. 72. P. 1–12. https://doi.org/10.1109/TIM.2023.3265107.Walter V., Staub N., Franchi A. et al. UVDAR System for visual relative localization with application to leader–follower formations of multirotor UAVs // IEEE Robotics and Automation Letters. 2019. Vol. 4, no. 3. P. 2637–2644. https://doi.org/10.1109/LRA.2019.2901683.Walter V., Staub N., Franchi A. et al. UVDAR System for visual relative localization with application to leader–follower formations of multirotor UAVs // IEEE Robotics and Automation Letters. 2019. Vol. 4, no. 3. P. 2637–2644. https://doi.org/10.1109/LRA.2019.2901683.Salimpour S., Morón P. T., Yu X. et al. Exploiting redundancy for UWB anomaly detection in infrastructure-free multi-robot relative localization // Frontiers in Robotics and AI. 2023. Vol. 10. https://doi.org/10.3389/frobt.2023.1190296.Salimpour S., Morón P. T., Yu X. et al. Exploiting redundancy for UWB anomaly detection in infrastructure-free multi-robot relative localization // Frontiers in Robotics and AI. 2023. Vol. 10. https://doi.org/10.3389/frobt.2023.1190296.Li B., Wen S., Yan Z. et al. A survey on the control Lyapunov function and control barrier function for nonlinear-affine control systems // IEEE/CAA Journal of Automatica Sinica. 2023. Vol. 10, no. 3. P. 584–602. https://doi.org/10.1109/JAS.2023.123075.Li B., Wen S., Yan Z. et al. A survey on the control Lyapunov function and control barrier function for nonlinear-affine control systems // IEEE/CAA Journal of Automatica Sinica. 2023. Vol. 10, no. 3. P. 584–602. https://doi.org/10.1109/JAS.2023.123075.Duan H., Huo M., Fan Y. From animal collective behaviors to swarm robotic cooperation // National Science Review. 2023. Vol. 10, no. 5. https://doi.org/10.1093/nsr/nwad040.Duan H., Huo M., Fan Y. From animal collective behaviors to swarm robotic cooperation // National Science Review. 2023. Vol. 10, no. 5. https://doi.org/10.1093/nsr/nwad040.Long K., Dhiman V., Leok M. et al. Safe control synthesis with uncertain dynamics and constraints // IEEE Robotics and Automation Letters. 2022. Vol. 7, no. 3. P. 7295–7302. https://doi.org/10.1109/LRA.2022.3182544.Long K., Dhiman V., Leok M. et al. Safe control synthesis with uncertain dynamics and constraints // IEEE Robotics and Automation Letters. 2022. Vol. 7, no. 3. P. 7295–7302. https://doi.org/10.1109/LRA.2022.3182544.Zhang S., So O., Garg K. et al. GCBF+: A neural graph control barrier function framework for distributed safe multiagent control // IEEE Transactions on Robotics. 2025. Vol. 41. P. 1533–1552. https://doi.org/10.1109/TRO.2025.3530348.Zhang S., So O., Garg K. et al. GCBF+: A neural graph control barrier function framework for distributed safe multiagent control // IEEE Transactions on Robotics. 2025. Vol. 41. P. 1533–1552. https://doi.org/10.1109/TRO.2025.3530348.Nguyen L. V. Swarm intelligence-based multi-robotics: A comprehensive review // AppliedMath. 2024. Vol. 4, no. 4. P. 1192–1210. https://doi.org/10.3390/appliedmath4040064.Nguyen L. V. Swarm intelligence-based multi-robotics: A comprehensive review // AppliedMath. 2024. Vol. 4, no. 4. P. 1192–1210. https://doi.org/10.3390/appliedmath4040064.Dawson C., Gao S., Fan C. Safe Control with learned certificates: A survey of neural Lyapunov, barrier, and contraction methods for robotics and control // IEEE Transactions on Robotics. 2023. Vol. 39, no. 3. P. 1749–1767. https://doi.org/10.1109/TRO.2022.3232544.Dawson C., Gao S., Fan C. Safe Control with learned certificates: A survey of neural Lyapunov, barrier, and contraction methods for robotics and control // IEEE Transactions on Robotics. 2023. Vol. 39, no. 3. P. 1749–1767. https://doi.org/10.1109/TRO.2022.3232544.Ge R., Lee M., Radhakrishnan V. et al. Vision-based relative detection and tracking for teams of micro aerial vehicles // 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), October 23–27, 2022, Kyoto, Japan. New York, NY : Institute of Electrical and Electronics Engineers, 2022. P. 380–387. https://doi.org/10.1109/IROS47612.2022.9981115.Ge R., Lee M., Radhakrishnan V. et al. Vision-based relative detection and tracking for teams of micro aerial vehicles // 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), October 23–27, 2022, Kyoto, Japan. New York, NY : Institute of Electrical and Electronics Engineers, 2022. P. 380–387. https://doi.org/10.1109/IROS47612.2022.9981115.Ávila-Martínez E. J., Barajas-Ramírez J. G. Flocking motion in swarms with limited sensing radius and heterogeneous input constraints // Journal of the Franklin Institute. 2021. Vol. 358, no. 4. P. 2346–2366. https://doi.org/10.1016/j.jfranklin.2021.01.022.Ávila-Martínez E. J., Barajas-Ramírez J. G. Flocking motion in swarms with limited sensing radius and heterogeneous input constraints // Journal of the Franklin Institute. 2021. Vol. 358, no. 4. P. 2346–2366. https://doi.org/10.1016/j.jfranklin.2021.01.022.Zhu P., Dai W., Yao W. et al. Multi-robot flocking control based on deep reinforcement learning // IEEE Access. 2020. Vol. 8. P. 150397–150406. https://doi.org/10.1109/ACCESS.2020.3016951.Zhu P., Dai W., Yao W. et al. Multi-robot flocking control based on deep reinforcement learning // IEEE Access. 2020. Vol. 8. P. 150397–150406. https://doi.org/10.1109/ACCESS.2020.3016951.

The authors declare that there are no conflicts of interest present.