Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory
An important action-planning problem is considered for participants of the pursuit–evasion game with multiple pursuers and a high-speed evader. The objects of study are mobile robotic systems and specifically small unmanned aerial vehicles (UAVs). The problem is complicated by the presence of signif...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/23/4869 |
| _version_ | 1797399823295447040 |
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| author | Mikhail Khachumov Vyacheslav Khachumov |
| author_facet | Mikhail Khachumov Vyacheslav Khachumov |
| author_sort | Mikhail Khachumov |
| collection | DOAJ |
| description | An important action-planning problem is considered for participants of the pursuit–evasion game with multiple pursuers and a high-speed evader. The objects of study are mobile robotic systems and specifically small unmanned aerial vehicles (UAVs). The problem is complicated by the presence of significant wind loads that affect the trajectory and motion strategies of the players. It is assumed that UAVs have limited computing resources, which involves the use of computationally fast and real-time heuristic approaches. A novel and rapidly developing intelligent–geometric theory is applied to address the discussed problem. To accurately calculate the points of the participant’s rapprochement, we use a geometric approach based on the construction of circles or spheres of Apollonius. Intelligent control methods are applied to synthesize complex motion strategies of participants. A method for quickly predicting the evader’s trajectory is proposed based on a two-layer neural network containing a new activation function of the “s-parabola” type. We consider a special backpropagation training scheme for the model under study. A simulation scheme has been developed and tested, which includes mathematical models of dynamic objects and wind loads. The conducted simulations on pursuit–evasion games in close to real conditions showed the prospects and expediency of the presented approach. |
| first_indexed | 2024-03-09T01:46:39Z |
| format | Article |
| id | doaj.art-1a6bf119fdbe44f8ac8a4a56d37730bd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T01:46:39Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1a6bf119fdbe44f8ac8a4a56d37730bd2023-12-08T15:22:00ZengMDPI AGMathematics2227-73902023-12-011123486910.3390/math11234869Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control TheoryMikhail Khachumov0Vyacheslav Khachumov1Ailamazyan Program Systems Institute of Russian Academy of Sciences, 152021 Pereslavl-Zalessky, RussiaAilamazyan Program Systems Institute of Russian Academy of Sciences, 152021 Pereslavl-Zalessky, RussiaAn important action-planning problem is considered for participants of the pursuit–evasion game with multiple pursuers and a high-speed evader. The objects of study are mobile robotic systems and specifically small unmanned aerial vehicles (UAVs). The problem is complicated by the presence of significant wind loads that affect the trajectory and motion strategies of the players. It is assumed that UAVs have limited computing resources, which involves the use of computationally fast and real-time heuristic approaches. A novel and rapidly developing intelligent–geometric theory is applied to address the discussed problem. To accurately calculate the points of the participant’s rapprochement, we use a geometric approach based on the construction of circles or spheres of Apollonius. Intelligent control methods are applied to synthesize complex motion strategies of participants. A method for quickly predicting the evader’s trajectory is proposed based on a two-layer neural network containing a new activation function of the “s-parabola” type. We consider a special backpropagation training scheme for the model under study. A simulation scheme has been developed and tested, which includes mathematical models of dynamic objects and wind loads. The conducted simulations on pursuit–evasion games in close to real conditions showed the prospects and expediency of the presented approach.https://www.mdpi.com/2227-7390/11/23/4869pursuit–evasion gamesintelligent controlgeometric controlunmanned aerial vehiclepath planningtrajectory tracking |
| spellingShingle | Mikhail Khachumov Vyacheslav Khachumov Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory Mathematics pursuit–evasion games intelligent control geometric control unmanned aerial vehicle path planning trajectory tracking |
| title | Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory |
| title_full | Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory |
| title_fullStr | Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory |
| title_full_unstemmed | Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory |
| title_short | Modeling the Solution of the Pursuit–Evasion Problem Based on the Intelligent–Geometric Control Theory |
| title_sort | modeling the solution of the pursuit evasion problem based on the intelligent geometric control theory |
| topic | pursuit–evasion games intelligent control geometric control unmanned aerial vehicle path planning trajectory tracking |
| url | https://www.mdpi.com/2227-7390/11/23/4869 |
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