On the equivalence of pursuer strategies and the lack of nash equilibrium in a visibility pursuit-evasion game |
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| Institution: | 1. Centro de Investigación en Matemáticas (CIMAT), Guanajuato, México;2. Consejo Nacional de Ciencia y Tecnología (CONACYT), Mexico City, México;1. College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;2. Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education, Anhui Polytechnic University, Wuhu, 241000, China;3. School of Marine Engineering, Jimei University, China;4. NARI Group Corporation (State Grid Electric Power Research Institute), Nanjing 211000, China;1. Project Assistant, Department of Aerosapce engineering, IISc, Bangalore, India;2. Professor, Department of Aerosapce engineering, IISc, Bangalore, India;1. School of Electrical Engineering, Guangxi University, Nanning 530004, China;2. Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, China;3. School of Mathematics and Information Science, Guangxi University, Nanning 530004, China;4. Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, Guangxi University, China;1. Department of Systems Science, School of Mathematics, Southeast University, Nanjing 210096, China;2. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China;3. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, P.R. China |
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| Abstract: | This work addresses a finite-time visibility-based target tracking problem. The aim of the pursuer is to keep the evader within its field of view, while the evader wants to escape the pursuer’s surveillance. Some main contributions of the work are the following: (1) It is proven that minimizing the travel time is equivalent to maximizing the definite integral of the angular speed of the border of the pursuer visibility region. (2) Using Euclidean geometry and set theory methods, the optimality of the player trajectories is demonstrated. (3) It is shown that the motion strategies provided in previous works are not always in Nash equilibrium. |
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