Pursuit-Evasion on a Sphere and When It Can Be Considered Flat
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913278346657792 |
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| author | Milutinovic, Dejan Von Moll, Alexander Manyam, Satyanarayana G. Casbeer, David W. Weintraub, Isaac E. Pachter, Meir |
| author_facet | Milutinovic, Dejan Von Moll, Alexander Manyam, Satyanarayana G. Casbeer, David W. Weintraub, Isaac E. Pachter, Meir |
| contents | In classical works on a planar differential pursuit-evasion game with a faster pursuer, the intercept point resulting from the equilibrium strategies lies on the Apollonius circle. This property was exploited for the construction of the equilibrium strategies for two faster pursuers against one evader. Extensions for planar multiple-pursuer single-evader scenarios have been considered. We study a pursuit-evasion game on a sphere and the relation of the equilibrium intercept point to the Apollonius domain on the sphere. The domain is a generalization of the planar Apollonius circle set. We find a condition resulting in the intercept point belonging to the Apollonius domain, which is the characteristic of the planar game solution. Finally, we use this characteristic to discuss pursuit and evasion strategies in the context of two pursuers and a single slower evader on the sphere and illustrate it using numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_15188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pursuit-Evasion on a Sphere and When It Can Be Considered Flat Milutinovic, Dejan Von Moll, Alexander Manyam, Satyanarayana G. Casbeer, David W. Weintraub, Isaac E. Pachter, Meir Optimization and Control Systems and Control Algebraic Geometry Differential Geometry 58E10, 86A30, 37D40, 91A23, 49L12, 49Q10 In classical works on a planar differential pursuit-evasion game with a faster pursuer, the intercept point resulting from the equilibrium strategies lies on the Apollonius circle. This property was exploited for the construction of the equilibrium strategies for two faster pursuers against one evader. Extensions for planar multiple-pursuer single-evader scenarios have been considered. We study a pursuit-evasion game on a sphere and the relation of the equilibrium intercept point to the Apollonius domain on the sphere. The domain is a generalization of the planar Apollonius circle set. We find a condition resulting in the intercept point belonging to the Apollonius domain, which is the characteristic of the planar game solution. Finally, we use this characteristic to discuss pursuit and evasion strategies in the context of two pursuers and a single slower evader on the sphere and illustrate it using numerical simulations. |
| title | Pursuit-Evasion on a Sphere and When It Can Be Considered Flat |
| topic | Optimization and Control Systems and Control Algebraic Geometry Differential Geometry 58E10, 86A30, 37D40, 91A23, 49L12, 49Q10 |
| url | https://arxiv.org/abs/2403.15188 |