Pursuit-Evasion on a Sphere and When It Can Be Considered Flat
arxiv(2024)
摘要
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.
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