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Pursuit-Evasion on a Sphere and When It Can Be Considered Flat

Document Type

Conference Proceeding

Publication Date

3-22-2024

Abstract

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.

Comments

The "Link to Full Text" on this page opens or saves the preprint version of the paper as hosted at the arXiv e-print repository, as cited below.

This is an Open Access paper published in the arXiv eprint repository and distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.CC BY-NC-ND 4.0

The paper is to be submitted to 2024 Conference on Decision and Control in Milan, Italy. (Held in December 2024). https://cdc2024.ieeecss.org/.

DOI

arxiv:2403.15188

Source Publication

arXiv.org e-print repository

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