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.
DOI
arxiv:2403.15188
Source Publication
arXiv.org e-print repository
Recommended Citation
Milutinovic, D., Von Moll, A., Manyam, S. G., Casbeer, D. W., Weintraub, I. E., & Pachter, M. (2024). Pursuit-evasion on a sphere and when it can be considered flat (No. arXiv:2403.15188). arXiv. https://doi.org/10.48550/arXiv.2403.15188
arXiv:2403.15188 [math.OC]
Comments
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The paper is to be submitted to 2024 Conference on Decision and Control in Milan, Italy. (Held in December 2024). https://cdc2024.ieeecss.org/.