2024/03/22 by Dejan Milutinović, Milutinovic, Dejan, Alexander Von Moll +9
Engineering · #37D40 #49L12 #49Q10 #58E10 #86A30 #91A23 #Algebraic Geometry (math.AG) #Computational Fluid Dynamics and Aerodynamics #Differential Geometry (math.DG) #FOS: Electrical engineering #FOS: Mathematics #Guidance and Control Systems #Optimization and Control (math.OC) #Sports Dynamics and Biomechanics #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2403.15188
openalex publication_date 2024/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.