Core Concepts
Investigating equilibrium strategies in pursuit-evasion games on a sphere.
Abstract
The content delves into the pursuit-evasion game dynamics on a sphere, exploring the equilibrium intercept point and Apollonius domain. It discusses the relationship between agents' motions, geodesics, and optimal strategies. The paper presents theoretical derivations, applications to multiple pursuers scenarios, and target guarding games. Key concepts include Hamilton-Jacobi-Isaacs equation, Apollonius circle/domain, and geodesic paths.
I. Introduction and Background:
Classical works on planar differential pursuit-evasion games.
Study of pursuit-evasion game on a sphere.
Relation of equilibrium intercept point to Apollonius domain.
II. Problem Description:
Two agents restricted to motion on a spherical surface.
Pursuer (P) and slower evader (E) defined by positions and velocities.
Control variables for P and E in pursuit-evasion game.
III. Pursuit-Evasion Equilibrium Strategies:
Derivation of angular distance rate between P and E.
Equilibrium strategies for P and E based on Hamilton-Jacobi-Isaacs equation.
Special cases when α = 0 or π analyzed.
IV. Apollonius Domain and Intercept Point:
Definition of Apollonius domain A on the sphere.
Relationship between relative position α, intercept points, and boundary of A.
V. Results:
Illustration of Apollonius domain for different scenarios.
Application to two-pursuer scenarios with cooperative strategies.
VI. Conclusion:
Summary of findings in pursuit-evasion games on a sphere.
Future research directions in multi-agent scenarios on spherical geometry.
Stats
This paper is based at AFRL Control Science Center supported by AFOSR LRIR 24RQCOR002.
Quotes
"The goal of P is to minimize J, i.e., time to capture."
"Equilibrium strategies are optimal for minimizing capture time."
"Apollonius domain exhibits similar properties to the planar case."