Brachistochrone Pursuit - Evasion Games and Riemann-Finsler Geometry

TL;DR

This paper introduces a geometric framework using Riemann-Finsler geometry to analyze pursuit-evasion differential games, providing optimal strategies through a closed-loop control approach inspired by the Brachistochrone problem.

Contribution

It presents a novel geometric method for solving pursuit-evasion games by integrating Riemann-Finsler geometry with optimal control theory.

Findings

Optimal pursuit strategies derived using Riemann-Finsler geometry

A closed-loop control approach for pursuit-evasion games

Connection to Brachistochrone problem enhances understanding

Abstract

A geometric approach to differential game theory is illustrated. The parallel pursuit is considered as a two-player zero-sum differential game. The optimal strategies of each player is designed based on Riemann-Finsler geometry. Our approach incorporates a closed loop optimal control and the presentation is familiar with a Brachistochrone type problem.