Planning and Formulations in Pursuit-Evasion: Keep-away Games and Their Strategies

TL;DR

This paper investigates pursuit-evasion keep-away games with stationary and dynamic anchors, introducing algorithms to determine winning strategies under velocity and acceleration constraints, bridging kinematic and dynamic problem solutions.

Contribution

It presents a geometric branch-and-bound algorithm for stationary anchors and extends it to dynamic constraints, enhancing pursuit-evasion strategy analysis.

Findings

Algorithm effectively solves stationary anchor pursuit-evasion problems.

Extension to dynamic constraints allows analysis of more realistic pursuit scenarios.

The approach bridges kinematic and dynamic problem-solving methods.

Abstract

We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the anchors. These anchors may or may not be stationary. When the velocity of the pursuers is limited and considered low compared to the evaders, we are interested in whether a winning strategy exists for the pursuers or the evaders, or the game will draw. When the anchors are stationary, we show an algorithm that can help answer the above question. The primary motivation for this study is to explore the boundaries between kinematic and dynamic constraints. In particular, whether the solution of the kinematic problem can be used to speed up the search for the problems with dynamic constraints and how to discretize the problem to utilize such relations best. In this work, we show that a geometric branch-and-bound type of approach can be used to solve the stationary anchor problem, and the approach and the solution can be extended to solve the dynamic problem where the pursuers have dynamic constraints, including velocity and acceleration bounds.