Pursuit-Evasion Between a Velocity-Constrained Double-Integrator Pursuer and a Single-Integrator Evader

TL;DR

This paper analyzes a pursuit-evasion game involving a velocity- and acceleration-constrained pursuer and a velocity-constrained evader, deriving optimal strategies and demonstrating conditions for successful capture.

Contribution

It introduces a comprehensive analysis of pursuit-evasion strategies for a double integrator pursuer and a single integrator evader, including geometric and numerical methods for strategy derivation.

Findings

Pursuer can capture evader if its maximum speed exceeds evader’s speed.

Optimal strategies are derived and validated as Nash equilibria.

Simulation results confirm strategy effectiveness.

Abstract

We study a pursuit-evasion game between a double integrator-driven pursuer with bounded velocity and bounded acceleration and a single integrator-driven evader with bounded velocity in a two-dimensional plane. The pursuer's goal is to capture the evader in the shortest time, while the evader attempts to delay the capture. We analyze two scenarios based on whether the capture can happen before the pursuer's speed reaches its maximum. For the case when the pursuer can capture the evader before its speed reaches its maximum, we use geometric methods to obtain the strategies for the pursuer and the evader. For the case when the pursuer cannot capture the evader before its speed reaches its maximum, we use numerical methods to obtain the strategies for the pursuer and the evader. In both cases, we demonstrate that the proposed strategies are optimal in the sense of Nash equilibrium through the Hamilton-Jacobi-Isaacs equation, and the pursuer can capture the evader as long as as its maximum speed is larger than that of the evader. Simulation experiments illustrate the effectiveness of the strategies.