Optimal Role Assignment for Multiplayer Reach-Avoid Differential Games in 3D Space

TL;DR

An optimal solution for the particular case of $n=m=1$ is provided and it is extended to a more general scenario of $n\geq m$ via an optimal role assignment algorithm based on a linear program.

Abstract

In this article an $n$-pursuer versus $m$-evader reach-avoid differential game in 3D space is studied. A team of evaders aim to reach a stationary target while avoiding capture by a team of pursuers. The multiplayer scenario is formulated in a differential game framework. This article provides an optimal solution for the particular case of $n=m=1$ and extends it to a more general scenario of $n\geq m$ via an optimal role assignment algorithm based on a linear program. Consequently, the pursuer and the evader winning regions, and the Value of the game are analytically characterized providing optimal strategies of the players in state feedback form.

Figures (4)

• Figure 1: Pathological cases
• Figure 2: Trajectories of a 3v3 game in $\mathsf R_P$
• Figure 3: Trajectories of a 3v3 game in $\mathsf R_E$
• Figure 4: Optimal assignments for dispersal surface

Theorems & Definitions (43)

• Remark 1
• Lemma 1
• proof
• Lemma 2
• proof
• Theorem 1: Pursuer winning region
• proof
• Remark 2
• Theorem 2: Evader winning region
• proof