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

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 $n\ge m$ 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.