Herding an Adversarial Swarm in Three-dimensional Spaces

Abstract: This paper presents a defense approach to safeguard a protected area against an attack by a swarm of adversarial agents in three-dimensional (3D) space. We extend our 2D `StringNet Herding' approach, in which a closed formation of string-barriers is established around the adversarial swarm to confine their motion and herd them to a safe area, to 3D spaces by introducing 3D-StringNet. 3D-StringNet is a closed 3D formation of triangular net-like barriers. We provide a systematic approach to generate three types of 3D formations that are used in the 3D herding process and modifications to the finite-time convergent control laws developed in \cite{chipade2020swarmherding} that are required for a 3D environment. Furthermore, for given initial positions of the defenders, we provide conditions on the initial positions of the attackers for which the defenders are guaranteed to gather as a specified formation at a position on the shortest path of the attackers to the protected area before attackers reach there.