Multiagent Planning and Control for Swarm Herding in 2-D Obstacle Environments Under Bounded Inputs

Herding an Adversarial Swarm in Three-dimensional Spaces

“…. Additionally, we require ρ sn ≥ ρ ac + b d where b d is tracking the error [1]. Due to practical limit of R max sn on the edge length, to obtain a formation with minimal number of defenders, ρ sn should be equal to its minimal value so…”

“…For instance, there may be cases where a group of adversarial robots is deployed nearby some safety-critical infrastructure (protected area) and considered as a threat. In our prior work [1], [3], we developed a method called 'StringNet Herding' in which a group of defending agents (defenders) herds the adversarial swarm away from the protected area by enclosing it in a closed formation of string-like barriers, called StringNet. We assumed that the risk-averse agents of the adversarial swarm tend to move away from the 2D StringNet formation formed by defending agents, and that the motion of all the agents is constrained to a plane of a fixed altitude.…”

“…1) Related work: Although most of the herding algorithms are developed for 2D scenarios, there are several approaches for 3D herding as well. The herding approaches, namely: n-wavefront herding [4], potential field approach [5], potential cage approach [6], switched system approach [7] that are cited in [1] also provide extensions to 3D environments or some hint to extend the 2D laws to the 3D environment. However, the 3D extensions also suffer from the same issues listed in [1].…”

“…2) Overview: In this paper, we build on the 2D StringNet herding approach [1] under the similar assumption of risk-averse adversarial attackers, i.e., attackers that adjust their course to avoid any obstacle. Similar to 2D StringNet herding, we propose 3D-StringNet herding.…”

“…We design three 3D formations of the defenders namely planar, hemispherical, spherical that are required to be achieved in the phases discussed above in order to effectively enclose the attackers and herd them to a safe area. The control laws designed in [1] are extended to 3D by considering 3D rigid body dynamics. We provide conditions on the initial positions of the attackers for which the defenders are able to achieve a specified formation at a point on the expected path (shortest path to the protected area) of the attackers before the attackers could reach that point.…”