Noncooperative Herding With Control Barrier Functions: Theory and Experiments

In this paper, we consider the problem of protecting a high-value unit from inadvertent attack by a group of agents using defending robots. Specifically, we develop a control strategy for the defending agents that we call "dog robots" to prevent a flock of "sheep agents" from breaching a protected zone. The sheep agents have no knowledge about the presence of the high-value unit and follow flocking dynamics to reach their goal. We take recourse to control barrier functions to pose this problem and exploit the interaction dynamics between the sheep and dogs to find dogs’ velocities that result in the sheep getting repelled from the zone. We solve a QP reactively that incorporates the defending constraints to compute the desired velocities for all dogs. Our proposed framework also allows for simultaneous inclusion of multiple protected zones by augmenting constraints on dogs’ velocities. We provide a theoretical proof of the feasibility of our strategy for the one dog/one sheep case. Additionally, we provide empirical results of two dogs defending the zone from up to ten sheep, averaged over a hundred simulations, and report high success rates. We also demonstrate this algorithm experimentally on non-holonomic robots. Videos of these results are available at https://tinyurl.com/4dj2kjwx.