Distributed Flocking Control with Ellipsoidal Level Sets

This paper proposes a framework for two- and three-dimensional distributed flocking control based on potential functions with ellipsoidal level sets. Contrary to most flocking frameworks in the existing literature, the presented approach allows for tuning the inter-agent distances in different directions individually. By defining a desired ellipsoidal lattice configuration based on an elliptic transformation matrix, the proposed flocking protocol can be formulated as a generalization of established spherical flocking protocols. Furthermore, it is shown how standard stability analysis can be extended seamlessly to the proposed framework without additional difficulties or assumptions. Simulation scenarios demonstrate the superior performance of the proposed scheme compared to existing ones.