Global swarming while preserving connectivity via Lagrange-Poincarè equations

In this paper, we exploit symmetry properties of multi-agent robot systems to design control laws that preserve connectivity while swarming. We start by showing that the connectivity controller is invariant under the action of the special Euclidean group SE(3) and therefore is amenable to reduction of the dynamics by this action. We then utilize the reduced Euler-Lagrange equations that split the Euler-Lagrange equations for the multi-agent system into horizontal and vertical parts. The invariance of the connectivity controller implies that its control effort has zero vertical component. We then use the resulting vertical equations of motion to design a control law that asymptotically stabilizes the centroid and the orientation of the swarm at a desired pose.