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 designing a connectivity control law for agents with configuration spaces R3R3 and SO(3)SO(3) that is invariant under the action of the special Euclidean group SE(3)SE(3) and the special orthogonal group SO(3)SO(3), respectively. Therefore, the dynamics of such multi-agent systems is amenable to be reduced by these group actions. We then utilize the Lagrange–Poincaré 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.