Stable flocking of multiple inertial agents on balanced graphs

In this note, we consider the flocking of multiple agents which have significant inertias and evolve on a balanced information graph. Here, by flocking, we mean that all the agents move with a common velocity while keeping a certain desired internal group shape. We first show that flocking algorithms that neglect agents' inertial effect can cause unstable group behavior. To incorporate this inertial effect, we use the passive decomposition, which decomposes the closed-loop group dynamics into two decoupled systems: a shape system representing the internal group shape and a locked system describing the motion of the center-of-mass. Then, analyzing the locked and shape systems separately with the help of graph theory, we propose a provably stable flocking control law, which ensures that the internal group shape is exponentially stabilized to a desired one, while all the agents' velocities converge to the centroid velocity that is also shown to be time-invariant. This result still holds for slow-switching balanced information graphs. Simulation is performed to validate the theory.