Stable flocking of multiple inertial agents on balanced graphs

We consider the flocking of multiple agents which have significant inertias and evolve on a balanced information graph. 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 formation, 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 formation is exponentially stabilized to a desired shape, while all the agents´ velocities converge to the centroid velocity that is also shown to be time-invariant. This result still holds for slowly-switching balanced information graphs. Simulation is performed to validate the theory