Graph factorization methods in linear formation control

Linear formation control is the most simple formation control strategy based on relative states. However, as the number of agents becomes larger, the formation graph becomes more complex and the computation will be increased. The Cartesian product of graphs and the factorization lemma indicates that a complex, connected graph can be decomposed as a Cartesian product of smaller graphs and the system dynamics will thus be simplified by this factorization approach. This work is an extension of the linear formation control strategy and has been examined effective.