Formation control with pole placement for multi-agent systems

The problem of distributed controller synthesis for formation control of multi-agent systems is considered. The agents (single integrators) communicate over a communication graph and a decentralized linear feedback structure is assumed. One of the agents is designated as the leader. If the communication graph contains a directed spanning tree with the leader node as the root, then it is possible to place the poles of the ensemble system with purely local feedback controller gains. Given a desired formation, first one of the poles is placed at the origin. Then it is shown that the inter-agent weights can be independently adjusted to assign an eigenvector corresponding to the formation positions, to the zero eigenvalue. Then, only the leader input is enough to bring the agents to the desired formation and keep it there with no further inputs. Moreover, given a formation, the computation of the inter-agent weights that encode the formation information, can be calculated in a decentralized fashion using only local information.