Formation control with pole placement for multi-agent systems

TL;DR

This paper presents a decentralized pole placement method for formation control in multi-agent systems with single integrators, enabling agents to achieve and maintain a desired formation using local feedback and communication.

Contribution

It introduces a novel decentralized approach for pole placement and formation encoding in multi-agent systems with directed communication graphs.

Findings

Agents can place poles at desired locations using local feedback.

Formation encoding can be computed in a decentralized manner.

The method ensures formation stability with minimal control inputs.

Abstract

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.