Leaderless collective motions in affine formation control

TL;DR

This paper introduces a distributed method for inducing various collective motions in multi-agent systems without leaders, enabling complex shape transformations through local interactions.

Contribution

It presents a novel affine formation control technique that achieves diverse collective motions by modifying Laplacian weights, avoiding leader-follower strategies.

Findings

Proves global stability of the proposed method.

Demonstrates effectiveness through numerical simulations.

Enables complex shape transformations like rotation, scaling, and shearing.

Abstract

This paper proposes a novel distributed technique to induce collective motions in affine formation control. Instead of the traditional leader-follower strategy, we propose modifying the original weights that build the Laplacian matrix so that a designed steady-state motion of the desired shape emerges from the agents' local interactions. The proposed technique allows a rich collection of collective motions such as rotations around the centroid, translations, scalings, and shearings of a reference shape. These motions can be applied in useful collective behaviors such as \emph{shaped} consensus (the rendezvous with a particular shape), escorting one of the team agents, or area coverage. We prove the global stability and effectiveness of our proposed technique rigorously, and we provide some illustrative numerical simulations.