Leaderless collective motions in affine formation control
This addresses the challenge of enabling flexible collective behaviors in multi-agent systems, such as shaped consensus or area coverage, but is incremental as it builds on existing affine formation control methods.
The paper tackles the problem of inducing collective motions in affine formation control without a leader, proposing a distributed technique that modifies Laplacian matrix weights to achieve motions like rotations, translations, scalings, and shearings, with proven global stability and effectiveness.
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.