Fast Multiagent Formation Stabilization with Sparse Universally Rigid Frameworks

TL;DR

This paper introduces a convex optimization approach to design stress matrices for affine formation control, enabling sparser networks with faster convergence without predefining rigid graphs.

Contribution

It proposes a novel convex optimization framework for stress matrix design in AFC that reduces communication links while maintaining rapid convergence.

Findings

Achieves sparser network structures compared to existing methods.

Demonstrates faster convergence in simulations.

Maintains formation stability without predefined rigid graphs.

Abstract

Affine formation control (AFC) is a distributed networked control system that has recently received increasing attention in various applications. AFC is typically achieved using a generalized consensus system where the stress matrix, which encodes the graph structure, is used instead of a graph Laplacian. Universally rigid frameworks (URFs) guarantee the existence of the stress matrix and have thus become the guideline for such a network design. In this work, we propose a convex optimization framework to design the stress matrix for AFC without predefining a rigid graph. We aim to find a resulting network with a reduced number of communication links, but still with a fast convergence speed. We show through simulations that our proposed solutions can yield a more sparse graph, while admitting a faster convergence compared to the state-of-the-art solutions.