Similar Formation Control of Multi-Agent Systems over Directed Acyclic Graphs via Matrix-Weighted Laplacian

TL;DR

This paper introduces a distributed formation control method for multi-agent systems over directed acyclic graphs using matrix-weighted Laplacian, enabling formation patterns with translation, rotation, and scaling.

Contribution

It extends similar formation control from undirected to directed acyclic graphs and offers algebraic criteria for leader selection.

Findings

Achieves formation control with translation, rotation, and scaling.

Provides algebraic criteria for leader selection.

Includes stability analysis and simulation validation.

Abstract

This brief proposes a distributed formation control strategy via matrix-weighted Laplacian that can achieve a similar formation in 2-D planar using inter-agent relative displacement measurement. Formation patterns that include translation, rotation, and scaling can be characterized by the null space of the matrix-weighted Laplacian associated with the topological graph. The main contribution of this brief is to extend the similar formation problem of undirected graphs to directed acyclic graphs and provide the necessary algebraic criteria for leader selection. Stability analysis, illustrative examples, and simulation results are provided.