# Directed Formation Control of n Planar Agents with Distance and Area Constraints

## TL;DR

This paper introduces a novel formation control method for planar multi-agent systems that combines distance and area constraints, ensuring almost-global convergence to the desired formation using directed graphs.

## Contribution

It generalizes existing distance-based formation control by incorporating area constraints and directed graphs, improving convergence guarantees.

## Key findings

- Ensures almost-global convergence to the correct formation.
- Works with directed graphs and triangulated formations.
- Applicable to n-agent systems in 2D.

## Abstract

In this paper, we take a first step towards generalizing a recently proposed method for dealing with the problem of convergence to incorrect equilibrium points of distance-based formation controllers. Specifically, we introduce a distance and area-based scheme for the formation control of $n$-agent systems in two dimensions using directed graphs and the single-integrator model. We show that under certain conditions on the edge lengths of the triangulated desired formation, the control ensures almost-global convergence to the correct formation.