# Distributed algorithm for controlling scale-free polygonal formations

## TL;DR

This paper introduces a distributed control algorithm for polygonal formations of mobile agents, enabling shape, scale, and movement control with fewer inter-agent links, supported by theoretical analysis and simulations.

## Contribution

It proposes a novel distributed algorithm for polygonal formations that reduces the number of control links and allows scale and movement control, extending existing rigid formation methods.

## Key findings

- The algorithm successfully controls polygonal formations with fewer links.
- The formation's scale can be adjusted by a single agent pair.
- Exponential stability ensures reliable formation control and steering.

## Abstract

This paper presents a distributed algorithm for controlling the deployment of a team of mobile agents in formations whose shapes can be characterized by a broad class of polygons, including regular ones, where each agent occupies a corner of the polygon. The algorithm shares the appealing properties of the popular distance-based rigid formation control, but with the additional advantage of requiring the control of fewer pairs of neighboring agents. Furthermore, the scale of the polygon can be controlled by only one pair of neighboring agents. We also exploit the exponential stability of the controlled formation in order to steer the formation as a whole with translations and rotations in a prescribed way. We provide both theoretical analysis and illustrative simulations.