Dispersion Formation Control: from Geometry to Distribution

Research paper

ABSTRACT: We introduce and develop the concept of dispersion formation control, bridging a gap between shape-assembly studies in physics and biology and formation control theory. In current formation control studies, the control objectives typically focus on achieving desired local geometric properties, such as interagent distances, bearings, or relative positions. In contrast, our dispersion formation control approach enables agents to directly regulate the dispersion of their spatial distribution, a global variable associated with a covariance matrix. Specifically, we introduce the notion of covariance similarity to define the target spatial dispersion of agents. Building on this framework, we propose two control strategies: a centralized approach to illustrate the key ideas, and a distributed approach that enables agents to control the global dispersion but using only local information. Our stability analysis demonstrates that both strategies ensure exponential convergence of the agents’ distribution to the desired dispersion. Notably, controlling a global variable rather than multiple local ones enhances the resiliency of the system, particularly against malfunctioning agents. Simulations validate the effectiveness of the proposed dispersion formation control.

@misc{jinchen2024cloudformationcontrol,
  title={Dispersion Formation Control: from Geometry to Distribution}, 
  author={Jin Chen, Jesus Bautista Villar, Hector Garcia de Marina, Bayu Jayawardhana},
  year={2024},
  url={https://arxiv.org/abs/2509.19784}, 
}

Features

This project includes both centralized and distributed implementations of our Dispersion Formation Control algorithm.

Installation

We recommend creating a dedicated virtual environment to ensure that the project dependencies do not conflict with other Python packages:

python -m venv venv
source venv/bin/activate

Then, install the required dependencies:

pip install --upgrade pip
pip install -r requirements.txt

requirements.txt contains the versions tested for compatibility with the simulator. Do not modify the versions to ensure stable and reproducible environments. Note that ssl_simulator already provides stable versions for the following core packages: numpy, matplotlib, tqdm, pandas, scipy, ipython.

Additional Dependencies

Some additional dependencies, such as LaTeX fonts and FFmpeg, may be required. We recommend following the installation instructions provided in the ssl_simulator README.

To verify that all additional dependencies are correctly installed on Linux, run:

bash test/test_dep.sh

Usage

For an overview of the project's structure and to see the code in action, we recommend running the Jupyter notebook simulations.ipynb located in the notebooks directory.

Credits

If you have any questions, open an issue or reach out to the maintainers:

• Jesús Bautista Villar (jesbauti20@gmail.com) – Main Developer