Multi-Agent Coordination with Cellular Sheaves
We use cellular sheaves to model multi-agent coordination. A cellular sheaf assigns data to the agents and communication links of a fleet, together with the maps that say when neighboring agents agree. The coordinated state is the harmonic extension of the sheaf Laplacian, which is the configuration on which every local agreement condition holds at once.
Posing coordination this way has two consequences. A moving target changes only the right-hand side of a linear system, so tracking, formation control, and consensus become the same computation under different data. And heterogeneous agents, which are difficult to handle with a hand-built controller, are different stalks over different vertices.
The project runs in two directions. The first is what can be posed this way: multi-target tracking, safety constraints expressed as control barrier functions, and coordination laws that tolerate agents updating at their own rates. The second is how to solve it. We factor the sheaf Laplacian once and cut it along its elimination tree, which turns each control step into a short exchange of messages, so that no machine holds the whole problem and the answer remains exact.
Project team
Project articles
- Hanks, T., Nino, C., Barcelo, J. B., Copeland, A., Dixon, W., & Fairbanks, J. (2026). Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves. In European Control Conference. IEEE. (to appear).
- Zhao, Y., Hanks, T., Riess, H., Cohen, S., Hale, M., & Fairbanks, J. (2026). Asynchronous Nonlinear Sheaf Diffusion for Multi-Agent Coordination. In IEEE American Control Conference. IEEE. (accepted).
- Currier, K., Leal, W., Rauta, G., Copeland, A., Dixon, W., & Fairbanks, J. (2026). Whitney Control Barrier Functions: A Mesh-based Geometric approach via Discrete Exterior Calculus. In IFAC. (in press).
- Hanks, T., Riess, H., Cohen, S., Gross, T., Hale, M., & Fairbanks, J. (2025). Distributed Multi-agent Coordination over Cellular Sheaves. In IEEE Conference on Decision and Control. IEEE. https://doi.org/10.48550/arXiv.2504.02049
Coordination of a multi-agent system can be posed as a cellular sheaf over the communication graph, making the coordinated state the harmonic extension of the sheaf Laplacian rather than the output of a purpose-built controller: the coordinated state solves $H q^\star = -B p$, where $H$ is the agent block of the Laplacian and $p$ the current targets. It is the problem statement the rest of our coordination work refines: every later paper either solves that linear system faster or relaxes an assumption it makes.
Read it for The sheaf construction and the Laplacian. The experiments can wait.