Formation Shape Control Using the Gromov-Wasserstein Metric
Abstract
This article introduces a formation shape control algorithm, in the optimal control framework, for steering an initial population of agents to a desired configuration via employing the Gromov-Wasserstein distance. The underlying dynamical system is assumed to be a constrained linear system and the objective function is a sum of quadratic control-dependent stage cost and a Gromov-Wasserstein terminal cost. The inclusion of the Gromov-Wasserstein cost transforms the resulting optimal control problem into a well-known NP-hard problem, making it both numerically demanding and difficult to solve with high accuracy. Towards that end, we employ a recent semi-definite relaxation-driven technique to tackle the Gromov-Wasserstein distance. A numerical example is provided to illustrate our results.
Cite
Text
Nakashima et al. "Formation Shape Control Using the Gromov-Wasserstein Metric." Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, 2025.Markdown
[Nakashima et al. "Formation Shape Control Using the Gromov-Wasserstein Metric." Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, 2025.](https://mlanthology.org/l4dc/2025/nakashima2025l4dc-formation/)BibTeX
@inproceedings{nakashima2025l4dc-formation,
title = {{Formation Shape Control Using the Gromov-Wasserstein Metric}},
author = {Nakashima, Haruto and Ganguly, Siddhartha and Morimoto, Kohei and Kashima, Kenji},
booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference},
year = {2025},
pages = {208-220},
volume = {283},
url = {https://mlanthology.org/l4dc/2025/nakashima2025l4dc-formation/}
}