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
@article{arxiv.2503.21538,
title = {Formation Shape Control using the Gromov-Wasserstein Metric},
author = {Haruto Nakashima and Siddhartha Ganguly and Kohei Morimoto and Kenji Kashima},
journal= {arXiv preprint arXiv:2503.21538},
year = {2025}
}
Comments
To appear in the proceedings of Learning for Dynamics and Control (L4DC) conference, PMLR, 2025