Formation Shape Control using the Gromov-Wasserstein Metric

Haruto Nakashima, Siddhartha Ganguly, Kohei Morimoto, Kenji Kashima
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:208-220, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v283-nakashima25a, 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}, pages = {208--220}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/nakashima25a/nakashima25a.pdf}, url = {https://proceedings.mlr.press/v283/nakashima25a.html}, 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.} }
Endnote
%0 Conference Paper %T Formation Shape Control using the Gromov-Wasserstein Metric %A Haruto Nakashima %A Siddhartha Ganguly %A Kohei Morimoto %A Kenji Kashima %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-nakashima25a %I PMLR %P 208--220 %U https://proceedings.mlr.press/v283/nakashima25a.html %V 283 %X 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.
APA
Nakashima, H., Ganguly, S., Morimoto, K. & Kashima, K.. (2025). Formation Shape Control using the Gromov-Wasserstein Metric. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:208-220 Available from https://proceedings.mlr.press/v283/nakashima25a.html.

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