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arXiv · 2503.21538

Formation Shape Control using the Gromov-Wasserstein Metric

Haruto Nakashima·Siddhartha Ganguly·Kohei Morimoto·Kenji Kashima
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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.

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Haruto Nakashima, Siddhartha Ganguly, Kohei Morimoto, Kenji Kashima. 2025-03-27. Formation Shape Control using the Gromov-Wasserstein Metric. https://arxiv.org/abs/2503.21538

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