Formation Shape Control using the Gromov-Wasserstein Metric
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913762672377856 |
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| author | Nakashima, Haruto Ganguly, Siddhartha Morimoto, Kohei Kashima, Kenji |
| author_facet | Nakashima, Haruto Ganguly, Siddhartha Morimoto, Kohei Kashima, Kenji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formation Shape Control using the Gromov-Wasserstein Metric Nakashima, Haruto Ganguly, Siddhartha Morimoto, Kohei Kashima, Kenji Optimization and Control Machine Learning Multiagent Systems Systems and Control 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. |
| title | Formation Shape Control using the Gromov-Wasserstein Metric |
| topic | Optimization and Control Machine Learning Multiagent Systems Systems and Control |
| url | https://arxiv.org/abs/2503.21538 |