Quotient Geometry and Persistence-Stable Metrics for Swarm Configurations
Swarm and constellation reconfiguration can be viewed as motion of an unordered point configuration in an ambient space. Here, we provide persistence-stable, symmetry-invariant geometric representations for comparing and monitoring multi-agent configuration data. We introduce a quotient formation space $\mathcal{S}_n(M,G)=M^n/(G\times S_n)$ and a formation matching metric $d_{M,G}$ obtained by optimizing a worst-case assignment error over ambient symmetries $g\in G$ and relabelings $σ\in S_n$. This metric is a structured, physically interpretable relaxation of Gromov--Hausdorff distance: the induced inter-agent metric spaces satisfy $d_{\mathrm{GH}}(X_x,X_y)\le d_{M,G}([x],[y])$. Composin...
| Authors | Mark M. Bailey |
|---|---|
| Primary category | cs.LG |
| Published | 14 March 2026 |
| Last updated at source | 14 March 2026 |
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