Phase transition equivalence in continuous-space robot swarms

Ascertain whether continuous-space robot swarms exhibit the same coordination phase transition observed in discrete grid implementations of the decentralized multi-agent system, including whether the critical density behavior persists under continuous motion and sensing.

Background

The study primarily employs discrete grid environments with neighborhood-based interactions. The authors emphasize that continuous-space navigation in physical robot swarms may differ materially from grid-constrained movement, raising uncertainty about the transferability of the observed phase transition.

This open question addresses the generalization of the validated phase transition from discrete simulation settings to continuous-space robotic deployments.

References

Several open questions warrant future investigation. Do continuous-space robot swarms exhibit the same phase transition observed in discrete grids?

— Emergent Collective Memory in Decentralized Multi-Agent AI Systems  (2512.10166 - Khushiyant, 10 Dec 2025) in Conclusion (Section 8), final paragraph

We conjecture that densely populated situations are underrepresented in the 20K dataset, limiting generalisation to crowded deployments.

— Learning Coordinated Visuomotor Box-Pushing from Solo Demonstrations  (2610.05677 - Matsumoto et al., 5 Oct 2026) in Section 4.1, Dataset and Loss Design