arXiv cs.MA· Ariel Barel·· 11 小时前AI 评分24
仅测距群体分散中的连通性保持与图拉伸
Connectivity Preservation and Graph Stretching in Range-Only Swarm Dispersion
AI 导读
研究在仅测距感知下匿名、同质且无记忆智能体的连通性保持有限跳分散问题，推导出仅凭距离测量即可证明安全的最大各向同性位移。规则只需最远可见邻居的距离：每个智能体随机选向并移动剩余可见裕度的一半，同步有限运动下可保持所有可见边与连通性。两智能体情形证明平方距离正条件漂移、几乎必然收敛到可见边界；百万次蒙特卡洛实验与精确首轮矩一致，估计约 9.5 轮可从重合初始位置达到 0.97V 距离。
正文 · 原文
Abstract:We study connectivity-preserving finite-jump dispersion of anonymous, identical, and oblivious agents under an idealized range-only sensing model. Each agent measures only the distances to its visible neighbors, without bearings, identifiers, communication, memory, or a shared coordinate system. We derive the largest isotropic displacement certifiable as safe from these measurements alone. The resulting rule requires only the distance to the farthest visible neighbor: each agent selects a random direction and moves by half of its remaining visibility margin. The rule preserves every existing visibility edge under synchronous finite motion and therefore preserves connectivity. For two agents, we prove positive conditional drift in squared distance, almost-sure convergence to the visibility boundary, and finite expected time to reach any fixed neighborhood of that boundary. A one-million-run Monte Carlo experiment agrees with the exact first-round moments and estimates approximately 9.5 rounds to reach distance 0.97V from coincident initial positions; an independent Bellman-equation computation gives the same estimate. For general swarms, 1,000 runs across five initial-topology classes reproduce the deterministic safety guarantee at implementation level and reveal a consistent topology-dependent ordering of attainable diameter under the tested protocol. These results provide a theoretical foundation for connectivity-preserving multi-robot dispersion under minimal sensing, while isolating the guarantees achievable from anonymous range measurements alone.
| Subjects: | Multiagent Systems (cs.MA) |
| Cite as: | arXiv:2609.28190 [cs.MA] |
| (or arXiv:2609.28190v2 [cs.MA] for this version) | |
| https://doi.org/10.48550/arXiv.2609.28190 arXiv-issued DOI via DataCite |
Submission history
From: Ariel Barel Dr. [view email]
[v1]
Wed, 23 Sep 2026 14:29:41 UTC (361 KB)
[v2]
Wed, 4 Nov 2026 11:43:10 UTC (2,459 KB)
来源：arXiv cs.MA · arxiv.org