仅测距群体散布中的连通性保持与图拉伸

中文摘要 AI 辅助

我们研究了在理想化的仅测距感知模型下，匿名、相同且无记忆的智能体进行保持连通性的有限跳跃散布问题。每个智能体仅测量其到可见邻居的距离，没有方位信息、标识符、通信、记忆或共享坐标系。我们推导了仅凭这些测量即可被认证为安全的最大各向同性位移。由此得到的规则仅需到最远可见邻居的距离：每个智能体选择一个随机方向，并移动其剩余可见余量的一半。该规则在同步有限运动下保持每条现有可见边，因此保持连通性。对于两个智能体，我们证明了平方距离的正条件漂移、几乎必然收敛到可见边界，以及到达该边界任意固定邻域的有限期望时间。一百万次运行的蒙特卡洛实验与精确的首轮矩一致，并估计从重合初始位置到达距离0.97V约需9.5轮；独立的贝尔曼方程计算给出相同估计。对于一般群体，跨越五种初始拓扑类别的1000次运行在实现层面复现了确定性安全保证，并揭示了所测协议下可达到直径的一致拓扑依赖性排序。这些结果为在最小感知下保持连通性的多机器人散布提供了理论基础，同时分离了仅凭匿名距离测量即可实现的保证。

英文摘要

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.

发表机构

• Faculty of Computer Science, Technion Israel Institute of Technology（以色列理工学院计算机学院）

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