This paper studies the gathering problem for a set of $N \ge 2$ autonomous mobile robots operating in the Euclidean plane under the distributed Look-Compute-Move model. We consider oblivious robots executing under the adversarial defected view model, in which an activated robot may observe only a restricted subset of robots due to adversarial visibility faults. Consequently, the information obtained during each Look phase may be incomplete and dynamically altered. The objective is to guarantee deterministic finite-time gathering at a location not known a priori despite such sensing restrictions. We present two distributed algorithms under distinct scheduling assumptions. In the fully synchronous (FSYNC) model, we prove finite-time gathering in the adversarial (4, 2) defected view setting, resolving a previously open case without requiring additional capabilities or coordinate agreement. In the asynchronous (ASYNC) model, we establish finite-time gathering under the general adversarial (N, K) defected view model, where an activated robot observes at most K of the other $N - 1$ robots for any $1 \le K < N - 1$. Both results hold under non-rigid motion. The proposed algorithm for the ASYNC model assumes agreement in the direction and orientation of one coordinate axis.
翻译:本文研究了在分布式"观察-计算-移动"模型下,于欧几里得平面中运行的 $N \ge 2$ 台自主移动机器人的聚集问题。我们考虑在对抗性缺陷视角模型下执行的无记忆机器人,其中被激活的机器人可能由于对抗性的可见性故障而仅能观测到受限的机器人子集。因此,在每个观察阶段获得的信息可能是不完整且动态变化的。目标是在此类感知限制下,保证在未知先验的位置实现确定性的有限时间聚集。我们在不同的调度假设下提出了两种分布式算法。在全同步(FSYNC)模型中,我们证明了在对抗性 (4, 2) 缺陷视角设置下可实现有限时间聚集,解决了先前未决的情况,且无需额外的能力或坐标一致性。在异步(ASYNC)模型中,我们在一般对抗性 (N, K) 缺陷视角模型下建立了有限时间聚集,其中对于任意 $1 \le K < N - 1$,被激活的机器人最多观测到其他 $N - 1$ 台机器人中的 K 台。两种结果均在非刚性运动条件下成立。所提出的 ASYNC 模型算法假设在一个坐标轴的方向和取向上达成一致。