无计算的自组织聚合中的死锁与噪声
Deadlock and Noise in Self-Organized Aggregation Without Computation
AI总结：
研究无计算自组织聚合算法在多机器人系统中的死锁问题，证明确定性运动下存在死锁构型，并发现少量误差可避免死锁，同时提出一种离散噪声版本。
摘要：
聚合是群体机器人学中的基本行为，要求系统聚集在一个紧凑、连通的集群中。2014年，Gauci等人提出了一种令人惊讶的算法，仅使用二进制视线传感器且无需算术计算或持久内存，即可可靠地实现群体聚合。该算法已被严格证明能够将一个机器人聚合到另一个机器人，但尚不清楚它是否总能像实验和模拟中观察到的那样聚合$n > 2$个机器人的系统。我们证明，当机器人的运动是均匀且确定性的时，对于$n > 3$个机器人，存在死锁构型，使得该算法无法实现聚合。从积极方面看，我们表明该算法（i）对小量误差具有鲁棒性，从而能够避免死锁，并且（ii）在使用锥形视线传感器时，对于$n = 2$的情况，可证明实现线性运行时间加速。最后，我们引入了该算法的一种带噪声的离散改编，更易于进行噪声的严格分析，其模拟结果与原始的连续算法定性一致。
英文摘要：
Aggregation is a fundamental behavior for swarm robotics that requires a system to gather together in a compact, connected cluster. In 2014, Gauci et al. proposed a surprising algorithm that reliably achieves swarm aggregation using only a binary line-of-sight sensor and no arithmetic computation or persistent memory. It has been rigorously proven that this algorithm will aggregate one robot to another, but it remained open whether it would always aggregate a system of $n > 2$ robots as was observed in experiments and simulations. We prove that there exist deadlocked configurations from which this algorithm cannot achieve aggregation for $n > 3$ robots when the robots' motion is uniform and deterministic. On the positive side, we show that the algorithm (i) is robust to small amounts of error, enabling deadlock avoidance, and (ii) provably achieves a linear runtime speedup for the $n = 2$ case when using a cone-of-sight sensor. Finally, we introduce a noisy, discrete adaptation of this algorithm that is more amenable to rigorous analysis of noise and whose simulation results align qualitatively with the original, continuous algorithm.
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