Collective perception is a foundational problem in swarm robotics, in which the swarm must reach consensus on a coherent representation of the environment. An important variant of collective perception casts it as a best-of-$n$ decision-making process, in which the swarm must identify the most likely representation out of a set of alternatives. Past work on this variant primarily focused on characterizing how different algorithms navigate the speed-vs-accuracy tradeoff in a scenario where the swarm must decide on the most frequent environmental feature. Crucially, past work on best-of-$n$ decision-making assumes the robot sensors to be perfect (noise- and fault-less), limiting the real-world applicability of these algorithms. In this paper, we derive from first principles an optimal, probabilistic framework for minimalistic swarm robots equipped with flawed sensors. Then, we validate our approach in a scenario where the swarm collectively decides the frequency of a certain environmental feature. We study the speed and accuracy of the decision-making process with respect to several parameters of interest. Our approach can provide timely and accurate frequency estimates even in presence of severe sensory noise.

翻译：集群感知是群机器人学中的一个基础问题，要求集群对环境达成一致的认知表征。集群感知的一个重要变体将其视为一种“最佳-n”决策过程，即集群必须从一组备选方案中识别出最可能的表征。以往关于该变体的研究主要聚焦于刻画不同算法如何在速度与准确性权衡中导航，其场景设定为集群需确定最常见的环境特征。关键的是，过往关于“最佳-n”决策的研究假设机器人传感器是完美的（无噪声、无故障），这限制了这些算法的实际应用。本文从第一性原理出发，为配备有缺陷传感器的极简群机器人推导出一个最优的概率框架。随后，我们在集群共同决策某环境特征频率的场景中验证了该方法。我们研究了决策过程相对于多个感兴趣参数的速度与准确性。即使在存在严重传感器噪声的情况下，我们的方法也能提供及时且准确的频率估计。