Minimalistic Collective Perception with Imperfect Sensors

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 apply optimal estimation techniques and a decentralized Kalman filter to derive, from first principles, a 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.