Response Threshold Distributions to Improve Best-of-N Decisions in Minimalistic Robot Swarms

Abstract

We aim to design algorithms that allow robot swarms to solve the best-of-n problem using as little resources as possible. Our minimalistic approach aims to create solutions suitable for simple robots with fewer memory and computational requirements than the state of the art algorithms require. While the long term goal is to implement decentralised algorithms for best-of-n decision making based on heterogeneous response thresholds, here we focus on what threshold distribution allows the swarm to best distinguish between options' qualities, in order to select the option with the highest quality. Each robot estimates the quality of a random option and gives a binary response-accept or reject-depending on the quality being above or below its threshold. This study investigates the normal distribution of thresholds that maximises the probability that the majority of the swarm favours the best alternative. We conduct our analysis for various types of environments, by considering different options' quality distributions and number of options. Our results form the basis to develop future decentralised algorithms for swarms of reactive binary robots able to make best-of-n decisions.