A Response Threshold Sigmoid Function Model for Swarm Robot Collaboration

We present a multi agent collaboration algorithm to recruit an approximate number of individually simple robots with controllable variance. We propose a sigmoid response threshold function motivated by task allocation in social insects, and describe macro-level models backed by micro-level simulations to predict the resulting team sizes and their variance. These results are further validated through physical experiments using the "Droplet" swarm robotics platform. We show that the slope of the response threshold function can be used to control the variance of group size, allowing agents to trade off deterministic team size with coordination speed, and making the proposed mechanism applicable to a variety of applications.