Anonymous leadership and stochastic resonance in collectives of self-propelled robots

We investigate the influence of an anonymous leader on a collective of self-propelled robots using Kilobot experiments and numerical simulations. Each robot possesses a binary internal state that determines the direction of its intrinsic rotational motion, leading to clockwise or counterclockwise circular trajectories. A single leader alternates deterministically between these two internal chiral states, while the other robots update their internal state through a stochastic majority rule based on local communication. The leader induces correlations with the collective response that peak at intermediate perturbation levels, resembling stochastic resonance. Numerical simulations confirm that this resonance arises when the leader's reversal period matches the mean residence time of the leaderless system. Our results contribute to understanding decision-making in active matter and suggest general principles for steering robotic swarms with minimal and anonymous leadership.