Coherent collective behaviour emerging from decentralised balancing of social feedback and noise

Decentralised systems composed of a large number of locally interacting agents often rely on coherent behaviour to execute coordinated tasks. Agents cooperate to reach a coherent collective behaviour by aligning their individual behaviour to the one of their neighbours. However, system noise, determined by factors such as individual exploration or errors, hampers and reduces collective coherence. The possibility to overcome noise and reach collective coherence is determined by the strength of social feedback, i.e. the number of communication links. On the one hand, scarce social feedback may lead to a noise-driven system and consequently incoherent behaviour within the group. On the other hand, excessively strong social feedback may require unnecessary computing by individual agents and/or may nullify the possible benefits of noise. In this study, we investigate the delicate balance between social feedback and noise, and its relationship with collective coherence. We perform our analysis through a locust-inspired case study of coherently marching agents, modelling the binary collective decision-making problem of symmetry breaking. For this case study, we analytically approximate the minimal number of communication links necessary to attain maximum collective coherence. To validate our findings, we simulate a 500-robot swarm and obtain good agreement between theoretical results and physics-based simulations. We illustrate through simulation experiments how the robot swarm, using a decentralised algorithm, can adaptively reach coherence for various noise levels by regulating the number of communication links. Moreover, we show that when the system is disrupted by increasing and decreasing the robot density, the robot swarm adaptively responds to these changes in real time. This decentralised adaptive behaviour indicates that the derived relationship between social feedback, noise and coherence is robust and swarm size independent