A quantitative micro-macro link for collective decisions: the shortest path discovery/selection example

In this paper, we study how to obtain a quantitative correspondence between the dynamics of the microscopic implementation of a robot swarm and the dynamics of a macroscopic model of nest-site selection in honeybees. We do so by considering a collective decision-making case study: the shortest path discovery/selection problem. In this case study, obtaining a quantitative correspondence between the microscopic and macroscopic dynamics--the so-called micro-macro link problem--is particularly challenging because the macroscopic model does not take into account the spatial factors inherent to the path discovery/selection problem. We frame this study in the context of a general engineering methodology that prescribes the inclusion of available theoretical knowledge about target macroscopic models into design patterns for the microscopic implementation. The attainment of the micro-macro link presented in this paper represents a necessary step towards the formalisation of a design pattern for collective decision making in distributed systems.