I. Introduction
Collective decision-making is an essential capability of large-scale decentralised systems like robot swarms, and is often key to achieve the desired goal. In swarm robotics, a large number of robots coordinate and cooperate to solve a problem, and often consensus among the robots is necessary to maximise the system performance [1]–[3]. The design of controllers for consensus decision is often inspired by models of collective behaviour derived from studies in the ethology of social systems [4], [5], as well as from studies about the emergence of social conventions and cultural traits [6]–[8]. Theoretical models represent idealised instances of collective decentralised systems in which consensus can be somehow attained. Among the different available models, a particularly interesting case is the one of the naming game (NG), which represents the emergence of conventions in social systems, such as linguistic, cultural, or economic conventions [9]–[11]. The appeal of this model consists in the ability to describe the emergence of consensus out of a virtually infinite set of equivalent alternatives, yet requiring minimal cognitive load from the agents composing the system [10], [12]. Moreover, the NG has been successfully demonstrated on a network of mobile point-size agents [13]. Such a collective decision-making behaviour can be very useful in swarm robotics in case consensus is required with respect to a possibly large number of alternatives (e.g., the location and structure for cooperative construction [14], [15], or the most functional shape for self-assembly [16], [17]).