Majority-rule opinion dynamics with differential latency: A mechanism for self-organized collective decision-making

Collective decision-making is a process whereby the members of a group decide on a course of action by consensus. In this paper, we propose a collective decision-making mechanism for robot swarms deployed in scenarios in which robots can choose between two actions that have the same effects but that have different execution times. The proposed mechanism allows a swarm composed of robots with no explicit knowledge about the difference in execution times between the two actions to choose the one with the shorter execution time. We use an opinion formation model that captures important elements of the scenarios in which the proposed mechanism can be used in order to predict the system's behavior. The model predicts that when the two actions have different average execution times, the swarm chooses with high probability the action with the shorter average execution time. We validate the model's predictions through a swarm robotics experiment in which robot teams must choose one of two paths of different length that connect two locations. Thanks to the proposed mechanism, a swarm made of robot teams that do not measure time or distance is able to choose the shorter path.