The problem of finding a suitable qualitative representation for robots to reason about activity spaces where they carry out tasks such as leading or interacting with a group of people is tackled in this paper. For that, a Qualitative Spatial model for Group Robot Interaction (QS-GRI) is proposed to define Kendon’s F-formations [16] depending on: (i) the relative location of the robot with respect to other individuals involved in that interaction; (ii) the individuals’ orientation; (iii) the shared peri-personal distance; and (iv) the role of the individuals (observer, main character or interactive). An iconic representation is provided and Kendon’s formations are defined logically. The conceptual neighborhood of the evolution of Kendon formations is studied, that is, how one formation is transformed into another. These transformations can depend on the role that the robot have, and on the amount of people involved.