A complete characterization of the behavior in human-robot interactions (HRI) includes both: the behavioral dynamics and the control laws that characterize how the be-havior is regulated with the perception data. In this way, this work proposes a leader-follower coordinate control based on an impedance control that allows to establish a dynamic relation between social forces and motion error. For this, a scheme is presented to identify the impedance based on fictitious social forces, which are described by distance-based potential fields. As part of the validation procedure, we present an experimental comparison to select the better of two different fictitious force structures. The criteria are determined by two qualities: least impedance errors during the validation procedure and least parameter variance during the recursive estimation procedure. Finally, with the best fictitious force and its identified impedance, an impedance control is designed for a mobile robot Pioneer 3AT, which is programmed to follow a human in a structured scenario. According to results, and under the hypothesis that moving like humans will be acceptable by humans, it is believed that the proposed control improves the social acceptance of the robot for this kind of interaction.