Thanks to recent technological improvements that enable novel applications beyond the industrial context, there is growing interest in the use of robots in everyday life situations. To improve the acceptability of personal service robots, they should seamlessly interact with the users, understand their social signals and cues and respond appropriately. In this context, a few proposals were presented to make robots and humans navigate together naturally without explicit user control, but no final solution has been achieved yet. To make an advance toward this end, this paper proposes the use of wearable Inertial Measurement Units to improve the interaction between human and robot while walking together without physical links and with no restriction on the relative position between the human and the robot. We built a prototype system, experimented with 19 human participants in two different tasks, to provide real-time evaluation of gait parameters for a mobile robot moving together with a human, and studied the feasibility and the perceived usability by the participants. The results show the feasibility of the system, which obtained positive feedback from the users, giving valuable information for the development of a natural interaction system where the robot perceives human movements by means of wearable sensors.