We present a novel robot social-aware navigation framework to walk side-by-side with people in crowded urban areas in a safety and natural way. The new system includes the following key issues: to propose a new robot social-aware navigation model to accompany a person; to extend the Social Force Model, "Extended Social-Force Model" (ESFM), to consider the person and robots interactions; to use a human predictor to estimate the destination of the person the robot is walking with; and to interactively learning the parameters of the social-aware navigation model using multimodal human feedback. Finally, a quantitative metric based on people's personal spaces and comfortableness criteria, is introduced in order to evaluate quantitatively the performance of the robot's task. The validation of the model is accomplished throughout an extensive set of simulations and real-life experiments. In addition, a volunteers' survey is used to measure the acceptability of our robot companion's behavior.