Abstract-Mobile robot companions are service robots that are mobile and designed to share our living space. For such robots, mobility is essential and their coexistence with humans adds new aspects to the mobility issue: the first one is to obtain appropriate motion and the second one is interaction through motion. We encapsulate these two aspects in the term Human-Robot Motion (HRM) with reference to Human-Robot Interaction. The long-term issue is to design robot companions whose motions, while remaining safe, are deemed appropriate from a human point of view. This is the key to the acceptance of such systems in our daily lives. The primary purpose of this paper is to explore how the psychological concept of attention can be taken into account in HRM. To that end, we build upon an existing model of attention that computes an attention matrix that describes how the attention of each person is distributed among the different elements, persons and objects, of his/her environment. Using the attention matrix, we propose the novel concept of attention field that can be viewed as an attention predictor. Using different case studies, we show how the attention matrix and the attention field can be used in HRM.