## 1 Introduction
### Research Questions and Hypotheses  
Given the reasons specified in the previous section, the final aim of the current study involves designing a robot that works as a walking trainer for elderly individuals. Training refers to the double task of motivating a user to walk more and to assisting him/her. The motivational task is designed based on intrinsic motivation theories (Section 2.1), and it should ensure that a user understands the importance of walking. Conversely, an assistive task consists of monitoring the user's gait (Section 2.3) and offering a type of physical support even through light touch contact. An appropriate design allows the same robot to make two contributions to the interaction, namely social and gait assistive contributions (Figure 1). The target users correspond to older individuals who can walk by themselves or by using a walking aid, e.g., a cane or a walker and are sufficiently mentally healthy to use a robot. The specific scenario corresponds to the development of a personal robot that can stay at home with a user and convince him/her to go out given the advantages of leaving the house and meeting other individuals outside as described in Section 1.1. An initial step involves performing experiments in a care facility for elderly individuals because it includes caregivers who are familiar with the needs of their older patients, and thus useful feedback can be obtained. Additionally, a robot in a nursing home or a hospital is an attractive option because it brings a sense of novelty and enjoyment to the fixed routines of these facilities and works with overworked staff to aid them in completing tasks. In these places, a mobile robot encourages patients to walk for health benefits or to go to common areas to talk to other individuals. A hypothesis with respect to the design is as follows: in the past, physically embodied social robots were designed to exhibit human-like social behaviours to create an interaction as similar as possible to an interaction between two individuals in which a human user knows the rules and knows how to behave. Thus, a human-shaped robot can perform human-like actions, and therefore its gestures can be easily understood and it is accepted if an appropriate behaviour is selected. Several studies indicated that physically embodied robots offer more engaging, enjoyable, and effective social interactions when compared to those of virtual agents [16]. Figure 1: Potential walking method with a socially assistive humanoid robot. The picture highlights different aspects of the interaction: the same robot guides a user by encouraging him/her to walk more by using its voice and its tablet and simultaneously monitors his/her gait. A proper design is definitely required to fulfil a double task of motivating the user to walk more and assisting him as well as being accepted by elderly individuals. An understanding of the needs and expectations of target users' in a specific situation involving walking with a robot improves the design of the robot. A user-centred design approach involves including target users at the beginning of the design process and maximises the acceptability of the system [17]. The robot corresponds to an application in a real-world setting, and thus it is necessary to first understand its setting and its future users. A user-centred approach aids in designing a more natural and engaging human-robot interaction. Therefore, the first step in the current study involved performing a first feasibility study by using a commercially available robot. At this starting point, the main research questions were as follows:  
* To observe the reactions of elderly individuals, i.e., if and how they accept a humanoid robot that asks them to walk together;
* To test the effectiveness of the experimental procedure and the instruments selected for evaluation;
* To investigate the strengths and the weaknesses of the current robot, its feasibility as a safe and entertaining walking trainer, and to consider improvements based on users' preferences.