Recently, several robotic solutions for the elderly have been proposed. However, to date, the diffusion of these devices has been limited: available robots are too cumbersome, awkward, and expensive to become widely adopted. Another key issue which reduces the appeal of assistive robots is the lack of socio-emotional interaction: affective interchanges represent key requirements to create sustainable relationships between elderly and robots. In this paper, we propose a new approach to enhance the acceptability of robotic systems, based on the introduction of affective dimensions in human-robot interaction. This strategy is aimed at designing a new generation of relational and cognitive robots fusing information from embodied unobtrusive sensory interfaces. The final objective is to develop embodied interfaces, which are able to learn and adapt their affective responses to the user's behavior. User and robot will engage in natural interactions, involving verbal and non-verbal communication, improving empathic exchange of moods and feelings. Relevant independent living and quality of life related issues will be addressed: on-going monitoring of health parameters, assistance in everyday's activities, social support and cognitive/physical exercises. We expect that the proposed strategy will enhance the user's acceptance and adoption of the assistive robotic system.