In this paper I propose the use of the ethics of care as a theoretical and political framework for rethinking 'robotics' and 'artificial intelligence' (AI) in healthcare. Using the theoretical perspective of Science and Technology Studies, I develop an approach based on the idea of a continuum between care, politics, ethics and technologies. I propose a reflection on the controversies surrounding robotics and AI from a non-naive position, from a logic of conflict and confrontation with the imaginaries that accompany the technological innovation market. Conceptually, this proposal revolves around two notions: heterogeneity and creativity, and how they express the radical potential of the ethics of care as a utopia that challenges neoliberal utopia. From these considerations I articulate a way of understanding human-robot relations that seeks to overcome the traditional dyadic human-machine relationship. Taking as a unit of analysis the network of care relations in which the robot is embedded (Robot Embedded in a Network -REN-), new controversies emerge that make visible the daily practices of care with these artefacts, and the relations of inequality that accompany them. Similarly, in order to guarantee the design and introduction of responsible technologies, at the service of the common good and individual and collective well-being, I suggest the need to integrate the various actors involved in care into the debate, as well as to establish mechanisms for monitoring and permanent public scrutiny of the design and introduction of robots in healthcare.