During our daily routines, we regularly participate in intricate, adaptive, and personalized interactions with our partner, whose sensory and motor skills may diverge from our own. Conforming to our partners' perceptions involves grasping what they will experience and adjusting our actions accordingly. Adaptation is an essential competence in natural (biological) cognitive agents, observable at both behavioral and physiological levels. Therefore, adaptability stands out as a crucial requirement in developing an artificial cognitive agent, empowering it to seamlessly integrate into new environments, navigate alterations in its surroundings, and establish the groundwork for a sophisticated, human-like interaction with other agents. This thesis proposes to exploit the adaptability of the humanoid robot iCub to personalize a physical human-robot interaction.