HARIA re-defines the nature of physical human-robot interaction (HRI), laying the foundations of a new research field, i.e., human sensorimotor augmentation, whose constitutive elements are: i) AI-powered wearable and grounded supernumerary robotic limbs and wearable sensorimotor interfaces; ii) methods for augmentation enabling users to directly control and feel the extra limbs exploiting the redundancy of the human sensorimotor system through wearable interfaces; iii) clear target populations, i.e., chronic stroke and spinal cord injured individuals, and real-world application scenarios to demonstrate the extraordinary value of the paradigm shift that HARIA represents in HRI and the great impact on the motivation to re-use the paretic arm(s), with consequent improvement of the quality of life. Supernumerary limbs will be partially controlled by artificial intelligence, and partially under the direct control of the human who gains the agency of some motion parameters of the supernumerary limbs. From the control point of view, it is fundamental to find the right trade-off between motion task parameters that are controlled by the user, and the level of robot autonomy. This interplay is enabled by the wearable sensorimotor interface that establishes a connection between the human sensorimotor system and the system of actuators and sensors of the robot, allowing reciprocal awareness, trustworthiness and mutual understanding. HARIA finds its natural application in assisting people with uni- or bi-lateral upper limbs chronic motor disabilities. Technology and methodology developments will follow a user-centered design approach, as only patients with disabilities are fully aware of their real (still unmet) needs in real life activities. This project will also go beyond the application to health, starting a new era of intuitive and seamless human-robot augmentation by wearable sensorimotor interfaces and supernumerary limbs.