Hospitals are rightfully considered a field of indoor logistic robotics of high commercial potential. However, today, only a handful of mobile robotic solutions for hospital logistics exist that have failed to trigger widespread acceptance by the market. This is because existing systems require costly infrastructure installation, they do not easily integrate to corporate IT solutions, are not adequately shielded from cybersecurity threats, and as a result, they do not fully automate procedures and traceability of the items they carry. Moreover, existing systems are limited on scope, focusing only on delivery services, and hence do not provide any other type of support to the medical and nursing staff. ENDORSE system will address the aforementioned technical challenges and functional limitations by pursuing four innovation pillars: (i) infrastructure-less multi-robot indoor navigation; (ii) advanced Human-Robot Interaction (HRI) for resolving deadlocks and achieving efficient sharing of space resources in crowded environments; (iii) deployment of the ENDORSE software as a cloud-based service facilitating its integration with corporate software solutions, complying with GDPR data security requirements; (iv) reconfigurable and modular hardware architectures so that diverse modules can be easily swapped. ENDORSE functionality will be demonstrated via the integration of an e-diagnostic support module for vital signs monitoring on a fleet of mobile robots, facilitating connectivity to cloud-based Electronic Health Records (EHR), and validated in an operational hospital environment for realistic assessment.