The medical robotics market in the global healthcare industry have spread and extended in these several years. Internet of Medical Robotics Things (IoMRT) is also growing and Internet of Things is extending a new field of healthcare application. Whereas, the previous paper suggested that, in the field of robotics, the cloud platforms for Internet of Robotics Things (IoRT) were gradually developed; therefore, the digital platform and architecture for IoMRT of the healthcare industries should be formulated when necessary. An open healthcare platform for IoMRT is expected to promote and implement the robotics and the IoMRT applications for medical and healthcare communities efficiently. In this paper, we suggest that various medical robotics and the IoMRT-related applications will be designed and verified, while the open platform for medical, healthcare-related Robotics should be proposed and verified by the research initiative named “Open Healthcare Platform 2030–OHP2030.” In addition, the vision for enabling medical robotics and the IoMRT-related applications in the OHP2030 research initiative is explained.