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The huge spreading of COVID-19 viral outbreak to several countries motivates many of the research institutions everywhere in numerous disciplines to try decreasing the spread rate of this pandemic. Among these researches are the robotics with different payloads and sensory devices with wireless communications to remotely track patients’ diagnosis and their treatment. That is, it reduces direct contact between the patients and the medical team members. Thus, this paper is devoted to design and implement a prototype of wireless medical robot (MR) that can communicate between patients and medical consultants. The prototype includes the modelling of a four-wheeled MR using systems' identification methodology, from which the model is utilized in control design and analysis. The required controller is designed using the proportional-integral-derivative (PID) and Fuzzy logic (FLC) techniques. The MR is equipped onboard with some medical sensors and a camera to acquire vital signs and physical parameters of patients. The MR model is obtained via an experimental test with input/output signals in open-loop configuration as single–input–single–output from which the estimation and validation results demonstrate that the identified model possess about 89% of the output variation/dynamics. This model is used for controllers' design with PID and FLC, the response of which is good for heading angle tracking. Concerning the medical measurements, more than two thousand real recorded Photo-plethysmography (PPG) signals and Blood Pressure (BP) are used to find the appropriate BP estimation model. Towards this objective, some experiments are designed and conducted to measure the PPG signal. Finally, the BP is estimated with mean absolute error of about 4.7 mmHg in systolic and 4.8 mmHg in diastolic using Artificial Neural Network.