The accuracy of autonomous motion is the main challenge for mobile medical robots, especially running in narrow space conditions to transport the casualties in the hospital. This article mainly centers on the human-robot transmission of the mobile medical robot for narrow space autonomous motion. In order to enable mobile medical robots to autonomously and smoothly transport hospital casualties through narrow aisles, in this paper, we present a robot skill transfer technology, namely a human-robot skill transfer framework of mobile medical robots for autonomous motion with teaching by demonstration, which is that a smooth optimal path is planned through the human motion, and then the Kinect sensor is used to detect human bone movement to learn its motion trajectory so as to achieve trajectory tracking control. Meanwhile, using the Remote Center of Motion (RCM) constraint to minimize the error between the actual trajectory of the medical robot and the tracking reference path to control the motion trajectory accurately, human-computer interactive mobile medical robots can smoothly pass through narrow channels. Through research and analysis, it is demonstrated that the mobile medical robot proposed in this paper has great feasibility, which is of great reference value in the field of medical rescue.