Abstract: To add a variable-diameter function to the spherical robot, a variable-diameter spherical shell mechanism consisting of 20 hexagonal cells, 12 pentagonal cells and their connectors is designed, with a layer of curved elements covering the surface of the spherical shell to ensure the smoothness of the spherical shell during rolling. In order to ensure that the internal mechanism is always in the center of the spherical shell, a differential centering mechanism is designed. The relationship between the structure size of the differential centering mechanism and the diameter of the spherical shell is analyzed, and a PID (proportional-integral-derivative) controller is used to enable the spherical robot to control its diameter within 220 \sim 329 mm. In case of a fall to the ground, the change in diameter of the spherical shell and the resistance torque of the motors in the centering mechanism are used to reduce the impact and protect the internal structure of the robot. In order to equip the spherical robot with omnidirectional motion in the horizontal plane, the motion of the robot is decomposed into linear and steering motions. The Lagrangian dynamics equation is used to analyze the linear forward motion, and the closed-loop control of the rotational angular velocity of the forward motor enables the robot to more accurately track the target velocity curve based on the Gaussian function. The Newton-Euler method is used to analyze the steering motion, and the closed-loop control is applied to the center-of-mass lateral bias inside the robot to achieve a uniform circular motion with a radius of about 1 m.