Quadruped robots have good mobility and agility in complex environments, but dynamic control of locomotion for quadruped robots has long been a big challenge for researchers. In this paper, we build the center of inertia (COI) dynamic model of a general quadruped robot and give the exponential coordinates of COI on the special Euclidean space SE(3). The COI model takes the whole quadruped robot as one body, so that the only concern is the movement of the COI rather than the body or legs when the robot walks. As a result, the COI model has fewer dimensions of state variables than the full dynamic model, which helps to reduce the computational load. A control method for quadruped robots is presented based on the dynamic model which is constituted of force loop and position loop. This method controls the movement of the COI directly, so it facilitates to guarantee the robot's stability. The virtual body of the quadruped robot is defined to describe the configuration of the quadruped robot. The proportional-derivative (PD) control method on SE(3) is applied to control the movement of the virtual body, which makes the movement more in line with the group theoretic viewpoint. Finally, some simulation experiments have been conducted to verify the validity of our method.

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