Abstract: When the robot is used to sort coal gangue, in order to solve the problems such as inaccurate positioning of gangue, failure of grasping by end of the manipulator and load impact caused by slippage and left-right swing of belt conveyor, a track planning method of coal gangue sorting robot for dynamic target stable grasping based on machine vision is proposed. Firstly, the target gangue is identified and the pose of the target gangue is obtained by using the HU moment invariants image matching algorithm. Secondly, the kinematic equations of the robot and the camera-robot are established respectively, and the forward and inverse solutions are carried out to realize the accurate positioning of the target gangue based on vision. Finally, the position-velocity-acceleration three-loop PID control algorithm is used to dynamically track the target gangue. The input of the position loop controller is the obtained precise position of the target gangue, the output of the position loop controller is used as the input of the velocity loop controller, the output of the velocity loop controller is used as the input of the acceleration loop controller, and the output of the acceleration loop controller is superimposed on the servo motor. Therefore, the end of the manipulator and the target gangue can achieve the effect of synchronous movement of position and velocity, so as to achieve stable and fast grasping. Matlab is used to compare the three-loop PID control algorithm, the three-dimensional proportional navigation algorithm and the three-dimensional biased proportional navigation algorithm. The results show that in the following, synchronous and intercepting cases of the tracking and grasping of dynamic targets, the response time and tracking and grasping time of the three-loop PID control algorithm are better than those of the proportional navigation algorithm and the biased proportional navigation algorithm. And the three-loop PID control algorithm is continuous and smooth in the speed and acceleration of each axis in the whole process without sudden change, which can realize synchronous tracking of dynamic targets and precise grasping. The three-loop PID control algorithm, proportional navigation algorithm and biased proportional navigation algorithm are applied to the coal gangue sorting system platform to carry out adaptability experiments. The results show that the three algorithms do not exceed the limit of each joint during robot operation. The average time of the three-loop PID control algorithm to complete the grasping is shorter than those of the proportional navigation algorithm and the biased proportional navigation algorithm. The average speed error of the three-loop PID control algorithm at the grasping point is about 1 mm/s, and the tracking speed error is small, which can meet the requirements of synchronous tracking and precise grasping of high-speed targets.