Aiming at the problem of mobile manipulator tracking and grasping dynamic targets, this paper designs the speed control equation of the wheeled mobile chassis of the mobile manipulator to track the dynamic target to track the target object, and uses the Kalman filter algorithm to adaptively adjust the target relative to the mobile manipulator. position information to achieve accurate grasp of the target object. Firstly, according to reducing the position and steering error between the moving chassis and the dynamic target, and considering that the moving chassis can approach the dynamic target in the fastest and stable way, the control equations of the linear speed and angular speed of the moving chassis are established, and then the control is verified by the Lyapunov function. The asymptotic stability of the equation; then the moving manipulator is tracked within the specified range, and the position of the dynamic target is predicted and refreshed by the Kalman filter algorithm, so as to reduce the error caused by the environmental influence, so as to realize the precise grasp of the dynamic target by the manipulator. Finally, modeling and simulation experiments are carried out on the Gazebo platform to verify the feasibility of the mobile chassis tracking dynamic target control equation and the superiority of using the Kalman filter algorithm for position prediction.