To meet the need of mobile manipulators operating on constrained motion mechanisms, a real-time method for whole body motion planning and control of mobile manipulators based on model predictive control (MPC) and impedance control (IC) is proposed. The mobile mechanical arm is allowed to sense the dynamic change of the environment in the operation process and avoid obstacles all over the body, so that the mobile chassis and the mechanical arm can move in a well-coordinated manner, and the interaction between the mobile mechanical arm and the environment is flexible. The simulation results of the door opening operation of the mobile manipulator show that the method is effective in the whole body motion planning and impedance control of the mobile manipulator, and has a good application prospect.