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Real-time trajectory planning using model predictive control with constraints is proposed for mobile manipulators. The proposed method employs Quadratic Programming( QP) for optimizing control inputs. The control inputs and outputs are limited corresponding to the required motion and the hardware specifications of the mobile manipulator. The required motion is changed frequently according to the situation and the hardware limitations, concretely the torque, the angular velocity, the mobile base velocity and the acceleration, which are subject to the hardware design. The velocity and acceleration of the tip of the hand depend on the motion required by the user or on the environmental situation, and the required motion has to be changed flexibly. Thus, the mobile manipulator has to possess a high degree of freedom and be able to manage redundant system flexibly under constraints. These issues are solved by using the generalized mobile manipulator model with model predictive controller. In this paper, first, the generalized 2-D mobile Manipulator model is shown. The holonomic and nonholonomic mobile base by changing the constraint of the mobile base output is simulated, and the effectiveness of the mobile manipulator control design is confirmed. The proposed method is implemented to a real mobile manipulator model and real-time trajectory modification is demonstrated on a real mobile robot.