This paper presents a novel Nonlinear Model Predictive Controller (NMPC) architecture for trajectory tracking of omnidirectional robots. The key innovation lies in the method of handling constraints on maximum velocity and acceleration outside of the optimization process, significantly reducing computation time. The controller uses a simplified process model to predict the robot’s state evolution, enabling real-time cost function minimization through gradient descent methods. The cost function penalizes position and orientation errors as well as control effort variation. Experimental results compare the performance of the proposed controller with a generic Proportional-Derivative (PD) controller and a NMPC with integrated optimization constraints. The findings reveal that the proposed controller achieves higher precision than the PD controller and similar precision to the NMPC with integrated constraints, but with substantially lower computational effort.