Trajectory tracking control presents a significant challenge in the application of omni-directional redundant mobile manipulators (OMRM) due to the combined influence of noise disturbances and physical constraints. However, most existing studies primarily address individual factors in the control system, offering limited insights into the combined effects of noise disturbances and physical constraints. In this paper,  a time-varying nonlinear problem with inequality constraints is proposedIn to deal with the trajectory tracking problem with physical constraints. The relaxation variable method is employed to transform the original system into a standard time-varying nonlinear system, facilitating more efficient problem-solving. To achieve real-time noise-robust control, a noise-suppression zeroing neural network (NSZNN) model is designed. Theoretical analysis proves that the NSZNN model guarantees global convergence even in the presence of noise disturbances. Numerical simulations and CoppeliaSim platform experiments confirm the effectiveness, superiority, and robustness of the proposed control scheme.