In the cyclic motion of redundant manipulators investigated in Chapter 2, the phenomenon of the joint-angle drift constantly occurs, which may cause deviations of the actual path from the desired one. For a redundant manipulator operating a given task, the noise perturbation is inevitable and hard to deal with, especially the time-varying noise. To address the above issues, an acceleration-level cyclic-motion (ALCM) scheme is presented for eliminating the joint-angle drift with the noise rejection in this chapter. Specifically, the presented ALCM scheme sets the joint-angle drift as an optimization goal and simultaneously takes into account the error feedback. Furthermore, a noise-rejection dynamic neural network (NRDNN) model is explored to process the ALCM scheme online. To address the unavoidable noise perturbation, the constructed NRDNN model incorporates adaptive mechanisms for handling the time-varying polynomial noise. Additionally, rigorous convergence analyses are provided, covering both noise-free and noisy scenarios. Furthermore, numerical simulations using a PUMA 560 redundant manipulator validate the presented method’s effectiveness in compensating for the joint-angle drift. Finally, comparative analyses across various noise scenarios confirm the enhanced performance of the presented NRDNN model in addressing the formulated control problem.