Noise and physical constraints of redundant manipulators are the two major challenges in the repetitive motion planning (RMP) problems. Therefore, this paper proposed a power-exponent-type modified recurrent neural network (PET-MRNN) to simultaneously address both noise and physical constraints. Moreover, PET-MRNN model is activated by a new Sbp-sinh type nonlinear activation function proposed in this paper. The Sbp-sinh type activation function is first applied to such time varying quadratic program (TVQP) solving and possesses excellent convergence performance. Theoretical analysis proves that the PET-MRNN model can completely eliminate noise disturbance through learning and compensation during the convergence process, and then converge the residual error to zero and obtain the theoretical solution. Finally, simulation and experiments further proved the superiority of the PET-MRNN and the Sbp-sinh type activation function.