Input disturbances and physical constraints are important issues in the kinematic control of redundant manipulators. In this chapter, we present a novel recurrent neural network to simultaneously address the periodic input disturbance, joint angle constraint, and joint velocity constraint, and optimize a general quadratic performance index. The presented recurrent neural network applies to both regulation and tracking tasks. Theoretical analysis shows that, with the presented neural network, the end-effector tracking and regulation errors asymptotically converge to zero in the presence of both input disturbance and the two constraints. Simulation examples and comparisons with an existing controller are also presented to validate the effectiveness and superiority of the presented controller.