This paper proposes a robust dual-quaternion based H∞ task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, and their influence upon the kinematics of the end-effector pose, we adapt H∞ techniques-suitable only for additive noises-to unit dual quaternions. The noise to error attenuation within the H∞ framework has the additional advantage of casting aside requirements concerning noise distributions, which are significantly hard to characterize within the group of rigid body transformations. Using dual quaternion algebra, we provide a connection between performance effects over the end-effector trajectory and different sources of uncertainties and disturbances while satisfying attenuation requirements with minimum instantaneous control effort. The result is an easy-to-implement closed form H∞ control design criterion. The performance of the proposed strategy is evaluated within different realistic simulated scenarios and validated through real experiments.