This paper is concerned with the design of a state feedback control scheme for variable stiffness actuated (VSA) robots, which guarantees prescribed performance of the tracking errors despite the low range of mechanical stiffness. The controller does not assume knowledge of the actual system dynamics nor does it utilize approximating structures (e.g., neural networks and fuzzy systems) to acquire such knowledge, leading to a low complexity design. Simulation studies, incorporating a model validated on data from an actual variable stiffness actuator (VSA) at a multi-degrees-of-freedom robot, are performed. Comparison with a gain scheduling solution reveals the superiority of the proposed scheme with respect to performance and robustness.