Most of the current industrial applications (like food packaging, waste sorting, machining, etc.) use parallel kinematic manipulators (PKMs) owing to their high speed and accuracy. However, parallel robots are exposed to highly nonlinear dynamics, time-varying parameters and uncertainties, especially in those applications. Considering all these issues, the synthesis of advanced and robust control schemes for PKMs is considered a challenging task. A new control scheme based on the Robust Integral of the Sign of the Error (RISE) control scheme is proposed in this work. A revision of the standard RISE control law is proposed by considering, in the control loop, a compensation term computed from the dynamic model of the robot, the measured and the desired trajectories, and the tracking error. In addition, we propose to extend the resulting controller with a nonlinear feedback function to compensate for the errors resulting from using the desired trajectories instead of the measured ones in the dynamic compensation term. The proposed control contribution can compensate for PKM parameter uncertainties and high nonlinearities as well as improve the robustness of the standard RISE controller. Numerical simulations have been conducted on a parallel robot, called T3KR, in a pickand-throw task under different operating conditions to confirm the effectiveness of the proposed control scheme.