Control of Cable-Driven Parallel Robots (CDPRs) is considered as a challenging task due to their highly nonlinear dynamic behavior, abundant uncertainties, low-stiff cables, parameters variation, cable tensions, and actuation redundancy. Hence, a robust controller is needed to obtain higher performance despite the above mentioned issues. In this paper, we propose a Robust Integral of the Sign of the Error (RISE) control scheme to solve the problem of reference trajectory tracking. RISE feedback control is a robust nonlinear continuous controller which can guarantee a semi-global asymptotic tracking under limited assumptions on the system's structure. RISE ensures the closed-loop system robustness towards parametric uncertainties and external disturbances. The proposed control solution is designed and implemented in real-time experiments on a fully constrained 4-DOF Cable-Driven Parallel Robot (CDPR) named PICKABLE. The obtained experimental results show that the proposed controller outperforms the classical PID controller and the first-order Sliding Mode Control (SMC) in terms of tracking performances and robustness towards payload variations.