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Control inputs of fully constrained cable-driven parallel robots (CDPRs) are constrained by the positiveness of the cables tension, as cables merely apply tensile forces. The positive tension distribution (PTD) in CDPRs is usually guaranteed with iterative optimization techniques, utilizing the redundant actuation of the CDPR. The iterative nature of the conventional PTD limits their real-time application since the worst-case computation time of the iterative methods is not predictable. In addition, optimization methods are prone to model uncertainties. This article addresses the PTD problem in the fully constrained CDPRs with a control viewpoint. In the proposed approach, the PTD algorithm is an integral part of the controller, which explicitly generates positive values for the cables tension. To this aim, a saturation-type function is coupled with the controller, and its effect is compensated using a nonlinear disturbance observer. The stability of the proposed control scheme is also investigated in detail through Lyapunov’s second method, considering a nonsingular terminal sliding mode controller. Furthermore, the performance of the proposed methodology is compared with the conventional method for a six-degrees-of-freedom CDPR, in the presence of uncertainties. Finally, the effectiveness of the proposed control scheme is investigated through experiments. [ABSTRACT FROM AUTHOR]