A redundant cable-driven platform (CDP) is composed of m cables that exceed the degree-of-freedom (DoF) of the end-effector. The choice of tension along the cables admits infinite solutions. This paper proposes the use of the analytic center to solve the tension distribution problem. Adopting this technique allows finding tensions far from the tension limits, namely, robust as well as tension profiles continuous and differentiable in time. The continuity, differentiability, and uniqueness of the solution are also proven. Moreover, the possibility of including non-linear constraints acting on the tensions (e.g., friction) is a further contribution. The computational time with the proposed approach is compared to the existing techniques to assess its real-time applicability. Finally, several simulations using several cable-driven parallel robots’ (CDPRs) architectures are reported to demonstrate the method’s capabilities.