This paper proposes an H_∞ methodology for position control of 6-DoF Cable-Driven Parallel Robots, which is then applied to the redundant 6-DoF cable-robot INCA with 8 cables. The issue is to control a non-linear coupled MIMO system with constrained states. The control scheme is composed of two cascade parts: position and force control. The position is controlled in the operational space, making use of the end-effector pose measured by a vision-tracking system, where a four-blocks H_∞ design scheme with finely adjusted weighting filters ensures good trajectories tracking and disturbances rejection properties while handling properly the non-linear and coupling effects. The force control allows then to generate the control inputs that maintain the cables under feasible tensions. The methodology is evaluated by simulations with a model of the INCA 6D robot.