This paper deals with the modeling and vision-based control of large-dimension cable-driven parallel robots. Inverse kinematics and instantaneous inverse kinematics models are derived from the elastic catenary cable modeling. These models turn out to be dependent on the pose of the mobile platform (end-effector), on the cable tangent directions and on the cable tensions. In order to control the motion of the robot, a position-based visual servo control is used, where the mobile platform pose is measured by vision and used for regulation. A multi-camera setup and load cells provide the aforementioned desired measurements, i.e., the mobile platform pose, the directions of the tangents to the cables, and the cable tensions. The proposed approach was validated in experiments on the large-dimension cable-driven parallel robot prototype CoGiRo of global dimensions 15 m x 11 m x 6 m (L x l x h). A maximum error of less than 1 cm in position and 0.5° in orientation was achieved. Moreover, in the case of cable-driven parallel robots larger than the prototype CoGiRo, simulations were conducted in order to assess the influence on the vision-based control of four instantaneous inverse kinematics models.