Cable-driven systems are of great interest in applications for which remote actuation is required, like for instance to operate within medical imaging devices. In such applications, robotic architectures based on remotely actuated cable-driven manipulators (CDM) offer innovative design options. However, unlike more conventional CDM, such designs involve specific control problems. This paper deals with the control of CDM in the presence of friction, as experienced when particular design constraints have to be taken into account (size, materials, length of transmissions). In this case, the influence of friction on the manipulator motions is such that dynamic modeling, identification and control, are no longer adapted, nor even possible. As a result, for quasi-static positioning tasks, we propose a CDM position control strategy resulting from a cascade structure, with an internal cable tension control loop to handle friction. Cable tension is measured using an original instrumented compliant structure. From the control point of view, the originality of the present paper comes in particular from the development of a feasibility algorithm which allows us to limit cables tensions within a specified range. This strategy is experimentally assessed on a robot for image-guided medical procedures.