The intrinsic interaction of a robotic system that includes two 6-degree-of-freedom cable-driven platforms sharing a common workspace might result in cable interferences for random trajectories. This paper presents and analyzes computational methods for geometrically determining and managing these interferences for any trajectory constrained with variable loads. The algorithms considered determine which cable can be released from an active actuation state while allowing control in a minimal tension state, thereby ensuring that both platforms stay in a controllable workspace. The process of managing cable interferences constitutes a challenge as one must take into account the inherent limitations of the workspace, which not only include the possibility of interference itself, but also the geometry of the cable-driven locomotion interface (CDLI), its dynamics, the nonideal behavior of real cables, and the requirement that both platforms must be completely constrained at any time. As releasing a cable from an active actuation state might generate tension discontinuities in the other cables, this paper also proposes collision prediction schemes that are only applied to redundant actuators in order to reduce or completely eliminate such discontinuities. Finally, a simulation of a CDLI embedded as a peripheral in a virtual environment, in which the load applied on each platform comes from the wrench measured under the foot for a natural gait walking, is thoroughly analyzed.