Cable-Driven Parallel Robots (CDPRs) contain numerous advantages over conventional manipulators mainly due to their large workspace. Reconfigurable Cable-Driven Parallel Robots (RCDPRs) can increase the workspace of classical CDPRs by modifying the geometric architecture based on the task feasibility. This paper introduces a novel concept of RCDPR, which is a Mobile CDPR (MCDPR) mounted on multiple mobile bases allowing the system to autonomously reconfigure the CDPR. A MCDPR composed of two mobile bases and a planar CDPR with four cables and a point mass is studied as an illustrative example. As the mobile bases containing the exit points of the CDPR are not fixed to the ground, the static and dynamic equilibrium of the mobile bases and the moving-platform of the MCDPR are firstly studied. Then, a real time Tension Distribution Algorithm (TDA) that computes feasible and continuous cable tension distribution while guaranteeing the static stability of mobile bases and the equilibrium of the moving-platform of a n = 2 Degree of Freedom (DoF) CDPR driven by n+2 cables is presented.