Some tasks of mobile robots motion control with "clinging" propulsion devices that work only in the "pullup" mode to a fixed support are considered, which is due to the flexibility of the cables used in propulsors. A method of moving by means of "clinging" anchor-cable propulsion devices attached to an underwater platform with a small positive buoyancy is described. The principle of the operation of robots of vertical motion with cable drives and the problems of calculating their modes of motion are described. Methods for solving the problem of mobile robots motion control with "clinging" propulsion devices with excessive nonstationary connections are given.