It is considered of a space manipulation robot function in the regime of the free drift at which the task of control by a manipulator is solved in the class of systems with feedback. As the control object free-flying space manipulation robot represents the mechanical system consisting of the case and a swivel link to it the bodies system (the iterative manipulator). The case is supplied by own control system of position in space. The possibility of building a combined energy-saving motion control of a free-flying space manipulation robot is considered. The problem of the free-flying space manipulation robot reduction in an initial state before payload installation is solved. The notion of technical controllability of the free-flyer was introduced. Conditions of applicability of simplified mathematical model are defined at synthesis of control algorithms by the manipulator which is carrying out operations in a robot working zone.