As the control object free-flying space manipulation robot represents the mechanical system consisting of the case (bearing rigid body) 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 problem of the free-flying space manipulation robot reduction in an initial state before payload installation is solved. Conditions of applicability of simplified mathematical model are defined at synthesis of control algorithms by the manipulator which is carrying out operations in a working zone of the robot.