The authors discuss a possibility of application of the feedback principle for the task of control of a free-flying space handling robot (SHR) in the mode of handling operation. They propose a robot consisting of the main body (case), which has the control system by rotation and translational movement, and the three-links manipulator with rotation degree of freedom for each link. The SHR is expected to have a system of technical vision for obtaining information about the location of the target and the distance to it. The mathematical model of the space handling robot is introduced. For simplicity reasons the plane motion of the SHR is considered. The model has the coordinates of a grip deflection from a target in the inertial space in an explicit form. An algorithm is proposed for estimation of the coordinates with account of the information about the direction of the target and the distance to it. This information is obtained with the use of the range finder built in the video camera which is placed on the SHR case. The task of the control algorithm formation by the target capture in the inertial space is solved. The control task is determined as the solution of the three subtasks: 1) continuous target tracking, 2) accessibility of the target and 3) guarantee of soft-docking. The first subtask is an auxiliary one. But its solution is necessary for realization of measurements of the distance between the grip and the target. As a way to solve the second subtask the authors suggest a modification of the well-known random search with a return algorithm. Its efficiency is guaranteed by taking into account only the successful random steps of control which decrease the distance to the target. For soft docking (subtask 3) the area of the suggested algorithm must be restricted by the time moment when the SHR enters the small area which includes point A (target). An example of the free-flying space robot dynamics computer simulation is presented, which proves the efficiency of the proposed algorithm.