The paper deals with the motion analysis of the objects with vibration components in cases where the relative velocity is very small, or even in the case when velocity direction is changed on opposite, including stopping time moments. The area of velocities practically has not been studied in scientific works. This is primarily caused by the fact that experimentally it is difficult to identify the forces in a low-velocity region or in time moments corresponding to changing the flow in the opposite direction. A new model in the form of a velocity power function for determination of interaction forces within the Stokes flow area is proposed. The theory is validated in application to the motion in water of the two degrees of freedom system under the vibration excitation. The simplified relationships describing the interaction of a vibrating object with the fluid are obtained. These interconnections may be used to solve the motion control tasks in synthesis of robotic systems. For this purpose, it is proposed to switch over the law for the speed of the interaction described by a power function. In the presented example of synthesis, the system motion is excited by the antiphase internal harmonic force. The results of research can be used to develop drive mechanisms of diving robots, as well to perform calculations of the robots flying in air with the aid of vibrating wings. The information on diving robots R10 and R11 developed in RTU on the base of the proposed theory is presented