This paper presents development of a circuit solution design for a bidirectional wireless energy transfer system, based on a resonant self-oscillator. The operation principle of the developed circuit solution in receiving and transmitting mode is described and the elementary circuit diagram is presented together with design ratios. Coil parameters for the resonant circuit are calculated, optimal number of turns in coils is presented, based upon the specified limit value of permissible current. The dependencies of system efficiency from transmitted power, maximum transmitted power, and energy transmission distance are obtained. The developed design, which includes the step-up DC-DC converter, allows to obtain the voltage on the output of the receiving system, equal to or higher than the voltage of the power source of the transmitting system. The specific feature of the proposed system is that it does not require a dedicated control system for operation in resonant mode and changing direction of power transfer. Resonance in transmitting and receiving coils can be maintained, even when their mutual layout is changed, due to utilization of identical resonant circuits and a self-oscillator. Application of the proposed solution is relevant for energy transfer among autonomous robots with limited positioning accuracy, as well as for energy transfer from power supply to robot or in reverse direction.