Mobile robotic systems are employed to perform a wide range of transportation and technological tasks. One of the main requirements to these systems is their high capability to traverse complex terrains and surfaces. Future applications of wheel-walking mobile systems largely define the problem of their energy efficiency. This paper presents a mobile robotic system with wheel-walking propulsion that can increase the system’s traverse capability on support surfaces with low bearing properties due to a new chassis layout and algorithms controlling the walking module. A cyclogram of the energy efficient step of the mobile robotic system with wheel-walking propulsion is developed, which provides high indicators of traverse capability on support bases with low bearing capacity.