Abstract <p>Continuous variation of the support wheel radius of a vehicle enables the possibility of continuous control of its operational properties. These properties include driving stability, controllability, offroad ability, etc. This variation should be implemented in a way that minimizes thermal losses in the actuator. The motion without slippage of a rigid wheel with a continuously changing radius on a flat horizontal nondeformable surface is considered. A mathematical model is proposed to describe the dynamics of constant-speed plane-parallel motion of the specified wheel while controlling the value of its radius. It is based on the hypothesis that there is not slippage in the contact between the wheel and the supporting plane. The obtained mathematical dependencies allow us to determine the optimal control mode when changing the radius based on the criterion of minimum heat loss in the actuator responsible for this change. The results of the research can be used to control the parameters of vehicles’ operational properties, as well the wheeled robots moving on unstructured surfaces.</p>