On Optimal Control of the Wheel Radius When Rolling Along a Horizontal Non-Deformable Surface

Continuous change of the support wheels radius of the vehicle provides the possibility of continuous control of its operational properties. These properties include: driving stability, controllability, cross-country ability, etc. It change is rational to make while minimizing heat losses in the actuator. The motion without slip of a rigid wheel with a continuously changing radius on a flat horizontal non-deformable 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 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 that ensures 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 unorganized surfaces.