The research works carried out in this paper deal with the control of a fast double-steering off-road mobile robot. Such kind of robots requires very high stable and accurate controllers because their mobility is particularly influenced by wheel-ground interactions. Hence, the vehicle dynamics should be incorporated in the control circuit to take into account these issues, which is developed based on the road geometry parameters and the slippage-friction conditions at the wheel-ground contacts. Relying on this dynamic model, we present in this paper the design and application of a constrained Model Predictive Control (MPC). It is based on the minimization of a cost function (optimizing the devi-

This paper proposes a new wheel motion generator to track the centroidal motion of one quadrupedon-wheel robot which has the ability to cross various rough terrains with the model based wholebody torque control. The generator is used to track the whole-robot centroidal motion reference. Firstly, the wheel contact model and the whole-body inverse kinematics model are derived using spatial vectors. The wheel motion is extracted out mathematically depending on the base and the legged motions, which serves as the kinematics model. Then the wheel motion generator is developed by combining both the kinematics model and the robot centroidal momentum/dynamics model. The models are decomposed into three components relating to the base motion, the legged motion and the wheel motion. The adaptive wheel motion references are derived in a detailed mathematical way and several algorithms are developed for the model decompositions. Finally, the robot is simulated to be driven on various rough terrains using the operational space control framework mixed with our proposed compatible prioritized impedance controller. The required torque for multiple tasks is generated by the feed-forward and feedback controllers while fulfilling the contact constraints.