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Control of two-wheeled humanoid robots poses several challenges due to the unstable dynamics of their mobile base and the coupling between the upper and lower body dynamics. The problem is often faced in the literature with methods based on the linearized or simplified models that fail in exploiting the whole body dynamic capabilities of the platform in use. In this letter, we tackle the problem of whole-body dynamic control for a mobile wheeled unstable humanoid robot. Compared to the existing approaches based on online optimization to guarantee respect of the constraints, we propose a control method that takes into account the nominal constrained dynamics of the robot in the quasi-velocities through an internal model, thus reducing the computational burden. A computed-torque control law in the quasi-velocities is used to stabilize the robot around the upper position. We report on preliminary experimental …