In this paper, we tackle the problem of trajectory tracking for a particular class of underactuated vehicles with full torque actuation and a single force direction (thrust), which is fixed relative to a body attached frame. Additionally, we consider that thrust reversal is not available. Under some given assumptions, the control law that we propose is able to track a smooth reference position trajectory while minimizing the angular distance to a desired orientation. This objective is achieved robustly, with respect to bounded state disturbances, and globally, in the sense that it is achieved regardless of the initial state of the vehicle. The proposed controller is tested in an experimental setup, using a small scale quadrotor vehicle and a motion capture system.