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) that is fixed relative to a body attached frame. Additionally, we consider that thrust reversal is not available. We present the design of a hybrid controller that, under some given assumptions, is able to globally asymptotically stabilize the vehicle to a reference position trajectory while minimizing the angle to the desired attitude trajectory. This objective is achieved robustly and globally, in the sense that small perturbations do not lead to instability and it is achieved regardless of the initial state of the vehicle. The algorithm is tested in a experimental setup, using a small scale quadrotor vehicle and the VICON motion capture system.