A quaternion-based feedback is developed for the attitude stabilization of rigid bodies. The control design takes into account a priori input bounds and is based on nested saturation approach. It results in a very simple controller suitable for an embedded use with low computational resources available. The proposed method is generic not restricted to symmetric rigid bodies and does not require the knowledge of the inertia matrix of the body. The control law can be tuned to force closed-loop trajectories to enter in some a priori fixed neighborhood of the origin in a finite time and remain thereafter. The global stability is guaranteed in the case where angular velocity sensors have limited measurement range. The control law is experimentally applied to the attitude stabilization of a quadrotor mini-helicopter. ► Attitude stabilization of rigid bodies with a bounded feedback is considered. ► The control is generic and suitable for embedded limited computational resources. ► The almost global stability is formally proved. ► The design considers the slew rate limits avoiding rate gyro saturations. ► Experiments are performed on a quadrotor helicopter.