A class of abstract aerial robotic systems is introduced, the laterally bounded force vehicles, in which most of the control authority is expressed along a principal thrust direction, while along the lateral directions a (smaller and possibly null) force may be exploited to achieve full-pose tracking. This class approximates platforms endowed with noncollinear rotors that can modify the orientation of the total thrust in a body frame. If made possible by the force constraints, the proposed SE(3)-based control strategy achieves the independent tracking of position-plus-orientation trajectories. The method, which is proven using a Lyapunov technique, deals seamlessly with both underactuated and fully actuated platforms, and guarantees at least the position tracking in the case of an unfeasible full-pose reference trajectory. Several experimental tests are presented that clearly show the approach practicability and the sharp improvement with respect to state of the art.