With the gradual development and maturity of UAV technology, micro UAVs are increasingly widely used in tasks that require high dynamic flight, such as obstacle crossing, tracking and shooting. According to Newton’s second law and Euler’s equation, the rigid body model including kinematics, dynamics and attitude motion equations is derived; Derive the control effectiveness model and implement the connection between the control effectiveness model and the rigid body model. We take crossing a 30° gap as the background. Through literature review, it was determined that the UAV close the controller before crossing the gap and use inertia to cross the gap. After obtaining the velocity and acceleration constraints before crossing the gap, use the Pontryagin minimum principle to plan a trajectory close to the gap which is the desired position; Using the property of differential flatness, the desired roll and pitch angles are calculated with the desired position and the determined yaw angle. Finally, a quadrotor UAV controller based on model predictive control is designed. The quadrotor UAV model is linearized. The controller model is built, and the parameters are adjusted to achieve the integrated control of the position and attitude of the micro quadrotor UAV when it approaches the gap. Simulation shows that model predictive control can achieve the above goals.