I. Introduction
In recent years, quad-rotor have become more and more widely used in civil unmanned aerial vehicles (UAVs), especially consumer UAVs due to their small size, simple structure, and easy handling. However, as the application scenarios of quad-rotor become increasingly complex, collisions may occur during flight, causing irreversible damage to the propulsion system (e.g. propeller break or motor stop). Traditional quad-rotor, as a typical under-driven controlled object, have relatively low reliability. Once a propeller or motor fails, it will almost certainly crash or destroy the aircraft. Although [1] realized the space position control when one or two propeller failures under the traditional quad-rotor structure, the aircraft was always in the state of spinning around the yaw axis during the flight. As a result, the method provided by [1] cannot satisfy the stable control of the attitude angle, i.e., it will cause damage to the airborne equipment. The safety problem has dramatically limited the broader application of quad-rotor.