Stability and control of a quadrocopter despite the complete loss of one, two, or three propellers

This paper presents periodic solutions for a quadrocopter maintaining a height around a position in space despite having lost a single, two opposing, or three propellers. In each case the control strategy consists of the quadrocopter spinning about a primary axis, fixed with respect to the vehicle, and tilting this axis for translational control. A linear, timeinvariant description of deviations from the attitude equilibrium is derived, allowing for a convenient cascaded control design. The results for the cases of losing one and two propellers are validated in experiment, while the case of losing three propellers is validated in a nonlinear simulation. These results have application in multicopter fault-tolerant control design, and also point to possible design directions for novel flying vehicles.