Fundamental Actuation Properties of Multirotors: Force-Moment Decoupling and Fail-Safe Robustness

In this paper, we shed light on two fundamental actuation capabilities of multirotors. The first is the degree of coupling between the total force and total moment generated by the propellers. The second is the ability to robustly fly completely still in place after the loss of one or more propellers, in the case of mono-directional propellers. These are formalized through the definition of some algebraic conditions on the control allocation matrices. The theory is valid for any multirotor, with arbitrary number, position, and orientation of the propellers. As a show case for the general theory, we demonstrate that standard star-shaped hexarotors with collinear propellers are not able to robustly fly completely still at a constant spot using only five of their six propellers. To deeply understand this counterintuitive result, it is enough to apply our theory, which clarifies the role of the tilt angles and locations of the propellers. The theory is also able to explain why, on the contrary, both the tilted star-shaped and the Y-shaped hexarotors can fly with only five out of six propellers. The analysis is validated with both simulations and extensive experimental results showing recovery control after rotor losses.