Fundamental Actuation Properties of Multi-rotors: Force-Moment Decoupling and Fail-safe Robustness

In this paper we shed light on the fundamental actuation capabilities of multi-rotors, such as force-moment decoupling and ability to robustly fly still in place after the loss of propellers. These two actuation properties are formalized through the definition of some necessary algebraic conditions on the control force and control moment input matrices of generically tilted multi-rotors. Standard quadrotors are not able to robustly fly still at a constant spot after the loss of a propeller. The increased number of actuators of a hexarotor does not always help to overcome this limitation. To deeply understand this counterintuitive result, we apply the developed theory on the analysis of fail-safe robustness of hexarotor platforms, and clarify the role of the tilt angles and locations of the propellers in the vehicle. We show that standard star-shaped hexarotors are unable of robust static hovering after a propeller failure, while both the tilted star-shaped hexarotor and the Y-shaped hexarotor possess this important property. The analysis is validated with both simulation and experimental results testing the control of six-rotor vehicles subject to rotor loss.