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

Giulia Michieletto 1, 2 Markus Ryll 1 Antonio Franchi 1
1 LAAS-RIS - Équipe Robotique et InteractionS
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : In this paper we shed light on two fundamental actuation capabilities of multi-rotors. The first is the amount of coupling between the total force and total moment applied by the propellers to the whole body. The second is the ability to robustly fly completely still in place after the loss of one or more propellers, when the used propellers can only spin in one direction. These two actuation properties are formalized through the definition of some algebraic conditions on the control allocation matrices. The theory is valid for any multi-rotor, with arbitrary number, position and orientation of the propellers, including the more classic ones. As a show case for the general theory we show and explain why 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 in the vehicle. The theory is also able to explain why, on the contrary, both the tilted star-shaped hexarotor and the Y-shaped hexarotor can fly with only five out of six propellers. The analysis is validated with both simulations and experimental results testing the control of multi-rotor vehicles subject to rotor loss.
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Giulia Michieletto, Markus Ryll, Antonio Franchi. Fundamental Actuation Properties of Multi-rotors: Force-Moment Decoupling and Fail-safe Robustness. IEEE Transactions on Robotics, IEEE, 2018, 34 (3), pp.702-715. ⟨10.1109/TRO.2018.2821155⟩. ⟨hal-01612602v2⟩

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