Static Hovering Realization for Multirotor Aerial Vehicles with Tiltable Propellers

Abstract

This paper presents a theoretical study on the ability of multi-rotor aerial vehicles (MRAVs) with tiltable propellers to achieve and sustain static hovering at different orientations. To analyze the ability of MRAVs with tiltable propellers to achieve static hovering, a novel linear map between the platform's control inputs and applied forces and moments is introduced. The relation between the introduced map and the platform's ability to hover at different orientations is developed. Correspondingly, the conditions for MRAVs with tiltable propellers to realize and sustain static hovering are detailed. A numerical metric is then introduced, which reflects the ability of MRAVs to sustain static hovering at different orientations. A subclass of MRAVs with tiltable propellers is defined as the Critically Statically Hoverable platforms (CSH), where CSH platforms are MRAVs that cannot sustain static hovering with fixed propellers, but can achieve static hovering with tilting propellers. Finally, extensive simulations are conducted to test and validate the above findings, and to demonstrate the effect of the proposed numerical metric on the platform's dynamics.

Full-pose Trajectory Tracking of Overactuated Multi-Rotor Aerial Vehicles with Limited Actuation Abilities

“…Furthermore, let us denote by N ∈ N >0 as the number of propellers, and let us assume for the sake of this paper, the generic case where each propeller can be tilted independently in S 2 (i.e., each propeller is actuated by 2 independent servo motors). Note that propellers tilting in S 1 or fixed are special cases of the above [17]. Let us denote by F pi as the propeller fixed frame, with O pi coinciding with the fixed attachment point of the i th propeller in body frame, denoted by p p i .…”

“…where S(•) is the skew-symmetric operator, r i = c τ /c f is the ratio between the drag coefficient and the lift coefficient, and I is the identity matrix. The matrix F , referred to as the full allocation matrix, is constant throughout the operation of the platform [17]. The full allocation matrix can be written as…”

Full-pose Trajectory Tracking of Overactuated Multi-Rotor Aerial Vehicles with Limited Actuation Abilities

“…Furthermore, let us denote by N ∈ N >0 as the number of propellers, and let us assume for the sake of this paper, the generic case where each propeller can be tilted independently in S 2 (i.e., each propeller is actuated by 2 independent servo motors). Note that propellers tilting in S 1 or fixed are special cases of the above [17]. Let us denote by F pi as the propeller fixed frame, with O pi coinciding with the fixed attachment point of the i th propeller in body frame, denoted by p p i .…”

“…where S(•) is the skew-symmetric operator, r i = c τ /c f is the ratio between the drag coefficient and the lift coefficient, and I is the identity matrix. The matrix F , referred to as the full allocation matrix, is constant throughout the operation of the platform [17]. The full allocation matrix can be written as…”