IEEE Robotics & Automation Magazine - September 2020 - 100

Each fixed-tilt concept is displayed in Figure 2 with an
illustrative plot of its rotor configurations. Table 2 presents the concepts' mapping-matrix variables, including
the rotor displacements, p i; orientations, u i; rotation
direction, a i; and design parameters for different versions
of the concepts.
Quad4Hor
The first concept is an extension of a conventional
quadrotor that achieves full actuation by adding four
(unidirectional) horizontal rotors (indexed 5-8). There
have been two different
implementations of this
Several fully actuated
concept in the literature. In Frankenberg
multirotor platforms were
and Nokleby [6], the
a ddit iona l rotors are
introduced during the past
positioned between the
quadrotor rotor arms, as
decade to overcome the
shown in Figure 2(a).
The added rotors do not
underactuation property of create a moment around
the CoM, and the airflow
conventional multirotors.
interference among the
rotors is minimized. The
other implementation is
by Salazar et al. [7], where the horizontal rotors are located
under the vertical ones. However, the airflow interference in
the design of [7] has negative effects on the controllability of
the UAV. It is worth mentioning that [7] was one of the

Table 1. The abbreviations used in the
"Fixed-Tilt UAV Concepts" and "Variable-Tilt
UAV Concepts" sections.

100

Concept

Abbreviation

Quadrotor with four horizontal rotors

Quad4Hor

Hexarotor with canted rotors

HexC

Hexarotor with canted and dihedral rotors

HexCD

Coaxial hexagon with 12 canted rotors

CoHexC

Double tetrahedron hexarotor

HexDTet

Heptarotor with minimized frame

HeptF

Heptarotor with maximized wrench

HeptW

Octarotor cube

OctCu

Octarotor beam

OctB

Quadrotor with variable cant rotors

QuadvC

Quadrotor with variable dihedral rotors

QuadvD

Quadrotor with variable cant and dihedral rotors

QuadvCD

Quadrotor with coupled variable cant and
dihedral rotors

QuadvCDc

Hexarotor with variable cant rotors

HexvC

Hexarotor with coupled variable cant rotors

HexvCc

IEEE ROBOTICS & AUTOMATION MAGAZINE

SEPTEMBER 2020

earliest attempts to obtain horizontal actuation with a multirotor UAV.
HexC
The HexC concept [Figure 2(b)] can be considered the simplest modification of conventional multirotors to achieve
fully actuated flight. The rotor's positioning is the same as
the conventional hexarotor's, with all six rotors placed on
the vertices of a planar hexagon. Full actuation is achieved
by tilting the rotors around the axis collinear with the rotor
arm. This tilting, denoted by a, is referred to as canting, as
discussed in the "Coordinate Frames" section. By canting
the rotors, they will produce thrust vertically and horizontally. The canting angle of all of the rotors is equal, and the
rotors' canting and rotation directions alternate (Table 2),
resulting in three symmetric rotor pairs with opposite rotation
directions. Due to the design's symmetry, the drag torque of the
rotors is counteracted. The amount of canting depends on
the application: a large cant angle leads to high horizontal
forces, while a small one results in higher flying efficiency.
The angle is limited by the minimum required upward
thrust for overcoming gravity.
This concept was proposed by Voyles et al. [8], [9] and
achieved fully actuated flight with a cant angle of a = 20°.
The same authors demonstrated in [10] that the HexC concept has better disturbance-rejection capabilities against lateral wind gusts than the conventional hexarotor. A higher
cant angle of 47° was used by Rashad et al. [11] to maximize
the horizontal force applied during a contact-based scenario. An experimental 2-kg HexC platform was able to apply
1 kg of force to a vertical surface without pitching. Omnidirectional versions of the HexC concept have been proposed
in [12] and [13]. In [12], a version with a cant angle optimized for a maximum wrench was proposed as a cobot for
space applications. Due to the absence of gravity during the
intended operation, the optimal cant angle was higher: 55°
instead of the 47° in [11]. Finally, another omnidirectional
version was proposed in [13] that utilized variable-pitch
propellers to generate bidirectional thrust, unlike the previously presented designs, which use fixed-pitch unidirectional propellers.
HexCD
The HexCD concept, displayed in Figure 2(c), is considered
an extension of the HexC. In this design, the rotors are canted
and tilted along the axis perpendicular to the rotor arms,
which is called a dihedral angle (b), as discussed in the "Coordinate Frames" section. This concept is the most studied/used
design in the literature so far, with different angles optimized
for different criteria. The concept was proposed by Rajappa
et al. [14] who chose a and b to minimize the required total
thrust for full-pose UAV controllability for a given trajectory.
The optimal angles depend heavily on the trajectory; for
instance, for an in-hover pitching maneuver, the optimal
dihedral angle was shown to be nonzero. It was demonstrated
in [14] that the direction of the dihedral angle (positive or

IEEE Robotics & Automation Magazine - September 2020

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