IEEE Robotics & Automation Magazine - December 2018 - 37

Pixhawk
Controller
Position
Controller
IMU

Control
Allocation

State
Estimation

Mixer

Actuators

Attitude
Controller

Motion
Capture

User Input

Figure 3. The flight controller structure.

core are a Pixhawk flight controller, a UP board-embedded
computer that provides additional computational power, and
the motion-control boards for the tilting motors.
The presented system has a total weight of 3.2 kg and a
flight time of around 8 min in its horizontal orientation. This
significantly decreases if the system is required to hover at a
large inclination angle.
Flight Controller
The Pixhawk flight controller (Figure 3) used on this platform
consists of an inertial measurement unit (IMU), a magnetometer, a barometer, and a Cortex-M4F microprocessor. The
Pixhawk runs the PX4 software [21], which handles full control of the multirotor as well as the interfaces with other
devices. It also provides a flexible modular framework that
allows the integration of new control schemes.
Using the built-in state estimation provided by the PX4
software, the sensor data obtained by the IMU and magnetometer are fused together with the external pose information
from a Vicon motion-capture system (or, in the case of outdoor flight, the position information from a global navigation
satellite system) to provide an estimate of the system's full
pose. This information enters the controller block together
with the desired pose trajectory, which is generated by the
user on an external computer.
This desired trajectory is then sent to the UP board via
Wi-Fi and ultimately to the Pixhawk through a serial connection. The controller block contains both the position and attitude controller, as well as an allocation block that maps the
desired forces and moments onto the 12 actuators. This is
crucial to the decoupling of position and orientation. After
the desired control inputs are calculated, they are fed into the
mixer block, which maps these values to the actuator pulsewidth modulation signals.

Modeling
Developing a system model for such a vehicle is a necessary
step for enabling model-based control synthesis and thorough
testing. To fulfill this task, a methodology was used that combines rigid-body dynamics with well-established aerodynamic modeling techniques.
Coordinates and Conventions
Here, we provide an overview of the coordinate systems and
notational conventions used subsequently.
Coordinate Frames
Overall, eight coordinate frames were used. The inertial frame
Fi is fixed on the ground, and its z axis points upward. In
contrast, the z axis of the body frame FB points downward,
as seen in Figure 4; its origin is at the center of gravity. Finally,
there are the six coordinate frames of the rotor units FR,i,

ezI

eyB
ezB

eyI

exB
5

exI
Figure 4. The inertial and body coordinate system.

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IEEE Robotics & Automation Magazine - December 2018

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