IEEE Robotics & Automation Magazine - June 2015 - 27

board. The price is similar to other embedded platforms in the
same class. Recent developments by OdROid suggest the
possibility of using the less powerful OdROid-W board since
the price is four times lower compared with the Odroid-XU,
but the OdROid-W has been recently released on the market.
Software Architecture
The OdROid-XU performs the following tasks:
● sensor fusion between Tango's pose and the vehicle's iMU
● nonlinear position-based control.
While both tasks could conceivably have been performed
on the Tango device, we used an independent processor to
facilitate the ease of prototyping and to ensure a more reliable approach to state estimation and control at a fixed rate
of 100 Hz.
A Java application routine is enabled on the phone for
pose streaming using the user datagram protocol (UdP). The
OdROid-XU runs a robot operating system (ROS)-based architecture (http://www.ros.org). The UdP packets are received by a ROS node and are subsequently converted into
ordinary ROS messages. it should be pointed out that the presented strategy allows the vehicle to run all the algorithms on
board. The base station is responsible only for visualization
and handling user interaction.
Modeling
A quadrotor is a system made of four identical rotors and propellers located at the vertices of a square. The first and the
third propellers rotate clockwise, and the second and the
fourth propellers rotate counterclockwise (see Figure 6). The
symbols used in this article are listed in Table 1.
Dynamic Model
Let us consider an inertial reference frame denoted by
" ev1; ev2; ev3 , and a body reference frame centered in the center
of mass (COM) of the vehicle denoted by " br 1; br 2; br 3 , . The
dynamic model of the vehicle can be expressed as
xo = v,
mvo = - Rxe 3 + mge 3,
t,
Ro = RX
o + X # JX = M,
JX

"
b3

Figure 5. The computer-aided design (CAD) model for the robot
platform and the Google Tango device.

(1)

"
b1

"
b2

"
e1

"
e3

"
e2

Figure 6. The quadrotor model.

Table 1. A glossary of important symbols.

fj ! R
!R
M ! R3

x ! R3
R ! SO (3)
R c ! SO (3)
m!R
J!R
X ! R3
Xc ! R3
a ! R3
g!R
d!R
xd ! R3
xo d ! R 3
xp d ! R 3
e x, e v ! R 3
e R, e X ! R 3
x ! R 13
ab ! R3
u ! R6

Force produced by the jth propeller
Sum of forces produced by all four propellers
Moments generated by propellers around
body axes
Position of robot's COM
Rotation matrix of the vehicle with respect to
the inertial frame
Commanded rotation matrix
Mass of the vehicle
Rotational inertia of robot about its COM
Angular velocity of robot in the body frame
Commanded angular velocity of robot
in the body frame
Linear acceleration of robot in the body frame
Gravitational acceleration
Distance of each rotor from the COM
Desired position
Desired velocity
Desired acceleration
Translational errors
Attitude errors
State estimation vector
Accelerometer biases
Estimator input

where x ! R 3 is the Cartesian position of the vehicle expressed in the inertial frame, v ! R 3 is the velocity of the
vehicle in the inertial frame, m ! R is the mass, X ! R 3
is the angular velocity in the body-fixed frame, and
J ! R 3 is the inertia matrix with respect to the body
frame. The hat symbol t$ denotes the skew-symmetry opt = x # y for all x, y ! R 3, g is the
erator according to xy
standard gravitational acceleration, and e 3 = 60 0 1@T .
June 2015

IEEE ROBOTICS & AUTOMATION MAGAZINE

http://www.ros.org

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2015