2012 American Control Conference
Fairmont Queen Elizabeth, Montréal, Canada
June 27-June 29, 2012
Design and Validation of an Attitude and Heading Reference System
for an Aerial Robot Prototype
Bojan Milosevic, Roberto Naldi, Elisabetta Farella, Luca Benini and Lorenzo Marconi
Abstract— In this paper we consider the design and the experimental validation of an attitude and heading reference system
for a miniature aerial robot prototype based on measurements
obtained from a low cost off-the-shelf inertial measurement
unit. Different estimation algorithms to process the raw inertial
data are implemented and validated in real indoor flight tests
by employing, as a reference, the accurate attitude estimation
obtained from a vision based motion tracking system. The
proposed experiments allow to accurately evaluate the performance of the different estimation algorithms and the effects of
disturbances, such as vehicle accelerations, vibrations and non
ideal magnetic fields, in a typical scenario of application for
the considered unmanned vehicle prototype.
I. INTRODUCTION
Nowadays unmanned aerial vehicles (UAV) have attracted
the interest of many engineering fields and have been widely
employed in several civil and military operations [1]. One
of the main reason of this large success derives from the
effectiveness of the flight control system, and in particular
of the low-level attitude control loop [2], which requires an
accurate estimation of the attitude of the system. Typically,
the attitude is obtained using low cost Inertial Measurement
Units (IMU). The outputs of these sensors however are characterized by noise and time varying biases and are affected
by the disturbances caused by the vehicle own motion, such
as accelerations and vibrations. Indeed, to obtain an accurate
estimation, suitable sensor fusion algorithms must be implemented [3]. Different approaches have been developed to
estimate the vehicle orientation from sensor data, including
Kalman filters [4] and non-linear particle filtering techiniques
[5]. We focus on the Kalman filter approach, comparing its
two most adopted implementations, the Extended Kalman
Filter (EKF) [6] and the the Unscented Kalman Filter (UKF)
[7], [8].
In this work we consider the problem of designing an
attitude and heading reference system for an aerial robot
prototype by employing only the measurements deriving
from a commercial low-cost IMU. The vehicle in question
is given by a small prototype of ducted-fan aircraft [10] that
has been specifically designed for indoor robotics operations,
and in particular for inspection of large infrastructures [9].
In this scenario, the lack of an accurate position measure, in
particular of the Global Positioning System (GPS) signal that
can be used to compensate for the effects of aircraft motion
B.Milosevic, R.Naldi, E.Farella, L.Benini and L.Marconi are with
DEIS - Dipartimento di Elettronica, Informatica e Sistemistica,
Universitá di Bologna, 40136 Bologna, Italy [bojan.milosevic,
roberto.naldi, elisabetta.farella,
luca.benini, lorenzo.marconi]@unibo.it
978-1-4577-1096-4/12/$26.00 ©2012 AACC
in the inertial data [3], and the presence of mechanical vibrations and magnetic disturbances may significatively affect the
accuracy of the vehicle’s attitude estimation obtained using
only the inertial data. The main idea is to use as a reference
the attitude obtained through a vision based motion tracking
system [11], that is not affected by the above disturbances, in
order to validate the design of attitude and heading reference
system and, more specifically, to compare the performance
of both the EKF and UKF estimation algorithms during real
flight tests. To validate the design of an AHRS and, more
specifically, to compare the performance of both EKF and
UKF estimation algorithms during real flight tests, we used
as a reference the attitude obtained through an independent
vision based motion tracking system [11], that is not affected
by the above disturbances.
Several works compare the effectiveness of EKF and
UKF algorithms in similar scenarios: [12] simulate the two
algorithms as sensor fusion techniques to estimate position
and orientation of a ground vehicle. The results report a
similar performance of the two in term of estimation error,
while the UKF has a much larger computational time. In
[13] a loosely coupled INS/GPS navigation solution is used
to test nonlinear filters for pose estimation, correcting the
inertial estimations with the drift-free GPS ones. It shows
a better performance of the UKF, especially during periods
with no visible satellite, when the EKF can no longer track
the INS drifts, so the predicted values diverge. The two works
compare the proposed algorithms, but don’t use an external
reference to validate the performance and the latter uses a
GPS correction which is not suitable for indoor applications.
An independent reference reconstructed by a multi-camera
video setup is used in [14] to validate the performance of a
wearable IMU, employed for human movement tracking. In
[15] an indoor test-bed solution for small size autonomous
vehicles (RAVEN ) is proposed. The system employs several
IR cameras to obtain an accurate estimation of the vehicles’
position and orientation. This solution has been used to
improve the design and test of UAVs, but has not been
employed to validate the performance of low power and low
cost IMUs, now being widely avilable.
The paper is organized as follows: the next Section introduces the sensors’ models and their calibration techniques
and in Section III the estimation algorithms are presented.
The subsequent Section V shows the experimental setup and
results, leading to the conclusions in the last Section.
1720
II. S ENSOR M ODELS
For this work we used a commercial low-cost IMU
platform, the ST iNemo [16], which embeds the sensors
presented in Table I. The board has a small form factor
(4 × 4cm) and is provided with a mini-USB connector to
easily stream data to a PC.
The raw measurements Yg from the gyroscope, Ya from
the accelerometer and Ym from the magnetometer, expressed
in body frame, are modeled as:
Yg = wib + bg + νg
Ya = aib − g + ba + νa
(1)
Ym = m + νm
where νi , i ∈ {g, a, m}, are uncorrelated Gaussian white
noise with variance σi2 , while bg and ba are time-varying
biases modeled as a first-order Gauss-Markov process
ḃ = βb + νb
(2)
characterized by time constant 1/β and uncorrelated Gaussian white noise νb with variance σb2 .
A. Calibration
The MEMS sensors employed are factory calibrated, but
for a correct use they need to be calibrated when mounted
on the UAV, with respect to the body frame.
The gyroscope is affected by a constant bias b0g , which
can be easily estimated. When still, the sensor should report
a null angular velocity along all three axes, but instead it has
a constant bias. To compensate this unwanted effect, we put
the sensor still for some seconds and take the mean value
of the readings along each axis as the offset to be removed
from future readings. The compensated gyro readings Y˜g can
be expressed as:
Y˜g = Yg + b0g .
(3)
The accelerometer measurements are affected by scale and
offset factors for each axis and misalignment factors between
the sensor’s axes and the body frame axes. The relationship
between the calibrated Ỹa and the raw measurements Ya can
be expressed as:
Y˜a = Ca Ya + b0a
imperfections and external magnetic sources. Intrinsic imperfections cause again scale, offset and misalignment factors
between the sensor’s axes. External magnetic distortions
can be divided into Hard-iron and Soft-iron distortion [17].
Hard-iron distortion is produced by materials that exhibit
a constant magnetic field, thereby generating a constant
additive bias to the output of each magnetometer axes. Softiron distortion is the result of a material that influences,
or distorts, a magnetic field, in a way that cannot only
be captured as the effect of an additive disturbance on the
magnetic measurements. Only the effects of materials that
have a constant position and orientation with respect to the
sensor can be compensated by the calibration procedure.
An extensive magnetometer calibration method is proposed in [17] and it is here applied to correct raw sensor
readings. In particular the magnetometer measurement model
adopted for the calibration is given by:
(4)
where Ca ∈ R3×3 summarizes misalignment and scale
factors while b0a ∈ R3 is an offset vector. The goal of
the accelerometer calibration is to determine Ca and b0a ,
so that the calibrated values can be obtained with any new
raw measurement. To estimate the parameters the sensor is
placed at 6 stationary positions with known desired output,
i.e. with the gravity vector aligned with the positive and
negative directions of the three axes. At each position we
compute the average of 10 seconds of accelerometer raw
data and then we apply the least square method to obtain
the optimal calibration parameters.
The magnetometer senses the Earth’s magnetic field,
which is weak and can be corrupted by intrinsic sensor
Ym = Cm Ỹm + b0m

1
2 sin ρ1
=
3 sin ρ2 cos ρ3
0
2 cos ρ1
3 sin ρ3

0
 Ỹm +b0m
0
3 cos ρ2 cos ρ3
(5)
where Ỹm is the desired corrected value, coefficients k represent the sensor scaling errors and ρk the sensor misalignment angles. Equation (5) is solved for Ỹm and substituted
into
2
2
2
2
+ Ỹmy
+ Ỹmz
(6)
Ỹm = Ỹmx
where Ỹm is the (known) local magnetic field amplitude.
This gives a quadratic polynomial in Ymx , Ymy , Ymz , whose
coefficients are nonlinear functions of k , ρk and b0m . The
numerical values of these coefficients are found from a leastsquares solution using Ym , namely the raw data. Thereafter,
the system of nonlinear equations is solved numerically, and
the magnetometer measurements are corrected using:
−1
Ỹm = Cm
(Ym − b0m ).
(7)
Magnetic measurement errors are more critical when
compared to the other two sensors and primarily affect the
yaw angle estimation [3]. The proximity of the UAV motor
influences the magnetic field sensed, but can be compensated
because it has a fixed position in the body frame (hard iron
disturbance). On the other hand, magnetic or metal objects
encountered while the vehicle is moving introduce a soft iron
disturbance that can’t be compensated. Hence the magnetic
calibration procedure should be available as an on-line routine to re-calibrate the sensor when needed. Same results are
shown by [18], where the impact of magnetometer calibration
is validated in a helicopter UAV navigation system.
To summarize, the calibration procedure is the following:
1) collection of static data with the device resting on the
6 different orientations;
2) computation of accelerometer and gyroscope offsets
and scale factors;
1721
TABLE I
IMU SENSORS
Sensor
Accelerometer
Magnetometer
Gyroscope Roll-Pitch
Gyroscope Yaw
Model
Type
LSN303DLH
Digital
LPR430AL
LY330ALH
Analog
Analog
Range
±2g
±2gauss
300dps
300dps
Sensitivity
1mg/digit
1mgauss/digit
3.33mV /dps
3.75mV /dps

−q1
 q1
Ωq = 
 −q4
q3
Fig. 1. Inertial (NED) and body reference frames as shown in the Optitrack
user interface.
3) three-dimensional rotations of the device, approximately around the three axis;
4) computation of the magnetometer parameters;
5) storage of all computed parameters and compensation
of future samples.
Steps 1-2 are executed offline before a flight test, while steps
3-4 can be executed on-line employing data collected during
flight. At the moment we tested the calibration procedure
offline with collected data and we will implement and
evaluate an on-line version of the algorithm.
III. AHRS E STIMATION
The vehicle attitude describes the relative orientation of the
axes of the body (b) and navigation (n) frames-of-reference
and it is expressed by the rotation matrix Rbn . The navigation
frame is aligned with the North-Est-Down [N ED] frame
with the x axis pointing North, the y axis pointing Est and the
z axis pointing down. The body frame has its origin fixed to
the center of mass of the vehicle with the z axis aligned
with the propeller’s spin axis. For an intuitive graphical
representation of the reference frames the reader is referred
to Figure 1.
The rotation matrix can be parameterized using the rollpitch-yaw Euler angles (φ, θ, γ) or unit quaternions q =
(q0 , q), where q ∈ R and q ∈ R3 are respectively the scalar
and vector part of the quaternion. Quaternions are employed
to represent the attitude kinematics in the filter equations,
while the more intuitive Euler angles are employed for user
output.
The attitude kinematics of a rigid body are governed by
the equation
1
b
q̇ = Ωq wbn
(8)
2
b
b
b
where wbn
= win
− wib
is the angular velocity of the body
frame with respect to the navigation frame, and
−q3
q4
q1
−q2

−q4
−q3 
.
q2 
q1
(9)
The details of attitude dynamics integration and quaternion
computations can be found in the Appendix of [3].
Since our application involves low speed flights of relatively short duration and distance, we consider the navigation
b
frame as an inertial frame and define win
= 0. Based on the
sensor model introduced in (1), we can estimate the angular
velocity of the body frame with respect to the navigation
frame from the gyroscope readings, having
b
wbn
= −(Ỹg − bg )
(10)
which can be integrated through eq. (8) to obtain the current
orientation. Due to sensor noise and bias, the integrated
orientation is subject to drift and can’t be used without
an external reference. For this purpose, accelerometer and
magnetometer measurements are used to compute another
estimate of the orientation and correct the integrated one.
The Kalman filter can be used to fuse that information and
update the orientation of the body. This approach must take
care that accelerometers measure specific force composed of
kinematic accelerations minus the gravitational acceleration,
as seen in section II, and without an external reference
we can’t separate the two effects. Since the orientation
estimation needs only the gravitation vector, the system needs
to detect when the vehicle is accelerating and to treat the
kinematic accelerations as an additional disturbance.
Based on the sensor models and the attitude dynamics, the
complete system con be modeled as follows:
1
b
q̇ = Ωq wbn
2
b˙g = βg bg + νbg
(11)
˙
ba = βa ba + νba
Ỹa = RqT g n + ba + νa
Ỹm = RqT mn + νm
(12)
where Rq is the rotation matrix Rbn obtained from the
integrated quaternion q, x = [q, bg , ba ]T is the system state
and y = [Ỹa , Ỹm ]T are the measurements. The predicted state
x̂ is obtained integrating the noise-free version of (11), which
can be corrected using the measurements y and one of the
two Kalman filter approaches.
The EKF aproach approximates the non-linear equations
(11) and (12) with the Taylor series expanded around the
1722
TABLE II
N OISE CHARACTERISTICS OF THE ON - BOARD SENSORS .
σa
[m/s2 ]
0.010
0.011
0.027
σg
[dps]
0.007
0.004
0.009
σm
[gauss]
2.853
3.068
3.005
b0a
[m/s2 ]
0.0245
0.0245
0.0245
b0g
[dps]
0.00089
0.00089
0.00089
(a)
estimated state vector x̂. To ensure a better convergence of
the linearized EKF, we use a complementary version of the
filter, which uses the errors δx = x − x̂ and δy = ỹ − ŷ
as system state and measurements. Full details of the filter
implementation can be found in [3].
The UKF uses a deterministic sampling technique known
as the unscented transform to pick a minimal set of sample
points (sigma points) around the mean of the estimated state
x̂. These sigma points are then propagated through the nonlinear functions, from which the mean and covariance of the
estimate are recovered. This technique removes the requirement to linearize the state and measurement functions and
explicitly calculate Jacobians, but the non-linear functions
have to be evaluated once for each sigma point. Full details
of the filter implementation can be found in [8].
IV. E XPERIMENTAL S ETUP
In order to validate the attitude obtained by processing
the inertial measurements with the different estimation algorithms, an independent off-the-shelf motion tracking system
based upon infrared cameras, the Optitrack System [11], has
been employed. The Optitrack System produces as output the
position and the orientation of a reference frame attached
to the selected rigid body with respect to a given inertial
reference frame fixed in the flight area at a rate up to
100Hz. The inertial frame can be manually changed by
the end-user and, for better comparison, has been aligned
with the NED frame. In order to estimate the attitude and
the position, a certain number of highly reflective markers
have been attached to the prototype. The accuracy of the
attitude estimation directly depends both on the accuracy of
the estimation of the position of each single marker and on
the position of the different markers on the rigid body. By
considering the camera calibration results, it turns out that
the position of a single marker is tracked with an error less
than 0.3 mm and then, placing the markers on the prototype
at a sufficiently large distance from each other, the attitude
error is expected to be less than 10−3 rad. In particular the
attitude noise covariances computed during the experimental
2
tests are given by σO
= [0.2 · 10−3 , 0.3 · 10−3 , 0.1 · 10−3 ]
rad.
The noise characteristics of the on-board sensors have
been identified experimentally, obtaining the values in Table II. The magnetometer has the highest noise covariance
among the three sensors, therefore we expected the yaw angle
estimation to be slightly noisier compared to the other two,
since it relies heavily on these measurements [3].
(b)
Fig. 2. Experimental setup: (a) cameras’ positions and (b) the ducted-fan
prototype with the on-board IMU and reflective markers.
All the raw sensors data obtained from the iNemo are synchronized with the video tracking information and streamed
to a ground-control station PC at a frequency of 100 Hz.
The aerial robot used in the experiments consists of a
miniature prototype of ducted-fan aircraft (see among others
[19]) specifically designed in order to accomplish service
robotics operations in potentially cluttered environments,
such as inspection of power plants and other infrastructures
[20]. A description of some of the prototype mechanical
characteristics is given in Table III. The sensor has been
attached to the duct fuselage (see Figure 2(b)) using compliant material in order to reduce the effects of mechanical
vibrations. The latter have been accurately taken into account
as described also in the following section. For the flight tests,
the inertial data obtained from the IMU have been converted
into the body frame attached to the center of mass of the
vehicle. A graphical sketch of the overall experimental setup
is given in Figure 2(a), showing also the position of the 12
IR cameras in the flight arena. The cameras are placed along
the edges of a 6 × 6 m square area, giving us an effective
field of view of 4 × 4 m.
1723
TABLE III
D UCTED -FAN AIROBOTS FIRST PROTOTYPE : FEATURES AND H W
Weight, payload, diameter
BLDC-Motor
Flight Time
MCU
Host communic.
1500 g, 300 g, 320 mm
custom carbon / fiberglass airframe
1 x Scorpion SII 3020
KV 1100, 840 W cont. power
approx. 7 minutes (with full payload)
Arduino MEGA, 18 MHz
XBee Pro 900Mhz
V. E XPERIMENTAL R ESULTS
Fig. 3.
Effects of magnetic calibration
from the IMU. In this respect it is also important to evaluate
the effectiveness of the attitude estimation during maneuvers
compatible with the ones required for the inspection operations to take place. This fact is possible with the use of the
Optitrack system, in which the attitude estimation does not
rely upon inertial measurements. The results obtained by the
two different attitude estimation algorithms during real flight
tests are then proposed in subsection V-C.
A. Magnetic Calibration
Fig. 4. Comparison between EKF and UKF estimations. In these tests the
sensor has been tilted manually by an operator to evaluate the estimation
without the disturbances introduced by the vehicle’s accelerations.
Fig. 5.
Effects of the vibrations induced by the motor.
The purpose of the experiments that are presented in this
section is to evaluate the performance of the AHRS designed
for the ducted-fan prototype considering the characteristics
of the envisaged application scenarios. Inspection operations,
in particular, can be carried out in environments potentially
rich of metal infrastructures and then also of magnetic disturbances. Accordingly in subsection V-A the impact of the
calibration of the magnetic sensors has been carefully taken
into account. The other interesting source of disturbances
derives from the mechanical vibrations induced by the BLDC
motor and the propeller. This fact is considered in subsection
V-B using the inertial data sensed during a hovering test.
The absence of an accurate GPS signal, moreover, implies
that the disturbances deriving from system motion may not
be properly compensated in the acceleration data obtained
First we tested the effectiveness of the magnetometer
calibration algorithm proposed in Section II-A by comparing
the filter outcome when using raw and calibrated data. The
results are illustrated in Figure 3, that shows the yaw angle
computed by using the EKF with respectively the raw and the
calibrated data. The obtained measure are finally compared
also with the Optitrack estimate. The following Tab. IV reports the Root Mean Square (RMS) of the prediction error =
q
P
1
(δ ρ̂)2 and the RMS of the euclidean distance between
n
q P
the inertial and Optitrack estimates, O = n1 (ρ̂ − ρO )2 .
The prediction error has low values in both cases, since
the filter can’t be aware of external disturbances, but the
predicted angles are good only in the calibrated case, as we
can see from the comparison with the Optitrack. Roll and
Pitch estimation are marginally affected by the magnetometer
calibration, since they rely on accelerometer measurements.
Using calibrated data, we compared the two proposed
estimators and obtained the results shown in Figure 4. Those
results were achieved rotating by hand the vehicle: at the
beginning of the plot we can observe rotations along each one
of the three body frame axes and then we have a composed
3D rotation. The two solutions have very similar results, with
the UKF having a slightly better performance at the cost
of higher computation times. Computations has been done
off-line in Matlab: the filters are initialized with the correct
angles and for both we have used the same set of noise
parameters, shown in Tab. II. The average execution time of
one iteration loop is 0.4 ms for the EKF and 33 ms for the
UKF, on the Intel Core i5 PC used for simulations.
B. Mechanical vibrations
Fig. 6. Effects of external acceleration applied to the body: the video
tracking data was used to estimate the acceleration and correct the IMU
measurements.
One of the major problem that arises when using inertial
sensors on rotary UAVs is given by the vibration introduced
by the motor, which generates a high frequency noise in
the inertial measurements. In the top graph of the Figure
5, we can see the accelerometer sampled values with the
motor turned on maintaining the vehicle still on the ground.
To mitigate the effects of the vibrations we pre-filtered the
sampled accelerations with a low-pass filter and re-estimated
the accelerometer’s noise parameters with the motor switched
on, obtaining the results shown in the lower graph of
Figure 5. We used a 4th order Butterworth low-pass filter
(LPF), with a 16 Hz cut-off frequency. The variance of the
estimated roll angle is shown in the Table V.
1724
TABLE IV
R AW AND CALIBRATED ESTIMATION ERRORS
Roll
Pitch
Yaw
[deg]
0.05
0.04
0.03
Raw
O [deg]
7.2
8.3
62.4
the presence of disturbances such as the aircraft motion,
vibrations and external magnetic fields affect the inertial and
magnetic measurements.
We are planning to continue experimental tests comparing also alternative estimation techniques, as the non-linear
complemetary filters. Future works also include an energy
efficient on-line implementation of hte algorithms, on a
resource constrained embedded platofrm.
Calibrated
[deg]
O [deg]
0.004
3.7
0.003
3.1
0.004
3.8
TABLE V
E FFECTS OF THE VIBRATIONS INTRODUCED BY THE MOTOR
σRoll [deg]
Motor OFF
Motor ON
EKF
UKF
EKF
UKF
KF
0.2
0.07
0.67
2.17
KF+LPF
0.18
0.07
0.53
1.39
VII. ACKNOWLEDGMENTS
This research has been partially framed within the collaborative project AIRobots (Innovative Aerial Service Robots
for Remote inspections by contact, ICT 248669) supported
by the European Community under the 7th Framework
Programme, and within the SOFIA project of the European
Joint Undertaking on Embedded Systems (ARTEMIS).
KF+LPF+noise
0.17
0.07
0.33
0.28
R EFERENCES
C. Flight tests
Finally, in Figure 6 we present the estimations of the UAV
orientation during a 2 minutes flight test in which the vehicle
performs small speed maneuvers simulating a real indoor
visual inspection. In the higher graph we can see the position
of the UAV, as tracked by the video system, from which
we estimated also the external accelerations applied to the
body aib , presented in the middle graph. The value of aib
can be used in the accelerometer sensor model equation (1)
to better estimate the gravity vector and thus to improve
the overall attitude estimation. With the small accelerations
involved in our tests, we didn’t notice a real improvement,
as we can see in the lower graph for the EKF or in Tab.
VI. In fact both filters produce almost the same estimation
regardless the knowledge of the acceleration aib . Once again
the two filters have comparable performance, with the UKF
producing slightly better estimations.
VI. C ONCLUSIONS
In this paper we have shown the design of an Attitude
and Heading Reference System for a miniature prototype
of aerial robot. In particular two different sensor fusion
algorithms, based on EKF and UKF respectively, have been
implemented using a low cost commercial off-the-shelf inertial measurement unit, composed of an accelerometer, a
gyro and a magnetic sensor, in order to estimate the attitude
of the vehicle. The performance of the different approaches
have been compared in real flight tests by employing, as a
reference, the attitude obtained from a vision-based motion
tracking system. This fact has allowed to validate the attitude estimation algorithms in a realistic scenario in which
TABLE VI
E STIMATION ERRORS DURING TEST FLIGHTS
O [deg]
Roll
Pitch
Yaw
Inertial
EKF
UKF
3.7
1.4
3.1
1.8
3.8
1.7
Moving
EKF
UKF
5.4
2.9
5
2.0
8.5
4.1
With
EKF
4
4.4
6.7
aib
UKF
2.9
2.0
4.1
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