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A novel online model-based wind estimation approach for quadrotor micro air vehicles using low cost MEMS IMUs

Authors:
A Novel Online Model-Based Wind Estimation Approach for Quadrotor
Micro Air Vehicles Using Low Cost MEMS IMUs
L.N.C. Sikkel, G.C.H.E. de Croon, C. De Wagter and Q.P. Chu
AbstractThis work extends the drag-force enhanced
quadrotor model by denoting the free stream air velocity as
the difference between the ground speed and the wind speed.
It is demonstrated that a relatively simple nonlinear observer
is capable of estimating the local wind components, provided
accelerometer and GPS-velocity measurements are available.
We perform a wind tunnel experiment at various wind speeds
using a quadrotor vehicle with a low-cost Inertial Measurement
Unit (IMU) and a motion tracking system to provide accurate
ground speed measurements. It is shown that the onboard
Extended Kalman Filter (EKF) accurately estimates the wind
components.
I. INTRODUCTION
Autonomous flight of Micro Air Vehicles (MAVs) has
gained much attention in recent years. Increasing effort is
taken in designing novel control approaches for trajectory
tracking and path-following in unknown and increasingly
complex environments [1]. Trajectory-tracking is similar to
the path-following as both control strategies require the
vehicle to converge to a predefined reference trajectory. How-
ever, the trajectory tracking problem adds a time reference
component to the trajectory itself, for which a time-optimal
solution should be found.
While flying in strong winds the trajectory reference
may need to slow down or speed up accordingly not to
overshoot some reference position [1]. Wind is a predomi-
nantly (slowly) varying disturbance, make the time reference
tracking task potentially very difficult if no wind information
is available to the system. For example, a predefined velocity
reference may, in a wind field, require a steadily increasing
bank angle. This might violate both the time and space
reference trajectory convergence requirements due to a loss
of altitude. Also, limited power capacity may require onboard
path generation to take advantage of the wind itself [2].
Typically, wind is estimated on a fixed-wing aircraft by
measuring the difference between the airspeed coming from
a pitot-static system and the GPS-velocity. If a GPS-velocity
estimate is unavailable an Extended Kalman Filter (EKF) is
used to estimate the wind field with respect to the aircraft
states and measured position [3]. The static port of an
airspeed measuring device is to be located in an area of
Micro Air Vehicle laboratory, Control and Simulation Division,
Faculty of Aerospace Engineering, Delft University of Technology
g.c.h.e.decroon@tudelft.nl. (c)2016 IEEE. Personal
use of this material is permitted. Permission from IEEE must be
obtained for all other users, including reprinting/ republishing this
material for advertising or promotional purposes, creating new collective
works for resale or redistribution to servers or lists, or reuse of any
copyrighted components of this work in other works. Original publication:
http://ieeexplore.ieee.org/document/7759336/
undisturbed air. The aerodynamic effects caused by the rotors
of a quadrotor and the interaction between the different
flow fields around each motor will disrupt the local airflow.
Therefore, it is assumed that a pitot-static tube cannot be
used to determine the airspeed of such a vehicle.
Fig. 1: The quadrotor MAV is shown to operate in front
of the cross section of the open-jet windtunnel. The vehicle
uses its onboard accelerometers and position measurements
to estimate the wind velocity.
Even though atmospheric disturbance rejection with re-
spect to quadrotor MAVs is widely studied, there does not
exist much literature on truly estimating the wind itself.
Often simulation studies are performed showing the effec-
tiveness of novel control approaches ignoring the actual
estimation of the wind [1], [4], [5], [6]. Researchers in the
past have created aerodynamic models of the vehicle. This
allows them to analytically compute the total force acting
on the vehicle as a result of the free stream air velocity The
difference between the accelerometer measurements and the
total predicted specific force can directly be attributed to the
wind components [7], [3].
More recently, interest in improving the traditional quadro-
tor dynamic model to allow for accurate estimates of at-
titude and velocity provided useful insight. Traditionally,
accelerometers were used to predict the attitude of a MAV,
assuming that they would measure some static component
of thrust [8]. Paradoxically, the traditional model states
that these planar accelerometers shouldnt measure anything
while in flight. Recently it was shown that those planar
accelerometers did indeed not measure a component of the
thrust force, but instead measured the so-called rotor drag.
This drag force appeared to be directly proportional to the
airspeed of the vehicle and a drag-force enhanced quadrotor
model was presented [9], [10], [11], [12], [8], [13]. The
airspeed is typically described as the difference between the
ground speed and the wind speed. Because the accelerometer
measurements are directly proportional to this difference an
analytical solution should exist from which one could derive
the wind components [7], [3], [14]. The unknown IMU bias
and GPS observation noise of real-time systems however
limit the use of such analytical definitions.
In [15] vehicle pose and wind component estimation
using a model-aided visual-inertial EKF is discussed. A
Visual Simultaneous Localisation and Mapping (VSLAM)
algorithm is shown to produce both unbiased position and
orientation measurements, which are then used to correct the
process model. Experimental results, generated by processing
IMU and motion tracking position measurements off-board,
infer that the estimator approximates the wind speed and
sensor bias quite accurately. The motion tracking system
served as a substitute for the vision system as these type
of sensors would add a large degree of complexity to the
system. Despite the accomplishments made in estimating the
wind, the applications of this method are limited as it requires
a complex vision system and is not applicable to unknown
highly-dynamic environments.
In this work the accelerometer measurements are inte-
grated with an exteroceptive GPS-velocity sensor, which
does not provide external pose information. This allows us
to reduce the order of the process model and consequentially
reduce the computational load. An EKF is employed to
estimate the wind speed components and sensor bias on an
embedded system. An observability analysis is added for
completeness providing a weak guarantee of the convergence
of the estimator. It is shown that the nonlinear observer is
capable of estimating the wind quite accurately. However, the
poor performance of the low-cost IMU in a highlydynamic
environment adds a significant noise component to the esti-
mated values. To the best of our knowledge this is the first
work in which the implementation of a GPS-velocity sensor
to determine the wind components on a real-time embedded
platform is investigated.
The paper is organised as follows: the augmentation of the
drag-enhanced quadrotor model with the wind components is
shown in Section II while the nonlinear observer is presented
in Section III. The observability of the observer is discussed
in Section IV. Finally, the results of conducted wind tunnel
test at various airspeeds are shown in Section V and some
concluding remarks are given in Section VI.
II. MODEL DESCRIPTION
The traditional quadrotor model relied on the assumption
that the most significant forces acting upon the vehicle were
gravity (Fg) and the thrust (T) generated by the actuators,
see Fig. 2. It may be described by a system of nonlinear
equations:
˙
φ
˙
θ
˙
ψ
=
1 sin
φ
tan
θ
cos
φ
tan
θ
0 cos
φ
sin
φ
0sin
φ
cos
θ
cos
φ
cos
θ
p
q
r
(1)
˙u
˙v
˙w
=Rb
E
0
0
g
+
vrwq
wp ur
uqvp
0
0
T/m
(2)
where Rb
Eis the rotation matrix from the inertial reference
frame Eto the body-fixed reference frame B,[u v w]T
{B}and [pqr]T∈ {B}are the linear velocity and angular
velocity along the principal axes of the body-fixed reference
frame. The gravitational acceleration is given by g, which is
assumed to point along the kEaxis.
Fig. 2: The quadrotor is assumed to be controlled by varying
the rotational velocity
ω
i,i=1,...,4 of each of its motors. A
body-fixed reference frame is attached to the vehicles center-
of-gravity. The ibaxis is pointing forward while jbpoints
towards the right. The kbaxis complements the system.
The thrust force is considered to be the input to the
system and, given the choice of reference frame, is aligned
with the kbaxis (Fig. 2). This paradoxically implies that
accelerometers aligned with the iband jbaxes will always
measure zero [8]. However, many researchers have used
the measurements of the accelerometer triad to estimate the
vehicles attitude successfully, implying that other external
forces must be acting on the body. It was recently shown that
the so-called rotor drag had been neglected in the traditional
model. The rotor drag is a force proportional to the linear
velocity of the quadrotor and it prevents the vehicle from
accelerating indefinitely [8].
An improved model was required and the drag-force
enhanced model was introduced [8], [13]. The vehicle is
assumed to consist of multiple independently rotating rotors
and the drag force is considered to be directly dependent
on the rotational velocity of the motors. During normal
operations the rotational velocity of the motors is quasi
constant, so a constant positive lumped rotor drag coefficient
(
µ
) is introduced such that
˙ub
˙vb
˙wb
=Rb
E
0
0
g
+
vrwq
wp ur
uqvp
0
0
T/m
(
µ
/m)u
(
µ
/m)v
0
(3)
in which the latter term describes the rotor drag force. The
accelerometers measure specific acceleration ab=1
m(FT
Fg), i.e. the difference between the gravitational acceleration
and the linear acceleration of the vehicle. It is assumed that
FTis the total force acting on the vehicle. The Coriolis terms
may be neglected, such that the accelerometer measurements
are assumed equal to the components of the drag force along
the principal axes of the body-fixed reference frame [8]
ab
x
ab
y=˙u+gsin
θ
+
β
x
˙vgsin
φ
cos
θ
+
β
y(
µ
/m)u+
β
x
(
µ
/m)v+
β
y(4)
in which
β
idescribes an unknown but constant bias. The
lumped drag coefficient is typically estimated [8], [13] or
found using test flight data. The latter approach requires an
accurate estimate of both the specific acceleration measured
by the accelerometers and the linear velocity of the vehicle.
Most researchers typically use a motion tracking system to
this end.
Extending the model to also include the effects of wind
requires looking at the free stream velocity of the ambient
air with respect to the quadrotor [15]. Wind is described
as the motion of the surrounding air. When a vehicle is
submerged in this flow field it is being accelerated by the
air particles up to the point it has an equal velocity as the
air itself. The dragforce- enhanced model presented in (3)
may be augmented
˙vb
x
˙vb
y
˙vb
z
=Rb
E
0
0
g
+
vb
yrvb
zq
vb
zpvb
xr
vb
xqvb
yp
0
0
T/m
µ
m
vb
xWb
x
vb
yWb
y
0
(5)
where Wb= [Wb
xWb
yWb
z]Tare the wind velocity compo-
nents along the axes of the body-fixed reference frame. The
linear velocity components V= [vb
xvb
yvb
z]Tconsequently
describe the ground speed of the vehicle in the body-fixed
reference frame. The accelerometer measurement model is
necessarily adopted to include the wind velocity components
as well
ab
x
ab
y=˙vb
x+gsin
θ
+
β
x
˙vb
ygsin
φ
cos
θ
+
β
y≈ −
µ
mvb
xWx+
β
x
vb
yWy+
β
y(6)
for which the same conditions as for the drag-enhanced
quadrotor model hold.
III. NOVEL EKF DESIGN FOR ESTIMATING WIND
It is assumed that the drag force coefficient is estimated
a-priori. The ground speed is most-likely available from
external sensors, e.g. GPS, but with considerable latency
and at a very low frequency. Despite the notion that (6)
is analytically solvable a nonlinear model-based observer is
proposed capable of providing a smooth estimate of the wind
components along the axes of the body-fixed reference frame
and the vehicles attitude.
We define a vehicle-carried Earth reference frame {E}
with the iEaxis pointing towards the North and jEaxis
pointing in the East direction. The kEcomplements the
reference frame and is aligned with the gravity vector. The
iEjE-plane is assumed to be tangent to the Earths surface.
Given the system as depicted in Fig. 2 a body-fixed reference
frame FBis defined in the center-of-gravity of the quadrotor.
The ibaxis is pointing forwards while the jbaxis points
towards the right. Again, the kbaxis complements the right-
handed system.
In order to keep the theoretical analysis as uncluttered as
possible, we make the following assumptions. The IMU is
to be located in the center-of-gravity of the vehicle and to
be perfectly aligned with the ibjb-plane. The accelerometers
are considered to be degraded by an unknown but constant
bias, which is a lumped term consisting of both electrical
noise and vibrations imposed onto the system by the motors.
Finally it is assumed that the gyroscopes are unbiased and
the contribution of the Coriolis terms are negligible.
The process model described by (1) and (5) assumes the
estimated wind components will persist until the next time
step, i.e. [˙
Wb
x˙
Wb
y˙
Wb
z]T=0. This assumption removes the
necessity of modelling the complex wind dynamics in real
time [7], [3]. It has to be noted that the wind component
along the kbaxis is not estimated as it is not directly
proportional to the body velocities. It may be shown that
Wb
zaffects to the total wind velocity through the rotor.
The aerodynamic power supplied to the air is a function
of the total wind velocity. Knowing the mechanical power
generated by the motor it would be possible to compute the
wind component along this kbaxis [16]. This is however
outside the scope of this work and left for future work.
The gyroscope measurements are assumed to be equal
to the angular rates of the quadrotor and are the inputs to
the system. The thrust force is considered to be directly
measurable with the accelerometer along the kbaxis [12].
The EKF relies on two distinct steps to estimate the state,
i.e. the prediction and measurement update steps. In the pre-
diction step the process model and model covariance are used
to predict the state for the next time step. In the measurement
update step the state predictions are corrected using the
measurement residual. The accelerometer measurements and
the GPS-derived body-fixed ground speed components are
assumed to be the available measurements for the innovation,
which is modelled as follows
y=
ab
x
ab
y
g
vb
GPS
=
µ
m(vb
xWb
x) +
β
x
µ
m(vb
yWb
y) +
β
y
ab
z+
β
z
vb
x
.(7)
It is assumed that the vibration-induced bias
β
is constant,
˙
β
=0, and imposed onto the accelerometer measurements
equally. This relation is therefore added to the process model.
Due to the inherent problems with latency and the output
frequency of the GPS module with respect to the periodic
frequency of the main control loop the body-fixed ground
speed estimates are corrected every time a new measurement
becomes available.
IV. OBSERVABILITY ANALYSIS
It is well-known that observability is a necessary condition
for a nonlinear observer to converge. To determine if the
(a) Ground speed provided by the motion tracking system (blue) and
the ground speed computed by adding the predicted wind speed to
the measured airspeed from the accelerometers (red).
(b) Ground speed provided by the motion tracking system (blue) and
the ground speed computed by adding the predicted wind speed to
the measured airspeed from the accelerometers (red).
(c) Euler attitude angles, the roll angle (blue), the pitch angle (red)
and yaw angle (magenta).
(d) Predicted wind components along the body-fixed x-axis (blue),
or the body-fixed y-axis (red), and the norm of the predicted
wind vector (magenta). The calibrated wind tunnel airspeed is also
indicated (black).
Fig. 3: Measurements and predictions from the nonlinear observer given a calibrated wind tunnel airspeed of 3[m/s] with a
predicted drag-force coefficient
µ
=0.20.
nonlinear system is observable, or whether there are unob-
servable states, we need to address nonlinear observability
theory. The observability rank condition will define if a
system is locally weakly observable [17]. This is not a
sufficient, but a necessary condition for observability. Given
a nonlinear system
˙
x=f(x,u),
y=g(x)(8)
, in which xRn,uRmand yRl, it can be shown that
the system is locally observable if for any arbitrary point x0
there exists a neighbourhood N(x0)in which every other x
is distinguishable from x0[17]. This condition implies that
at the point x0the rank of the observability matrix is equal
to n.
The observability matrix of a nonlinear system is defined
by the gradient of the measurement equations and the gradi-
ents of the kLie-derivatives evaluated around x0
O=
g(x)
x
.
.
.
dLk
fg(x)
(9)
for k=1,...,n1. For the system to be observable around
a point x0matrix Oshould be of rank n. This implies that
Oshould at least have nindependent rows or columns. The
observability of the nonlinear observer is analysed by using
a similar approach as in [12], [8], in which only the lon-
gitudinal dynamics of the quadrotor system are considered.
Referring to (5) we can reduce the system of equations to
˙
θ
˙u
˙
Wb
x
β
x
=
0
gsin
θ
µ
m(uWb
x)
0
0
+q
1
0
0
0
(10)
while assuming ˙
θ
=qis the input to the system. Considering
the following measurements equation
y=ab
x=
µ
m(vb
xWb
x) +
β
x(11)
the observability matrix may computed by taking the corre-
sponding Lie-derivatives
O=
0
µ
m
µ
m1
g
µ
cos
θ
m
µ
2
m2
µ
2
m20
g
µ
2cos
θ
m2
µ
3
m3
µ
3
m30
g
µ
3cos
θ
m3
µ
4
m4
µ
4
m40
(12)
Observability matrix Ois of rank 2 because the second
and third column are linearly dependent. The observability
matrix states that the difference between the ground speed,
wind speed and the measurement bias is unobservable, thus
additional measurement equations are required. By adding
the longitudinal GPS-derived body-fixed ground speed com-
ponents the observability matrix is extended to
(a) Ground speed provided by the motion tracking system (blue) and
the ground speed computed by adding the predicted wind speed to
the measured airspeed from the accelerometers (red).
(b) Ground speed provided by the motion tracking system (blue) and
the ground speed computed by adding the predicted wind speed to
the measured airspeed from the accelerometers (red).
(c) Euler attitude angles, the roll angle (blue), the pitch angle (red)
and yaw angle (magenta).
(d) Predicted wind components along the body-fixed x-axis (blue),
or the body-fixed y-axis (red), and the norm of the predicted
wind vector (magenta). The calibrated wind tunnel airspeed is also
indicated (black).
Fig. 4: Measurements and predictions from the nonlinear observer given a calibrated wind tunnel airspeed of 5[m/s] with a
predicted drag-force coefficient
µ
=0.17.
O=
0
µ
m
µ
m1
g
µ
cos
θ
m
µ
2
m2
µ
2
m20
g
µ
2cos
θ
m2
µ
3
m3
µ
3
m30
g
µ
3cos
θ
m3
µ
4
m4
µ
4
m40
0 1 0 0
gcos
θ
µ
m
µ
m0
µ
mgcos
θµ
2
m2
µ
2
m20
µ
2
m2gcos
θ
µ
3
m3
µ
3
m30
(13)
which is of rank 4 justifying the augmentation of the mea-
surement equations of the EKF. The system is considered
to be locally observable, but this is not a guarantee for
global observability. Note, however, that considering the
observability conditions posed in [12], [8] the proposed
observer is merely locally weakly observable except during
hover when 0=gsin
θ
µ
m(uWb
x)(14)
as it becomes impossible to distinguish between
θ
and (u
Wb
x), i.e. during unaccelerated flight.
V. RESULTS
The experiment was conducted using a custom-build
quadrotor running two STM32F105RC 74 MHz Microcon-
troller units (MCUs) in parallel to share the computational
load. The first MCU will run the Paparazzi1 autopilot soft-
ware while the second one carries out the operations required
to estimate the wind components at 512 Hz. An inter-
MCU communication bridge was established. An onboard
Fig. 5: Experimental set-up, the vehicle is shown to operate
in front of the cross section of the open jet wind tunnel.
IMU running at 512 Hz was used to estimate the attitude
and the body angular rates of the vehicle. To reduce the
adverse effect of vibrations onto the system, a second-order
Butterworth filter with a cut-off frequency of 1 Hz was used
to filter the IMU measurements.
The ground position and ground velocity estimates are
provided by an Optitrack motion tracking system. These
measurements are transmitted to the vehicle through a ded-
icated uplink at 120[Hz]. Even though the measurements of
this motion tracking system do not resemble the performance
of a typical low-cost GPS receiver, by resampling the discrete
signal the position and velocity data are purposely degraded.
The received GPS position signal is often perturbed by a
Gaussian noise term due atmospheric disturbances, so adding
such a perturbation to the motion tracking position signal
will increase the representability of the signal. A 10[Hz]
subsampling rate and Gaussian noise with a .1[m/s] standard
deviation were used during the experiment. To synchronise
the GPS with the two-samples delayed IMU measurements,
the GPS velocity was filtered as well.
Previous research regarding the rotor drag of quadrotor
MAVs focussed on assessing the validity of the EKF and
determining the drag force coefficient. Given that the states
of the system become unobservable during unaccelerated
flight, the vehicle is commanded to transverse the cross
section of the wind tunnel, see Fig. 5. The requirement that
the quadrotor should also be moving is relaxed by the fact
that due to inaccuracies and uncertainty within the position
controller it is never truly stationary.
Fig. 6: Estimation results of the magnitude of the wind speed
vector for various calibration wind tunnel airspeeds. The
wind tunnel was set to an airspeed of 1[m/s] (blue),
µ
=0.25,
2[m/s] (red),
µ
=0.25, 3[m/s] (magenta),
µ
=0.2, 4[m/s]
(black),
µ
=0.2 and 5[m/s] (green) using
µ
=0.15.
Next, the performance of the nonlinear observer is anal-
ysed in a quasi-steady air flow. The quadrotor is placed
in an open-jet windtunnel, as is shown in Fig. 1. The
experiment was performed at various airspeeds while keeping
the vehicles ibaxis pointing towards true north as is shown in
Fig. 5. The windtunnel has an offset angle of 60[deg] (1.05
[rad]) with respect to true north, implying that two distinct
axes of the accelerometer triad will measure the projection
of the wind vector onto the body-fixed reference frame.
The results of two independent experiments, with wind
speeds of 3[m/s] and 5[m/s], are shown in Fig. 3 and 4 re-
spectively. There seems to be good correspondence between
the ground speed estimate provided by the GPS receiver and
the estimate derived from the accelerometers as is shown
in Fig. 3a or 4a. The latter requires to be corrected for the
wind speed, which is available from the nonlinear observer.
Discrepancies are assumed to be caused by mathematical
rounding errors and bias due to estimation errors. Also, as is
clearly apparent in Fig. 3, the standard deviation of the wind
estimate is considerable, while Fig. 4 shows that increasing
the wind speed increases this adverse effect. This is attributed
to the performance of the low-cost IMU in the presence of
strong vibrations. These vibrations are due to the unavoidable
mass-imbalance of the rotors and increased wind speed.
The results of the estimated wind speed components for
various calibrated wind tunnel airspeeds are summarised in
Fig. 6. The magnitude of the wind speed vector is shown
over time. Future work should focus on low-pass filtering
the accelerometer signal while retaining the information.
Initially it was assumed that the drag-force coefficient was
reasonably constant, however it was found that the drag-force
coefficient was necessarily decreased for the measurements
to coincide with the predicted states coming from the EKF.
For example Fig. 3 was composed using
µ
=0.2, while Fig.
4 was found using
µ
=0.15. This inherently implies that for
a proper estimation of the wind components the drag-force
coefficient should be estimated on-line. However, it is easily
shown that by adding the dynamic relation for the drag co-
efficient to the reduced process model expressed in equation
(10) the system again becomes (partially) unobservable. It
will be impossible to see the difference between the drag
coefficient, the ground speed and wind speed.
VI. CONCLUSIONS
The drag-force enhanced quadrotor model was augmented
with the wind components along the body-fixed axis parallel
to the rotor plane. This model was used to create a nonlinear
observer capable of accurately predicting the wind compo-
nents using only IMU and GPS-velocity measurements. The
accuracy of the observer is limited by the performance of the
low-cost IMU. In future work, we will also study estimating
the wind speed component along the vertical axis, kb, using
the relation between the thrust and the aerodynamic power.
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... However, they assume that the wind velocity and yaw rates of the vehicle are negligible, and the thrust is independent of the freestream velocity. More recently, Sikkel et al. [126] identified parameters of the blade flapping model by flying in a wind tunnel and used it for wind speed estimation. It may be concluded that related work, especially Waslander et al. [149], shows the feasibility of model-based wind estimation. ...
... They found that such a sensor would have to be mounted at least 2.5 rotor radii in front of the hub axis to compensate for induced flow effects. Sikkel et al. [126] flew a quadcopter in a wind tunnel to estimate an aerodynamic model based on blade flapping, and used it to estimate the wind velocity. ...
Thesis
Model-Based Control of Flying Robots for Robust Interaction under Wind Influence The main goal of this thesis is to bridge the gap between trajectory tracking and interaction control for flying robots in order to allow physical interaction under wind influence by making aerial robots aware of the disturbance, interaction, and faults acting on them. This is accomplished by reasoning about the external wrench (force and torque) acting on the robot, and discriminating (distinguishing) between wind, interactions, and collisions. This poses the following research questions. First, is discrimination between the external wrench components even possible in a continuous real-time fashion for control purposes? Second, given the individual wrench components, what are effective control schemes for interaction and trajectory tracking control under wind influence? Third, how can unexpected faults, such as collisions with the environment, be detected and handled efficiently and effectively? In the interest of the first question, a fourth can be posed: is it possible to obtain a measurement of the wind speed that is independent of the external wrench? In this thesis, model-based methods are applied in the pursuit of answers to these questions. This requires a good dynamics model of the robot, as well as accurately identified parameters. Therefore, a systematic parameter identification procedure for aerial robots is developed and applied. Furthermore, external wrench estimation techniques from the field of robot manipulators are extended to be suitable for aerial robots without the need of velocity measurements, which are difficult to obtain in this context. Based on the external wrench estimate, interaction control techniques (impedance and admittance control) are extended and applied to flying robots, and a thorough stability proof is provided. Similarly, the wrench estimate is applied in a geometric trajectory tracking controller to compensate external disturbances, to provide zero steady-state error under wind influence without the need of integral control action. The controllers are finally combined into a novel compensated impedance controller, to facilitate the main goal of the thesis. Collision detection is applied to flying robots, providing a low level reflex reaction that increases safety of these autonomous robots. In order to identify aerodynamic models for wind speed estimation, flight experiments in a three-dimensional wind tunnel were performed using a custom-built hexacopter. This data is used to investigate wind speed estimation using different data-driven aerodynamic models. It is shown that good performance can be obtained using relatively simple linear regression models. In this context, the propeller aerodynamic power model is used to obtain information about wind speed from available motor power measurements. Leveraging the wind tunnel data, it is shown that power can be used to obtain the wind speed. Furthermore, a novel optimization-based method that leverages the propeller aerodynamics model is developed to estimate the wind speed. Essentially, these two methods use the propellers as wind speed sensors, thereby providing an additional measurement independent of the external force. Finally, the novel topic of simultaneously discriminating between aerodynamic, interaction, and fault wrenches is opened up. This enables the implementation of novel types of controllers that are e.g. compliant to physical interaction, while compensating wind disturbances at the same time. The previously unexplored force discrimination topic has the potential to even open a new research avenue for flying robots.
... Instead of adding components on the UAV, an alternate solution is to estimate wind from the quadrotor motion, [6][7][8][9] . In 7 the different possible models are presented: static, kinematic or full dynamic. ...
... In 6,10 , experiments were led using a six-axis force balance, a very precise but fragile and expensive system. Finally, 8 presents a nonlinear observer able to accurately predict the wind components, using only low cost Inertial Measurement Unit (IMU) and ground speed measurements. The drag-force is considered proportional to the rotational speed of the motors, that is almost constant during operation, leading to a constant rotor drag coefficient, similar to 7,11,9,7 have performed outdoor flights and compared the results with ground reference measurements, demonstrating the feasibility of wind measurement from quarotor based on IMU and GPS measurements. ...
Article
Full-text available
The aim of this work is to estimate the average wind influencing a quadrotor drone only based on standard navigation sensors and equations of motion. It can be used in several situation, including atmospheric studies, trajectory planning under environmental constraints, or as a reference for studying flights in shear layer. For this purpose, a small quadrotor drone with spherical shape has been developed. Flight data are recorded from telemetry during indoor and outdoor flight tests and are post-processed. The proposed solution is based on a calibration procedure with global optimization to extract the drag model and a Kalman Filter for online estimation of the wind speed and direction. Finally, an on-board implementation of the real-time estimation is demonstrated with real flights in controlled indoor environment.
... Due to the aforementioned integration challenges, the prevailing approach to wind estimation on UAVs is to avoid flow sensors altogether and instead utilize existing onboard sensors (such as inertial measurement units and GPS) to indirectly estimate the wind speed [17,18,19]. However, this method is inherently reactive and relies on deviations from the UAV's desired flight path to estimate wind. ...
Preprint
Due to limitations in available sensor technology, unmanned aerial vehicles (UAVs) lack an active sensing capability to measure turbulence, gusts, or other unsteady aerodynamic phenomena. Conventional in situ anemometry techniques fail to deliver in the harsh and dynamic multirotor environment due to form factor, resolution, or robustness requirements. To address this capability gap, a novel, fast-response sensor system to measure a wind vector in two dimensions is introduced and evaluated. This system, known as `MAST' (for MEMS Anemometry Sensing Tower), leverages advances in microelectromechanical (MEMS) hot-wire devices to produce a solid-state, lightweight, and robust flow sensor suitable for real-time wind estimation onboard a UAV. The MAST uses five pentagonally-arranged microscale hot-wires to determine the wind vector's direction and magnitude. The MAST's performance was evaluated in a wind tunnel at speeds up to 5~m/s and orientations of 0 - 360 degrees. A neural network sensor model was trained from the wind tunnel data to estimate the wind vector from sensor signals. The average error of the sensor is 0.14 m/s for speed and 1.6 degrees for direction. Furthermore, 95% of measurements are within 0.36 m/s error for speed and 5.0 degree error for direction. With a bandwidth of 570 Hz determined from square-wave testing, the MAST stands to greatly enhance UAV wind estimation capabilities and enable capturing relevant high-frequency phenomena in flow conditions.
... Wind characteristics can be estimated using measurements from the flight controller's inertial measurement units (IMUs). Recursive Bayesian filters [46], Square-root unscented Kalman filters (sq-UKF) [81], extended Kalman filters (EKF) [76], and neural networks [77] estimators have been used for this task. For example, in a simulation study, Shastry and Paley [81] use a sq-UKF to fuse IMU and ground velocity sensor measurements. ...
Thesis
Full-text available
The use of multirotor unmanned aerial vehicles (UAVs) for applications close to the environment, such as physical sampling, inspection, and navigation in narrow environments, has increased drastically in recent years. Wind disturbances both increase the risks of collision and decrease the precision of the work performed by UAVs and are, therefore, a major limiting factor for these applications. This work aims to improve UAVs’ wind disturbance rejection performance by investigating the robust control of a canted-rotor octorotor capable of vectored thrust. A UAV dynamics model inclusive of aerodynamic forces and moments is first developed for use in robust control synthesis. Aerodynamic polars are fitted to static load-cell data and validated with free-flight station-keeping experiments in a wind tunnel. The model is found to predict the experimental root-mean-square (RMS) position error along the direction of the wind within 7%. A new vectored-thrust controller is then developed based on this model. It comprises a motor mixer converting desired torques and vectored thrust into motor commands, an off-the-shelf attitude controller, and a novel dynamic output feedback H-infinity position controller. Frequency-dependent weighting is applied to use attitude control to reject low-frequency disturbances and vectored thrust for high-frequency disturbances. Comparisons to PX4 Autopilot, a widely used baseline flight controller, are made both in simulation and in free-flight experiments in a wind tunnel at wind speeds up to 12.8 m/s. The H-infinity controller is found to halve the RMS position errors in most cases, at the cost of increased actuator usage. Finally, an investigation of the benefits of wind velocity feedback for station-keeping is conducted in simulation. Two feedforward pitch controllers are created and integrated with an existing controller, showing promising station-keeping results with RMS position errors up to 66% lower.
... To estimate the wind conditions affecting a MAV, some approaches use pressure sensors [11], ultrasonic sensors [12], or whisker-like sensors [13] to directly measure the wind conditions affecting the MAV. Another strategy is to employ model-based approaches [14,15], learning-based approaches [16,17], or hybrid (model-based and learning-based) solutions [18] that leverage the inertial effects produced by the wind on the MAV to obtain an estimate of the drag force. Ref. [19] compares model predictive and PID controllers that use a disturbance estimator capable of rejecting wind of up to 12 m/s. ...
Article
This paper presents an autonomous landing of a micro aerial vehicle (MAV) on a moving platform immersed in turbulent wind conditions. We estimate the 3D wind vector acting on the vehicle using a model-based and a deep learning-based approach. A disturbance-aware boundary layer sliding controller then uses this estimation to generate a control input that provides trajectory tracking guarantees in the presence of unknown, but bounded disturbances. The approach presented integrates our previous works on control and estimation, and we show its performance in a challenging setting. The experiments show that our methods enable fast landing on a moving platform in turbulent, unknown wind conditions.
... The ADS is unable to respond in time and compute accurately due to the rapid change in wind disturbance, which brings about measuring error of air data. In particular, true airspeed V T , angle of attack α, and angle of sideslip β, the three significant air data for the aerodynamic performance of aircraft, are difficult to measure and record accurately in wind disturbance [3,4]. ...
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Conference Paper
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We present a dead reckoning strategy for increased resilience to position estimation failures on multirotors, using only data from a low-cost IMU and novel, bio-inspired airflow sensors. The goal is challenging, since low-cost IMUs are subject to large noise and drift, while 3D airflow sensing is made difficult by the interference caused by the propellers and by the wind. Our approach relies on a deep-learning strategy to interpret the measurements of the bio-inspired sensors, a map of the wind speed to compensate for position-dependent wind, and a filter to fuse the information and generate a pose and velocity estimate. Our results show that the approach reduces the drift with respect to IMU-only dead reckoning by up to an order of magnitude over 30 seconds after a position sensor failure in non-windy environments, and it can compensate for the challenging effects of turbulent, and spatially varying wind.
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Conference Paper
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