Development of A Fixed-Wing mini UAV with Transitioning Flight Capability

Abstract

This study presents the development of the transitioning vehicle Cyclone, which has been specifically designed for meteorological and agricultural applications. The mission requirements demand takeoff and landing from a small area and the ability to cope with high wind speeds. In contrast with recent suggestions, our proposed design aims to be closer to a fixed-wing airplane rather than a rotary wing. In particular, the design focuses on a tilt-body style transitioning vehicle with blown-wing concept. The propeller wing interaction is calculated using a semi-empirical method. The total wing span and wing surface area are decided according to the mission performance requirements. For the control of the vehicle, incremental nonlinear dynamic inversion is used. This control method does not need the modeling of external forces or moments and is able to counteract the strong aerodynamic forces and moments acting on the vehicle through the feedback of its angular acceleration. Together with the design phases and manufacturing process, several test flights are presented. Particular difficulties of the proposed design are discussed, including lack of providing sufficient pitch-up moment and control reversal during descent. The test flights demonstrate the vertical takeoff and landing capabilities of the vehicle, as well as its transitioning into forward flight from hovering, and vice versa, for an efficient mission performance.

Full text

Development of A Fixed-Wing mini UAV with
Transitioning Flight Capability
Murat Bronz ∗
, Ewoud J J Smeur †
, Hector Garcia de Marina ‡
,
and Gautier Hattenberger §
ENAC, F-31055 Toulouse, France
University of Toulouse, F-31400 Toulouse, France
This study presents the development of the transitioning vehicle Cyclone, which has
been specifically designed for meteorological and agricultural applications. The mission
requirements demand take-off and landing from a small area and the ability to cope with
high wind speeds. In contrast with recent suggestions, our proposed design aims to be closer
to a fixed-wing airplane rather than a rotary wing. In particular, the design focuses on a tilt-
body style transitioning vehicle with blown-wing concept. The propeller wing interaction
is calculated using a semi-empirical method. The total wing span and wing surface area
are decided according to the mission performance requirements. For the control of the
vehicle, incremental nonlinear dynamic inversion is used. This control method does not
need the modeling of external forces or moments and is able to counteract the strong
aerodynamic forces and moments acting on the vehicle through the feedback of its angular
acceleration. Together with the design phases and manufacturing process, several test
flights are presented. Particular difficulties of the proposed design are discussed, including
lack of providing sufficient pitch-up moment and control reversal during descent. The test
flights demonstrate the vertical take-off and landing capabilities of the vehicle, as well as
its transitioning into forward flight from hovering, and vice versa, for an efficient mission
performance.
I. Introduction
Operational efficiency and compactness of small Unmanned Air Vehicles (UAV) increased their use in several
areas such as atmospheric research and agricultural applications.1These missions usually demand for take-
off and landing from a small area, where rotary-wing configurations are more suitable for their vertical or
short take-off and landing capabilities. However, good performance is expected on endurance, range and
also on climbing and high-speed flight, which are obtained more efficiently in fixed-wing configurations.
This complex mission profile has already been addressed by the unique flight characteristics of Verti-
cal/Short Takeoff and Landing (V/STOL) aircraft. However, their additional complexity reduces the oper-
ational efficiency, which is the focus point for small UAV in the first place. This problem can be improved
with a mission oriented optimization of the vehicle as previously shown by Bronz and Hattenberger.2,3This
approach requires a clear picture about how the final performance of the vehicle is affected by the main
design variables.
Figure 1shows some of the recent V/STOL trends. The first image from left shows ISAE’s tilt-body
MAVION ,4which is a good example of a hand-release vertical take-off and afterwards transition to cruise
flight concept. The tiltwing demonstrator form RWTH Aachen University,5shown second, is capable of
vertical take-off by tilting its wing and then transition for an efficient cruise. The DelftaCopter ,6shown
third, uses a helicopter setup, with a single rotor and a swash plate, to control the attitude. The collective
pitch enables optimization of the propeller pitch angle for both forward flight and hover. The GL-10 ,7
shown last, is a good example of a highly-Distributed Electric Propulsion (DEP) system, which can adapt
∗Assistant Professor on Applied Aerodynamics, ENAC UAV Lab, F-31055 Toulouse, France
†Ph.D. Candidate, MAVLab TUDelft, 2629 HS Delft, The Netherlands
‡Researcher on Guidance, Navigation, and Control, ENAC UAV Lab, F-31055 Toulouse, France
§Assistant Professor on Flight Dynamics, ENAC UAV Lab, F-31055 Toulouse, France
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Figure 1. Tilt-Body micro air vehicle MAVION from ISAE, a tiltwing demonstrator from RWTH Aachen University,
the DelftaCopter from MAVLab TUDelft, and a small demonstrator of NASA’s GL-10.
the rotation rate of its individual propellers located on the leading edge of the wing, in order to increase
efficiency. On DEP systems, the wings are immersed inside the distributed propeller slipstream, which
increases the dynamic pressure over them. Consequently, this results in a significant wing surface reduction
for traditional aircraft. This makes them more efficient during the cruise flight conditions as the drag caused
by the wing surface that is only needed for the take-off and landing is reduced.
A. Present Work
This work focuses on the design and flight testing of a fixed-wing aircraft with take-off and landing capabili-
ties, including full equilibrium low-speed flight during the transition phase. The design of such a configuration
requires a good understanding of the interaction between the DEP system and the airframe. Unfortunately,
the propeller wing interaction is very complex to model without certain simplifications, especially with
high-fidelity methods, as was concluded by Veldhuis.8
The paper is organized as follows. In Section II, the basis of the aerodynamic calculations are introduced
based on Jameson,9who has developed semi-empirical formulations in order to estimate the force and
moment generation on V/STOL vehicles. Section III describes the design philosophy and the steps to select
the main design variables such as wing span, wing surface area, and battery weight in order to obtain
optimum performance for a given mission definition. In Section IV the whole manufacturing process of the
prototype vehicle is shown. Section Vexplains the control system applied to the vehicle based on incremental
nonlinear dynamic inversion. Finally, in Section VI, flight tests demonstrating the vertical, horizontal, and
transitioning phases of the vehicle are shown.
II. Aerodynamic Model for Propeller Wing Combination
During the development of the vehicle, the complex propeller and wing interaction is modeled by a semi-
empirical method from Jameson.9Additional viscous drag, moment, and equilibrium case calculations are
added by Bronz and Drouin.10 The method has been already explained completely with detail in those
references,9,10 however in order to keep the consistency of this paper, the main points will be repeated in
the following subsections.
An arbitrary number of propeller slipstreams are defined, with individual thrust, actuator disk area,
position and orientation. The method is mainly based on momentum theory, which means that the swirl
effects of the propeller slipstream are not modeled.
Blown Sections
Unblown Sections
Figure 2. The creation of wing sections according to the fully developed propeller slipstream width. Note that for each
thrust value the sections dynamically are changed in order to take the contraction into account.
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A. Propeller Forces
The propeller forces are modeled according to actuator disk theory. For a given propeller thrust Tand
actuator area Sp, the ratio µbetween the free stream V∞and propeller jet slipstream Vj, is given by
µ=V∞
Vj
=s1−T
0.5ρV 2
jSp
(1)
It is assumed that each individual slipstream keeps a circular cross section such that their contraction is
estimated with
bpc =bpr1 + µ
2(2)
where bpis the propeller disk diameter, and bpc is the fully developed contracted slipstream diameter.
Once the contracted slipstream diameter is calculated, the wing can be separated into the sections that are
inside and outside of the propeller slipstream as shown in Figure 2. Note that the fully developed propeller
slipstream is taken for simplification reasons.
Inclined propellers deflect the free stream, consequently changing the angle of attack of the wing inside
this slipstream. This downwash can be determined using the inflow angle of the propeller αjas is described
by Ribner11 and De Young.12
∞
V
LT
j
V
ϵ
N
α +iw
D
α +ij
Figure 3. The wing incidence angle iw, jet incidence angle ij, angle of attack of the fuselage αwith the resultant lift
L, drag D, thrust Tand the propeller normal force N, propeller downwash , jet slipstream Vj.
B. Actuator Inflow Angle Change due to Wing, Fuselage and Other Propeller Jets Upwash
Each actuator is influenced by the fuselage, wing, and the other propeller jets. Taking these effects into
account, the inflow angle for each jet is the sum of
αj=α+ij+Uw(α+iw) + Ufα+X
otherjets
Uoj(3)
where Uwis the upwash due to the wing, Ufis the upwash due to the fuselage and U0jis the upwash due
to the other propeller slipstreams. For each propeller slipstream, αjcan be written as
αj1=α+ij1+Uw(α+iw) + Ufα+Uoj12 2+· · · +Uoj1nn
αj2=α+ij2+Uw(α+iw) + Ufα+Uoj21 1+· · · +Uoj2nn
αj3=α+ij3+Uw(α+iw) + Ufα+Uoj31 1+· · · +Uoj3nn
.
.
.
αjn =· · ·
for a half wing with npropellers mounted on the leading edge. The quantity Uoj12 presents the upwash
effect of the second actuator on the first one. As long as there is a fuselage between the propellers separating
the slipstreams, the upwash effects coming from the other wing can be neglected, leading to a set of linear
equations of the form Ax =b. Therefore, the inflow angles αjcan be directly calculated. Similarly, wing
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inflow angles for sections that are inside the freestream and that are inside the propeller slipstream can be
calculated as follows:
αwj1=α+iw+Ufα(4)
αwjµ =αwj1−+X
jets
U∞j(5)
The propeller normal force can be calculated with the assumption of being proportional to the sine
of the inflow angle αj, i.e.,
CN=CNαsin αj
The resulting lift slope in a slipstream is a function of the influenced mass flow around the wing.
The wing in free stream is influenced by a mass flow that is passing through a circular surface S∞with area
πb2/4, which contains the wing tips. However, the wing in a slipstream, passing through the surface Sj,
influences a smaller mass flow resulting in a reduction in the effective span or aspect ratio of the wing which
is given by
AR0=AR
1 + p(6)
where pis a positive value determined according to the jet slipstream aspect ratio.
The resultant lift can be simply estimated by the superposition of forces over the wing in free stream
and the individual parts that are immersed in slipstreams. The individual parts that are immersed in
slipstreams are calculated as isolated planforms. Thus, the additional increase on each isolated planform is
simply the difference between the planform in free stream V∞, and the planform immersed in a jet slipstream
Vjmoving with a forward speed of V∞. The difference in lift is then described by
∆L=1
2ρSwj(V2
jCLαj µ αwjµ −V2
∞CLα∞αwj∞) (7)
where CLαj µ is the lift slope of the wing part that is inside the jet slipstream with a velocity ratio of
µ=V∞/Vjby taking the aspect ratio as bj/Swj. The quantity CLα∞is the lift slope of the same wing part
in a freestream, or in other words when µ= 1, αwjµ is the angle of attack of the wing in jet slipstream, and
αwj∞is the angle of attack of the same part in free stream. It should be noted that the angle of attack of the
wing portion inside the jet slipstream is reduced, compared to the angle of attack in the free stream, by the
slipstream downwash . Additionally, an inclined slipstream to the free stream generates an external upwash,
which can be approximated by assuming the slipstream as a falling cylinder model. Then, the upwash at a
distance yfrom the center axis of the slipstream can be written as b2
j/2/y2.
According to Jameson,9the average upwash over the external part of the wing (outside the propeller
jets) is approximately Swj
S. Taking all upwash effects of propeller jets, the increase in lift can be calculated
by multiplying the sum of all slipstream upwash angles with the unblown surface area and the lift slope of
the complete wing in freestream CLα∞.
For small angles of attack, the lift force generated by the wing can be found by adding up the freestream
lift of the complete wing, the additional lift created from the unblown parts of the wing because of the
upwash effects of the jets, and finally the additional lift of the blown sections coming from the dynamic
pressure increase because of the jet velocities. This can be encompassed with the following expression
L= 0.5ρV 2
∞SC Lα∞+ 0.5ρV 2
∞SC Lα∞
S−X
jets
Swj
X
jets
Swj
S+X
jets
∆Lj(8)
A similar approach can be used to calculate the additional induced drag for the wing sections that are
inside the slipstream.
∆Di= 0.5ρV 2
∞SwjCLj∞(αij−αi∞)+∆Lαij(9)
Di= 0.5ρV 2
∞SkCL2
∞+X
jets
∆Dij(10)
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C. Effect of Flaps
The effect of the flaps is modeled by an increase of the wing angle of attack as presented by Jameson.9The
effective wing incidence angle iw∞becomes
iw∞=iw+α/δ∞δf(11)
where δfis the flap deflection, and the flap effectiveness of the three dimensional wing in free stream α/δ∞
is given by
α/δ∞=pα/δ2D+α/δ2DAR+4.5
AR+2 AR
pα/δ2D+AR+4.5
AR+2 AR (12)
Likewise for a wing section inside a propeller slipstream, the effective wing incidence iwjµ becomes
iwjµ =iw+α/δjµ δf(13)
D. Forces
So far only longitudinal flight dynamics are considered, so the lateral force and moments are assumed to be
zero Fy=Mx=Mz= 0 as in equilibrium. The contribution of the wing lift L∞, drag D∞, propeller thrust
T, and propeller normal force Nwill be taken into account as
Fz=L∞+X
jets
Tsin(α+ij) + X
jets
Ncos(α+ij) (14)
Fx=D∞−X
jets
Tcos(α+ij) + X
jets
Nsin(α+ij) (15)
E. Moments
∞
V
T
L
∞
D
∞
dL
dDdT
My
L
∞
D
∞
T
dL
dD
dT
Figure 4. Illustration of the moment arm length variation
during pitch attitude change.
The pitching moment is calculated by the resul-
tant wing forces and moments. The thrust moment
arm dTjdoes not change during the pitch variation.
Though variation of the pitch angle affects the po-
sition of the aerodynamic center of the wing, as was
experimentally shown by Draper and Kuhn,13 in this
analysis we will assume it to be fixed. As the air-
craft is capable of increasing its pitch attitude to 90
degrees, the moment arm between the wing aerody-
namic center and the center of gravity of the aircraft
changes during this rotation as it is shown in Figure
4. Therefore, the lift force moment arm dLand drag
force moment arm dDhave to be calculated at every
angle of attack. Finally, the total pitching moment of the aircraft is calculated by
My=MwingAC −X
jets
TjdTj−L∞dL+D∞dD(16)
F. Equilibrium Calculations
In order to fly in an equilibrium state at every flight speed (V∞), the aircraft must satisfy
Fx= 0 , Fz= 0 , My= 0,
via thrust (T) and the elevator deflections (δe). For steady cases, this is obtained by finding the roots via
the Newton-Raphson technique. This method requires an initial guess of the control inputs, close to the
actual inputs necessary, in order to find the convergence. This initial guess can be easily calculated for the
cruise flight case. The converged values of the cruise condition are then used as initial values for a slightly
slower speed, and so forth.
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III. Design of the prototype
This section presents the main steps and decisions for the design of the prototype. The methods explained
in the previous sections are embedded into a program that takes many input variables, such as wing-span,
wing-surface, motor number, propeller size, location, and incidence angles, thrust of each propeller, etc.
With the help of this program the lift, drag, and moment of any candidate configuration can be calculated
for a given flight velocity, propeller thrust and control surface deflection.
A. Design Evaluation
The primary design driver is the operational efficiency of the vehicle, therefore the priority of the iterative
optimization is to obtain the smallest and the most compact system that can satisfy the mission requirements.
Table 1shows the constraints for a representative mission.
Max Dimension ≤1.0 [m] (Limiting the wing span)
Cruise Speed = 14-16 [m/s] (Typical cruise speed)
Dash Speed ≥25 [m/s] (Penetrating into wind)
Endurance ≥90 [min] (At cruise conditions)
Payload Mass = 0.2 [kg] (Typical payload)
Total Mass ≤2.0 [kg] (Restricted by the regulations)
Table 1. Constraints of a representative mission.
A multi disciplinary optimization could have been applied to the development, with a detailed structural
model and weight estimation models included. However, for the simplicity and rapid development of the
prototype, the following highly simplified structural weight model is used
Wstructural =KSref b(17)
where Kis the structural weight coefficient which is found from previously build vehicles, Sref is the reference
wing surface area, and bis the wing span.
Afterwards, the total weight is estimated by summing up all of the component weights
Wtotal =Wstructural +Welectronics +Wpr opulsion +Wbattery +Wpayload (18)
The weight of the on-board electronics is already minimized and does not depend on the aircraft size in
this scale as we narrowed down the size limitation. Figure 5shows a picture of the autopilot board called
Chimera v1.0 a, which weighs approximately 30 grams. It runs the Paparazzi open-source autopilot system,
which contains software for communication, servo drivers, state estimation, etc.
Figure 5. Overview of Chimera v1.0 autopilot board from
Paparazzi Autopilot System
ARM Cortex M-7 CPU
9 DOF IMU (MPU 9250)
Barometer, Differential Pressure
High-Speed logging via SD card
8 x Servos (commercial plugs)
5 x UART
I2C , SPI, CAN
On-board XBee support
Companion Board ready
89 mm x 60 mm
Table 2. General specifications of
Chimera v1.0
awiki.paparazziuav.org/Chimera/v1.00
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The propulsion system total weight and efficiencies have been kept constant per motor during the con-
ceptual design evaluations. An appropriate motor and propeller couple has been selected afterwards by using
QPROP14 and wind-tunnel experiments.
B. Configuration
The maximum dimension restrictions eliminate most of the possibilities for the configuration selection. As
the main objective is high operational efficiency, the simplest and most compact configuration is a twin-
motor plank wing. Most of the meteorological sensors requires a clean front end without propellers or other
obstacles influencing the in coming flow. Therefore, a forward nose cone with sufficient inside volume for the
payload placement is required. With these decisions made, the configuration is almost fixed, only the exact
wing span and the surface area remain undefined. These quantities, as well as the battery weight, propeller
dimensions, and control surface sizing are selected with the help of the explained methodology. Possible
combinations of design variables are then evaluated using a computer program. Each candidate aircraft has
to be able to satisfy steady flight equilibrium for the full flight speed envelope. Among all, the most compact
vehicle dimensions have been selected.
C. Airfoils
During a typical mission, the aircraft flies with the propellers constantly blowing on the wing. Therefore the
wing section within this propeller slipstream will be working in turbulent conditions. The transition from
laminar to turbulent flow will also appear on the nose of the fuselage before the wing, which influences the
portion of the wing around the fuselage joint. Adding the transition around the wingtip to these, it can be
assumed that the complete wing will be always working in turbulent flow conditions.
Therefore the airfoils are designed for turbulent flow conditions by tripping the boundary layer artificially
around the leading edge. The design process is done by using XFOIL interactively. The trigger point for the
transition is selected to be at 0.05% of the chord length, both on the top and bottom surface of the wing.
The starting point for the design was a combination of MH45 and S5010 airfoils. The trailing edge gap
thickness is selected as 0.8mm and set specifically according to the local chord of each airfoil. This value
is mainly driven by the manufacturing technique used and the strength of the material on the trailing edge.
The total thickness of the airfoil has the biggest influence on the performance, therefore the thickness for
each section has been reduced as much as possible, without loosing too much on the spar strength. It has
to be mentioned that as the spar gets thinner, the total weight increases for a given strength. The loading
is modified on the aft part of the airfoil, so that an almost positive pitching moment is obtained for stable
flight during cruise phase.
D. Propulsion System
After selecting the twin-motor configuration, the weight of each combination of motor, propeller, speed
controller and required electrical cable is assumed to be approximately 90 grams during the iterations. This
assumption relies on the previous experience with similar propulsion systems using same required power.
A good fit from the existing off-the-shelf propellers is found to be the HQ-Prop 8×5, and an off-the-shelf
electric motor that has been used and tested in-house for several years is the AXI-2212/26. The Figure 6
shows the wind-tunnel test results of this motor/propeller combination at different speeds. The tests were
stopped around 6 Nof thrust, because of the limitations of the force sensor. The usage of a four-cell battery
with 14.8Vresults in approximately 10 Nof thrust in static (0 m/s) conditions, which will be sufficient for
hovering capability, even if we take an additional control safety margin into account.
E. Final Appearance
Table 3shows the final specifications, and Figure 7shows the manufactured prototype of the Cyclone. It
should be noted that, the first prototype is equipped with a different motor, which is AXI-2808/24 because
of possible heating problems during extensive durations of hovering flight. In reality, the vehicle will not be
hovering more than two minutes.
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
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Figure 6. Thrust and total system efficiency versus RPM plots at different wind tunnel speeds for the AXI2212-26
electric motor and HQ-Prop 8x5 propeller combination.
Figure 7. Overview of Cyclone
Wing Span 0.88 [m]
Wing Surface Area 0.15 [m2]
Mean Aero. Chord 0.17 [m]
Prop Diameter 0.21 [m]
Section Airfoil custom
Flight Speed Range 0-30 [m/s]
MTOW (hand-released) 1.5 [kg]
Payload Capacity 0-0.4 [kg]
Table 3. General sp ecifications of Cyclone
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IV. Manufacturing
In order to achieve the requested high quality surface and precise geometry, the manufacturing is all done
by high rpm CNC machined aluminum molds. This also helps to obtain the precision required by the thin
turbulent airfoils. Composite materials are used in order to achieve a light weight and robust airframe. The
skin of the wing is made up of Rohacell sandwich material covered with aramid on the top and glass fiber in
the inside. The main spar is made from a carbon fiber sleeve, and the spar caps are layed up directly to the
inner side of the wing skins, where the spar gets bonded afterwards. The inner reinforcements for the motor
mounts and for the hinge location is shown in the most right picture of the Figure 8. Vacuum bag technique
with wet lay-up is used, which is also shown in the third picture from the left in the Figure 8. Most of the
electronics and the control servos are placed and fixed inside the aircraft during the closing of the top and
bottom half of the molds together. The control surfaces are directly attached to the servo shafts on the root
and aluminum housings and pins are used for the hinge mechanism. The nose cone and the tail cone are
manufactured separately, and they can be removed for easy access to the internal payload and also for easy
transportation.
Figure 8. Manufacturing phases, CNC mold milling on the left, composite wet lay up vacuum bag in the middle, and
finished skins on the right before closing the molds together.
V. Control
This section deals with the attitude control of the vehicle across the flight envelope. The axis definitions of
the vehicle are based on the hover condition, as shown in Figure 9.
Y
X
Z
Figure 9. The body axis definitions of the Cyclone
The Cyclone has four independent actuators
that lead to four degrees of freedom for the con-
trol of the vehicle. The motors can provide a force
in the negative body Z axis, as well as a moment
around the body X axis. The flaps provide moments
around the body Y and Z axes and can provide these
moments even in hover flight, due to the propeller
slipstream.
From test flight data it appears that the torque
from the propellers is not very strong, possibly be-
cause of the interaction of the slipstream with the
wing. Nonetheless, the propellers spin in opposite
directions, such that the torques are canceled at
equal rotational speed. Test flights show that mo-
ments around the body Z axis due to typical changes in individual motor commands, caused by propeller
drag and inertia, are relatively small.
To transition to and back from forward flight without changing altitude, the Cyclone encounters very
large angles of attack, a stalled wing, and rapidly changing pitching moments. Modeling of the forces and
moments at different airspeeds and different angles of attack is costly and time consuming. Furthermore,
a controller based on this data will require accurate knowledge of the airspeed and angle of attack, which
is difficult to obtain, especially in gusty conditions. That is why Incremental Nonlinear Dynamic Inversion
(INDI) control method is chosen, which needs no modeling of the vehicle dynamics and is very strong at
disturbance rejection.
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A. Incremental Nonlinear Dynamic Inversion
In this paper we present the first application of INDI to a transitioning UAV. The controller is based on the
work of Smeur et al.15 and revolves around the control of the angular accelerations in an incremental way.
We proceed with a brief overview of the chosen control technique, for more details we refer to mentioned
paper.
First, consider the angular acceleration of the vehicle. Assuming that the gyroscopic moments can be
neglected, the angular acceleration of the vehicle becomes a function of the state and the input vector uas
follows
I˙
Ω=f(Ω,v) + g(u) (19)
where Iis the moment of inertia matrix, which is assumed to be diagonal, Ωis the angular rate vector and
vis the airspeed vector. In order to invert this equation for the inputs ugiven a desired angular acceleration
vector, the functions fand gneed to be accurately known. So instead, a first order Taylor expansion can be
applied to the (19) considering that the change in angular acceleration is caused by a change in the inputs
and states, namely
I˙
Ω=I˙
Ω0+∂
∂Ωf(Ω,v0)|Ω=Ω0(Ω−Ω0) + ∂
∂vf(Ω0,v)|v=v0(v−v0) + ∂
∂ug(u)|u=u0(u−u0) (20)
This equation describes how to predict the angular acceleration knowing the current angular acceleration, the
partial derivatives of the functions fand gand the change in state and inputs. Here, the current angular
acceleration is caused by the sum of moments from inputs, state and disturbances. Assume that we are
looking only a small time ahead, but long enough for the actuators to adopt their new values. We assume
that in this small time period, the change in Ωand vtimes their respective derivatives can be neglected.
If we divide by Iand assume that the partial derivative of gwith respect to ucan be approximated by a
static matrix for some part of the flight envelope, we arrive at
˙
Ω=˙
Ω0+G(u−u0) (21)
where Gis the control effectiveness matrix, which contains the effectiveness of each actuator on each axis.
Its values are determined with a least squares fit with changes in input and angular acceleration obtained
from flight data. The control law can now be obtained by inverting (21):
u=u0+G−1(ν−˙
Ω0) (22)
where the desired angular acceleration has become the virtual control ν. Since the angular acceleration is
now controlled, we can design a PD controller that will provide the virtual control, in order to control the
attitude. We have shown that the gains of this PD controller, if the assumptions hold, depend only on the
actuator dynamics.16
Of course the effectiveness of the actuators varies over the flight envelope. Especially the aerodynamic
surfaces become much more effective with increasing airspeed. To cope with this, we are changing the control
effectiveness of the flaps according to a predefined function of the square of the airspeed. This does require
measurement of the airspeed throughout the flight envelope. For this purpose, a Pitot tube is mounted on the
nose of the aircraft, pointing in the negative body Z axis. This sensor can not deliver accurate measurements
at low speeds and high angle of attack. Therefore, if the airspeed sensor measures less than six m/s, we use
the pitch angle to calculate the flap effectiveness.
Angle of attack and sideslip vanes are also mounted on the nose of the aircraft, though they are not used
for control. The data from these sensors is just used to evaluate the flights.
B. Modeling of the Actuators
Although with INDI we do not model increments in external moments, it is important to model the control
inputs. Consequently, a model of the actuator dynamics is essential. This will tell the controller what the
expected response is for the input increments he applies. The Cyclone is equipped with DS6125MINI servos,
directly attached to the control surfaces. To determine the response of these servos, we attached a wire to
what was believed to be the internal potentiometer signal, and read out the voltage using a logic analyzer.
For some step inputs at no load, the output signal could be roughly modeled with
A(z) = α
z−(1 −α)(23)
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where α= 0.1 for a sample frequency of 512 Hz and a rate limit of 272 degrees per second. We also
measured a delay of ten samples, but adding this in the model gave a slightly worse fit with the angular
acceleration measured in test flights. Therefore, the delay is not included in the final actuator model, and
more investigation is needed to determine whether it should be taken into account or not.
For the motors that drive the propellers, the actuator model is estimated just by fitting the angular
acceleration in roll with the signal to the motors filtered by equation (23), without a rate limit. The best
fit was obtained with α= 0.05. However, the tracking of angular accelerations is a bit slower than can be
expected based on this actuator model, so possibly this value of αis not very accurate. In practice, this
means that the P and D gains, that are normally designed based on the actuator model, need to be less
aggressive to avoid oscillations.
C. Generating Pitching Moment
One of the main difficulties of the design is to provide enough pitch-up moment to counteract the natural
pitch-down moment of a flying wing, specifically at high angle of attack flight. Even if an equilibrium can be
found for every velocity and angle of attack, disturbances or variations in the angle of attack and airspeed
will require some additional control margin. This is a particular problem for the type of vehicle presented in
this paper, as other vehicles equipped with multiple rotors or a swash plate can typically provide stronger
moments.
The center of gravity is placed close to the neutral point of the vehicle. Therefore, a potential solution
could be to move it more to the back. However, this results in a vehicle that is very unstable in forward
flight, dramatically reducing the control performance in this flight phase.
Another potential solution would be to create a pitch-up moment with the propellers, by changing the
value of dT(see Figure 4). Without any servo mechanism, this moment would be static. This means that it
may help when the vehicle pitches forward, but it will make things worse when pitching backward.
D. Descending while Hovering
Since the flaps rely on the slipstream of the propellers for dynamic pressure in hover flight, a large reduction
in thrust will lead to a loss of flap effectiveness. While hovering, achieving a stable vertical descent is quite
delicate. This is why the pilot, or the autopilot, should never give very low throttle. Additionally, a rapid
vertical descent can lead to flow reversal over the wing, leading to inversion of the flap effectiveness. This
will lead to the vehicle yawing and pitching the wrong way.
The pilot, or autopilot, can bring the vehicle back to a stable condition simply by adding thrust. With
higher thrust, the propeller slipstream will increase, leading to an increase in dynamic pressure on the flaps.
Additionally, the added thrust will result in an increase in airspeed, higher dynamic pressure and therefore
an increase in the flap effectiveness.
VI. Flight Tests
In order to demonstrate the viability of the vehicle, together with the proposed incremental control method,
and to show that the vehicle is able to hover, fly forward and gradually transition between the two, we have
conducted a series of flight tests. The preliminary flight tests were performed with a development version
of the Cyclone made out of foam, aramid and 3D printed pieces. A picture of the development version is
shown in Figure 10.
Figure 11 shows several variables during a flight in which the ground speed was commanded by a pilot.
The first two graphs show the desired and measured pitch and roll angles respectively. Note that the
rotation order of the Euler angles used is ’ZXY’, instead of the more conventional ’ZYX’, in order to avoid
the singularity at ninety degrees pitch angle.17 The vehicle starts out hovering with a pitch angle of around
-33 degrees, because of the presence of a bit of wind. Then an increasing velocity is commanded, and the
aircraft accelerates to 23 m/s airspeed. While in forward flight, several turns are performed, as can be seen
from the roll angle.
We also show the deflection of both flaps in the third graph of Figure 11. A positive deflection yields
a pitch-up moment and the maximum deflection is 30 degrees. Note how the vehicle needs considerable
flap deflections in order to avoid pitching down at low speed and pitch angles between -20 and -70 degrees.
Especially when additional pitch up moment is required, this can lead to saturations, as can be seen in the
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30 40 50 60 70 80
-100
-80
-60
-40
-20
0
θ [deg]
θ
θref
30 40 50 60 70 80
-60
-40
-20
0
20
40
φ [deg]
φ
φref
30 40 50 60 70 80
-10
0
10
20
30
40
u [deg]
u1
u2
30 40 50 60 70 80
Time [s]
0
5
10
15
20
25
va [m/s]
30 40 50 60 70 80
Time [s]
24
26
28
30
32
34
h [m]
-200 -150 -100 -50 0 50
E [m]
-50
0
50
100
150
200
N [m]
Figure 11. Flight test of the Cyclone. On the left side, from top to bottom: pitch angle, flap deflection and the height
above ground. On the right side: roll angle, measured airspeed and a top view of the trajectory.
figure at 40 seconds and at the end of the forward flight phase at 75 seconds. The tracking of the pitch and
roll reference is good throughout the flight, except when transitioning back from forward flight.
Figure 10. The development version of the Cyclone, in flight
with a camera mounted on the rear.
In this part of the flight, the vehicle needs to
pitch up more than the flaps can physically achieve.
We prioritize pitch over roll, which is why upon sat-
uration the roll control suffers as well. Additionally,
we change the effectiveness of the propellers on the
pitch axis to a nonzero value when both flaps are al-
most saturated. This makes the vehicle add thrust
in order to pitch up, which increases the propeller
slipstream velocity, making the flaps more effective.
Also, at high angle of attack, increasing the thrust
typically reduces the angle of attack, which reduces
the aerodynamic pitch moment.
These problems can be reduced by increasing the
altitude during the transition, such that the angle of
attack and the aerodynamic pitch moment remain
small. However, we require the vehicle to be able to
cope with strong winds, which requires flying at a
large angle of attack as well. In this case, the vehicle
is even descending when transitioning back to hover.
Finally, we highlight the satisfactory tracking of
pitch and roll during the first part of the flight with
the (non-saturated) required flap deflections. We
recall that we have not modeled the aerodynamic moments and still the vehicle is able to counteract them,
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even when the maximum flap deflections are required after 40 seconds of flight. This experiment shows
that the INDI control technique is able to cope with the unmodeled moments, even though they are strong
compared to the control input.
Although the guidance and navigation is not the main topic of this paper, Figure 12 shows preliminary
results of the capability of the Cyclone to autonomously travel over four waypoints in a square at 20 m/s.
The UAV is programmed to aim its ground speed vector to the current waypoint, and it switches to the next
waypoint (counter clockwise) when it has a distance of 30 m to the current waypoint. There was a mild
wind of approximately 4 m/s coming from West, which explains the asymmetry in the turns.
-350 -300 -250 -200 -150 -100
E [m]
20
40
60
80
100
120
140
160
180
200
N [m]
Figure 12. Ground track of navigation in forward flight at 20 m/s.
VII. Conclusion and Future Work
Within the objective of optimizing a fixed wing mini-UAV with transitioning flight capability, a brief de-
scription of the semi-empirical method for estimating force and moments generated by a wing, partially or
fully immersed inside distributed propeller slipstream is presented. The method is written as a program
and used during the conceptual design phase for performance evaluations of blown-wing type configuration.
According to the given mission requirements, an 88cm wing span vehicle, called Cyclone, is designed.
The applicability of incremental nonlinear dynamic inversion control to a hybrid vehicle is shown. This
control method does not depend on an extensive model of the vehicle, which makes it very easy to apply
to such a complex vehicle. Only a model of the actuators and the control effectiveness are needed, which
are relatively easy to obtain. Obtaining a model of the moments across the flight envelope through CFD or
windtunnel tests can be very expensive and time consuming, so avoiding this is beneficial.
Test flights are employed to evaluate the controller implementation and show the viability of the aircraft
design. The experiments show the ability of the Cyclone to hover, transition and fly forward, with good
attitude tracking. However, poor capability of generating positive pitching moment using aerodynamic
control surfaces has also been highlighted. This can lead to problems when descending with high angle of
attack, which may be necessary on windy conditions.
Therefore, future work will include improving the pitch moment generation without losing efficiency and
an in-depth analysis of the control of the attitude and position using INDI. Finally, the designed 90 minutes
of endurance capability has to be proven with additional flight tests.
Acknowledgments
Development of the prototype vehicle has been partly funded by the MISTRALE Project. The authors
would like to thank Xavier Paris for his contribution on the experimental setup and flight tests.
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