Quad-Tilting Rotor Convertible MAV: Modeling and Real-Time Hover Flight Control

J Intell Robot Syst (2012) 65:457–471DOI 10.1007/s10846-011-9589-x

Quad-Tilting Rotor Convertible MAV:Modeling and Real-Time Hover Flight Control

Gerardo Ramon Flores · Juan Escareño ·Rogelio Lozano · Sergio Salazar

Received: 16 February 2011 / Accepted: 18 April 2011 / Published online: 6 September 2011© Springer Science+Business Media B.V. 2011

Abstract This paper describes the modeling, con-trol and hardware implementation of an exper-imental tilt-rotor aircraft. This vehicle combinesthe high-speed cruise capabilities of a conven-tional airplane with the hovering capabilities ofa helicopter by tilting their four rotors. Changingbetween cruise and hover flight modes in mid-air is referred to transition. Dynamic model ofthe vehicle is derived both for vertical and hor-izontal flight modes using Newtonian approach.Two nonlinear control strategies are presentedand evaluated at simulation level to control, thevertical and horizontal flight dynamics of the ve-hicle in the longitudinal plane. An experimentalprototype named Quad-plane was developed toperform the vertical flight. A low-cost DSP-basedEmbedded Flight Control System (EFCS) was de-

This work was partially supported by the Institute forScience & Technology of Mexico City (ICyTDF) andthe French National Centre for Scientific Research(CNRS).

G. R. Flores (B) · J. Escareño · R. LozanoHeudiasyc Laboratory, University of Technology ofCompiègne, CNRS 6599, 60205 Compiègne, Francee-mail: [email protected]

S. SalazarFrench-Mexican Laboratory on Computer Scienceand Control, CINVESTAV, Mexico City, Mexico

signed and built to achieve autonomous attitude-stabilized flight.

Keywords Quad-plane UAV · Operationaltransition · Inner-outer loop control ·Backstepping · Embedded control system ·Convertible MAVs

1 Introduction

The applications of mini Unmanned Aerial Ve-hicles (UAVs) have widely diversified during thelast years. They comprise both military and civil-ian, though the latter has had a lower develop-ment rate. The key feature of UAVs is to providea mobile extension of human perceptions allowingnot only the security of the user (soldier, police-man, cameraman, volcanologist) but also gather-ing information such as images or video, locationscoordinates, weather conditions, etc., for eitheronline or offline analysis. As a result, the use ofaerial robots, specially miniature (mini and micro)UAVs (MAVs), has enhanced activities such assurveillance of sensible areas (borders, harbors,prisons), wildlife study, natural disasters assess-ment, traffic surveillance, pollution monitoring,just to mention a few.

However, there are missions whose scope isbeyond the capabilities of conventional MAVs

458 J Intell Robot Syst (2012) 65:457–471

designs since they require not only longer flightendurance but also hovering/VTOL capabilities.

Missions like the surveillance of both fast-moving and static targets, identification of cracksin pipelines or bridges, medical supplies (bloodsamples, saliva samples, medications), exchangebetween hospitals and clinics located in remoteareas, are missions which can not be acomplishedwith standard airplanes or helicopters. Besidesthese commonly used aerial vehicles, the Convert-ible MAVs, combining the advantages of horizon-tal and vertical flight, have been gaining popular-ity recently. By marrying the take-off and landingcapabilities of the helicopter with the forwardflight efficiencies of fixed-wing aircraft, the Quad-plane (Fig. 1) promises a unique blend of capabili-ties at lower cost than other MAV configurations.While the tilt-rotor concept is very promising, italso comes with significant challenges. Indeed it isnecessary to design controllers that will work overthe complete flight envelope of the vehicle: fromlow-speed vertical flight through high-speed for-ward flight. The main change in this respect (be-sides understanding the detailed aerodynamics)is the large variation in the vehicle dynamics be-tween these two different flight regimes. Severalexperimental platforms have been realized with abody structure in which the transition flight is exe-cuted by turning the complete body of the aircraft[1–5]. In [1] and [3] the authors described the de-velopment (modeling, control architecture and ex-perimental prototype) of Two-rotor tailsitter. Thecontrol architecture features a complex switch-ing logic of classical linear controllers to dealwith the vertical, transition and forward flight.Green and Oh [4] present a classical airplane

configuration MAV to perform both operationalmodes. The hover flight is autonomously con-trolled by an onboard control flight system whilethe transition and cruise flight is manually con-trolled. A standard PD controller is employedduring hover flight to command the rudder andelevator. In [5] some preliminary results are pre-sented for the vertical flight of a Two-rotor MAVas well as a low-cost embedded flight controlsystem. There are some examples to other tilt-rotor vehicles with quad-rotor configurations likeBoeing’s V44 [8] and the QTW UAV [9]. In[10] the authors present the progress of theirongoing project, an aircraft with four tiltingwings.

This paper reports current work on the model-ing, control and development of an experimentalprototype of a new tilt-rotor aircraft (Quad-planeMAV) that is capable of flying in horizontal andvertical modes. This mini aerial vehicle is one ofthe first of its kind among tilt-wing vehicles on thatscale range. The vehicle is driven by four rotorsand has a conventional airplane-like structure,which constitutes a highly nonlinear plant andthus the control design should take into accountthis aspect. A nonlinear control strategy, consist-ing of a feedback-linearizable input for altitudecontrol and a hierarchical control (inner-outerloop) scheme for the underactuated dynamic sub-system, is proposed to stabilize the aerial robotwithin the hovering mode. Backstepping [15], aLyapunov based method is presented to stabilizethe vehicle within the airplane mode. Through theuse recursive method, backstepping divides thecontrol problem into a sequence of designs forsimpler systems.

Fig. 1 Quad-tilting rotorconvertible UAV.a CAD. b Experimentalprototype

(a) (b)

J Intell Robot Syst (2012) 65:457–471 459

The organization of this paper is as follows: inSection 2, the mathematical model of the Quad-plane aircraft is obtained using the Newton formu-lation. In Section 3, we explain how the transitionflight is developed and how the velocities, forcesand angles interact. In Section 4, we develop astabilizing control law for the vehicle in hoverflight mode. In Section 5, we present a backstep-ping control law for the vehicle in forward flightmode. Simulation results of both controllers arepresented in Section 6. Experimental results areprovided in Section 7. Conclusions and perspec-tive are provided in Sections 7 and 8, respectively.

2 Modeling

This section presents the longitudinal equations ofmotion as well as the aerodynamics of the vehicle(Fig. 2). Due to the flight profile of the vehiclewe distinguish three operation modes: (1) HoverFlight (HV) the aircraft behaves as a rotary-wingplatform (|γ | ≤ π

6 ), (2) Slow-Forward Flight (SFF)(π

6 < |γ | ≤ π3 ) and finally (3) Fast-Forward Flight

(FFF), where the aerial robot behaves as a pureairborne vehicle (π

3 < |γ | < π2 ).

1. During the HF the 3D vehicle’s motion reliesonly on the rotors. Within this phase the ve-hicle features VTOL flight profile. The con-troller for this regime disregard the aerody-namic terms due to the negligible translationalspeed.

2. It is possible to distinguish an intermediateoperation mode, the SFF, which links the twoflight conditions, HF and FFF. This is proba-bly the most complex dynamics.

3. FFF regime mode (Aft position), at this flightmode the aircraft has gained enough speedto generate aerodynamic forces to lift andcontrol the vehicle motion.

2.1 Kinematics

– F i denotes the inertial earth-fixed frame withorigin, Oi, at the earth surface. This frame isassociated to the vector basis {ii, ji, ki}.

– Fb denotes the body-fixed frame, with origin,Ob , at the CG. This frame is associated to thevector basis {ib , jb , kb } (Figs. 3 and 4).

– Fa denotes the aerodynamic frame, with origin,Ob , at the CG. This frame is associated to thevector basis {ia, ja, ka}.

– The orthonormal transformation matrices Rbi

and Rab , respectively used to transform a vec-tor from Fb → F i and Fa → Fb within thelongitudinal plane (pitch axis), are given by:

Rbi =⎛⎝

cos θ 0 sin θ

0 1 0− sin θ 0 cos θ

⎞⎠ ,

Rab =⎛⎝

cos α 0 sin α

0 1 0− sin α 0 cos α

⎞⎠

Fig. 2 Operationaltransition


Fig. 3 Coordinate systems: inertial frame (Fi) and body-fixed frame (Fb )

2.2 Aerodynamics

It is important to consider these forces properlybecause they are fundamentally affected by thevehicle’s motion and thus they alter the basic dy-namics involved. The analysis used in the presentpaper will be based on a combination of a low-order panel method aerodynamic model coupledwith a simple actuator disc model of the flow in-duced by the propellers. In order to proceed withthe aerodynamic analysis, it is worth to mentionthe following assumptions:

– A1. The vehicle is a rigid body, i.e. the felex-ibility of the aircraft wings or fuselage will beneglected.

– A2. Non-varying mass is considered (m(t) = 0).– A3. The aerodynamic center (AC) and the

center of gravity (CG) are coincident.

In order to determine the aerodynamic forcesexerted on the vehicle, we need to know both thedirection and velocity of the total airflow vector.We can identify three wind vectors acting on thevehicle: the airflow speed Vp produced by the ro-tors, the Vb airflow generated by the translationalmotion of the body (U, W) and a third componentdue to the external wind (disturbance) Ve, gener-ally unknown. Hence, the total wind vector in thebody frame can be written as

Vtot = Vp(γ ) + Vb + Ve (1)

where Vtot = (vu, vw)T . The total wind vector Vtot

experienced by the wing varies depending on theflight mode. Within the HF and SFF regimes thewing is not washed by the propeller airflow Vp

(Fig. 5a), while in the FFF mode, it is assumed thatthe wing is significatively submerged (Fig. 5b) byVp. Therefore the propeller slipstream Vp is disre-garded in HF and SFF. To include the behavior ofVp in the equations let us introduce the followingfunction

ξ(γ ) =

⎧⎪⎨⎪⎩

0 i f γ ≤ π

3

1 i f γ >π

3

(2)

The parallel wind velocity vu and the normal windvelocity vw components at the wing encompassethe velocity that the vehicle experiments throughthe air and the corresponding components of Vp

Fig. 4 Free-body schemeshowing the forces actingon the quad-tilting MAV


(a) (b)

Fig. 5 Airflow profile generated by the rotors during the flight envelope. a Relative wind velocity in HF and SFF modes. bRelative wind velocity in FF mode

due the tilting of the rotors and the aleatory exter-nal wind Ve , i.e.

vu = (u + ξ(γ )vp sin(γ ) + veu

)ib (3)

vw = (w + ξ(γ )vp cos(γ ) + vew

)kb (4)

Assuming purely axial flow into the propellers,simple actuator disc theory [12] gives the inducedpropeller velocity for the ith rotor as

vpi =√

2Ti

ρ Ap(5)

where Ap is the total disc-area of the propellerand ρ the air density. Figure 4 shows the aero-dynamic forces on a small UAV with a tilt angleγ . The forces consist of a lift force, L, perpendic-ular to the total flow vector Vtot, a drag force Dparallel to Vtot, and the airfoil’s pitching moment,M, about the positive cartesian y-axis. The abovediscussion can be summarized by [6, 7]:

Cl = Clαα

Cd = Cdp + Cdi

Cm = Cmαα

where these equations are standard aerodynamicnon-dimensional lift, drag and moment coeffi-cients.1 To obtain the lift and drag forces andthe pitching moment on the aircraft it is onlynecessary to obtain the total wind velocity vectorVtot, see Eq. 1, the angle of attack and the aerody-namic parameters Clα , Cd, Cmα

which depend onthe geometry of the vehicle.

L = 1

2ClρV2

totS

D = 1

2CdρV2

totS

1C∗ slopes are obtained from the software XFOIL.

M = 1

2CmρV2

totSc

In these equations S and c are the area and thewing chord respectively. The angle of attack α andthe magnitude of Vtot are obtained through thefollowing equations

α = arctan(vw/vu) (6)

Vtot =√

v2w + v2

u (7)

The lift force will depend on the velocity Vtot

and the angle of attack. The Fig. 6 represents thedifferent values of lift for several speed conditions.

2.3 Forces Exerted on the Quad-Plane

The vector that contains the set of forces appliedto the Quad-plane (Fig. 4) is given by

mξ = RbiT b + Rbi R ab Aa + W i (8)

where, ξ = (x, y, z)T is the CG’s position vector inF i, Tb = (0, 0, −T)T is the collective thrust in F b ,

−100−50

050

100

0

5

10

15

20

−100

−50

0

50

100

speed [m/s]

α [deg]

Lift

[N]

Fig. 6 Lift values for different velocities


Aa = (−D, 0, −L)T is the vector of aerodynamicforces in F a and finally W i = (0, 0, mg)T denotesthe weight of the vehicle in F i. The four propellersproduce the collective thrust T, which can bemodeled as

T = Kl

i=4∑i=1

ω2i (9)

where ωi is the angular velocity of ith-rotor, Kl

is a lift factor depending on the aerodynamic pa-rameters of the propeller. Note that the vectorof aerodynamic forces Aa is not only involvedin translational motion, but also in the rotationalmotion of the vehicle, as is shown next.

2.4 Moments Acting on the Quad-Plane

The forces shifted away from the CG inducemoments causing the rotational motion. Thecorresponding vectorial equation grouping themoments exerted about CG is written as

τ b = τ bT + τ b

M + τ bG (10)

where τT is the induced moment due the differ-ence of thrust between T3,4 and T1,2, τM is theairfoil’s pitching moment, τG is the gyroscopicmoment. τT is obtained through

τ bT = l1

(−T3,4 cos γ + T1,2 cos γ)

jb (11)

where, l1 is the distance from the CG to the rotors.The airfoil’s pitching moment τM is obtained fromthe airfoil’s Cm slope and the lift contribution ofthe elevator.

τ bM = M jb (12)

The gyroscopic moment τG arises from thecombination of the airframe’s angular speed b =(p, q, r)T and the rotors angular speed ωi. TheτG vector is then modeled as

∑4i=1(

b × Ipωi),leading to

τ bG = Ip

[q(ω2 − ω1 + ω3 − ω4)ib

+p(ω1 − ω2 − ω3 + ω4) jb]

(13)

where, Ip represents the inertia moment of thepropeller. For simplicity we do not take intoaccount the drag torque due to the propeller dragforce. Since the present paper concentrates on thelongitudinal flight of the vehicle, the correspond-ing scalar equations modeling the forces andmoments applied to the vehicle are written as:

mX = −T3,4 sin (θ + γ ) − T1,2 sin (θ + γ )

− L sin (θ − α) − D cos (θ − α)

mZ = D sin (θ − α) − T1,2 cos (θ + γ )

− L cos (θ − α) − T3,4 cos (θ + γ ) + g

Iyyθ = M + l1(−T3,4 cos γ + T1,2 cos γ )

+ Ip p(ω1 − ω2 − ω3 + ω4) (14)

2.5 FFF Mathematical Model

In this regime the vehicle essentially behaves asan airplane, thus we can consider the commonlongitudinal aircraft model [13]. In addition to thebody-axis equations, it is important to express theequations of motion in the wind axis, because theaerodynamic forces act in these axis and Vtot (writ-ten as V from here onwards), α can be expressedin terms of u and w. This reference system is

Fig. 7 a Wind-axisreference frame.b Flight-path angledefinition

(a) (b)


used for translational equations because angle ofattack and velocity are either directly measurableor closed related to directly measurable quanti-ties, while the body axis velocities (u, w) are not.The equations of motion take the form

V = 1

m

[−D + Tt cos α

− mg (cos α sin θ − sin α cos θ)]

α = 1

Vm

[−L − Tt sin α

+ mg(cos α cos θ + sin α sin θ)] + q

θ = q (15)

The angles θ and α lie in the same verticalplane above the north-east plane (Fig. 7a), andtheir difference is the flight-path angle � = θ − α

(Fig. 7b). Under this definition and from the lastequation of Eq. 14 we obtain the next mathemati-cal model

V = 1

m

[−D + Tt cos α − mg sin �]

α = 1

Vm

[−L − Tt sin α + mg cos �] + q

θ = q

q = 1

IyyM (16)

3 Transition

The flight envelope of the vehicle encompassesdifferent flight conditions, achieved by means ofthe collective angular displacement of the rotors.Indeed, is this tilting that provides a continuousmechanism to perform the operational transition.To illustrates this, let us consider the followingscenario:

– Tt ≥ mg i.e. the vehicle flies at a stabilizedaltitude.

– θ ≈ 0 i.e. stabilized vertical flight.

Is clear that as γ is tilted the horizontal velocityincreases, while the vertical velocity is reduced(Fig. 8). These facts affect proportionally to theforces coming from the rotors and the wing.

0 20 40 60 80 1000

2

4

6

8

10

12

14

16

18

t [seg]

Vu,

Vw

[m/s

]

VuVw

α=35.8

α=19.1

α=3.02

Fig. 8 Behavior of velocities during the tilting of the rotors

Thus, both vertical and horizontal controllerscan still be used at the same time whose actionsis controlled by γ . The vertical collective thrust isgradually reduced inhibiting the action of verticalcontroller and allowing the action of the hori-zontal controller and viceversa. So, for example,for larger values of γ , i.e. γ > 45, the rotorcraftbehaves more like a classical airplane. As thevehicle is gaining speed due to rotors tilt (γ ),then aerodynamic forces arise. For this reason weconsider that the control of vertical and forwardflight are active during the whole flight envelope.

4 Control Strategy for Hover Flight Mode

The vertical flight of the Quad-plane representsa challenging stage due to the aircraft’s verticaldynamics are naturally unstable. In this regime,the Quad-plane aerial robot aims to emulate theflight behavior of a Quadrotor which features anon conventional Quadrotor design, i.e. an asym-metrical H-form structure.

Vertical flight regime encompasses two dy-namic subsystems: the altitude dynamics, actuatedby the thrust T, and the horizontal translationalmotion, generated by the pitch attitude. Takinginto account the item 1) presented in Section 2,we can consider a simplified model from whichis derived the controller in HF regime (i.e. α ≈ 0since γ = 0).


For simplicity we consider that the gyroscopicmoment is very small. These considerations allowsus to rewrite Eq. 14 as

X = −(

T3,4 + T1,2

m

)(sin θ)

Z = −(

T3,4 + T1,2

m

)(cos θ) + g

θ = −(

l1

Iyy

) (−T3,4 + T1,2)

(17)

If we rename the total thrust as Tt = T3,4 + T1,2,and the difference of these thrusts as Td = T1,2 −T3,4. Then

X = −Tt

msin θ

Z = −Tt

mcos θ + g

θ = − l1

IyyTd (18)

thus, we have derived a simple model, suitable forcontroller design. The altitude (last line in Eq. 18)can be stabilized via a feedback-linearizable inputthrough the total thrust Tt

Tt = −muz − mgcos(θ)

(19)

where uz = −kpz(z − zd) − kdz z with kpz , kdz > 0and zd is the desired altitude. Since the vehicleworks in an area close to θ ≈ 0, the singularity isavoided. For the θ − x subsystem (18), a two-levelhierarchical control scheme is used to stabilize itsdynamics. The outer-loop control stabilizes thetranslational motion (slow dynamics [11]) alongthe x-axis, while the inner-loop control stabilizesthe attitude (fast dynamics). Introducing Eq. 19into X dynamics of Eq. 18 and assuming that z ≈zd, namely uz → 0, leads to

x ≈ −g tan θ = −g tan ux (20)

For the horizontal motion (20), θ can be consid-ered as virtual control input ux. However, it isa state not an actual control. Given that θd isslowly time-varying, we will assume that the x-

dynamics converges slower than the θ -dynamics.The reference for the inner-loop systems is

ux = θd = arctan

(−vx

g

)(21)

ux = θd ≈ 0 (22)

where vx = kvx x + kpx x with kvx, kpx > 0. Usingthe linearizing control input Eq. 21 in Eq. 20 yields

x = vx, provided that θ = 0(i.e. θ = θd)

As the previous equation shows, the success of theouter-loop controller relies directly on the inner-loop attitude control performance, thus the innerloop controller must guarantee the stabilization ofthe attitude around the reference. For this reason,the stability analysis of the inner-loop controlleris presented next. Consider the following positivefunction which is an unbounded function

V(θ , θ

)= 1

2Iyyθ

2 + ln(

cosh θ)

(23)

Using Eq. 18 its corresponding time-derivativeyields

V(θ , θ

)= Iyyθ

(− l1

IyyTd

)+ ˙

θ tanh θ (24)

Considering ˙θ = θ , thus Eq. 24 may be rewrit-

ten as

V(θ , θ

)= θ

(−l1Td + tanh θ

)(25)

Using the control input

Td = tanh θ + tanh θ

l1(26)

in Eq. 25 yields

V(θ , θ

)= −θ tanh θ , (27)

where V(θ , θ ) ≤ 0. Therefore, the origin (θ , θ ) isstable and the state vector remains bounded. Theasymptotic stability analysis can be obtained fromLaSalle’s Theorem. Therefore, θ → 0 and θ → 0as t → ∞.


5 Control Strategy for Forward Flight Mode

In this section the flight path angle � will be con-trolled using the backstepping algorithm takingthe following approximations into consideration:

– The air speed is assumed constant, V = 0 [14].– From the definition of flight-path angle, the

dynamics � = θ − α yields � = 1mV [Tt sin α +

L − mg cos �].– The thrust term Tt sin α in Eq. 16 will be ne-

glected as it is generally much smaller than lift.– Cm = Cmδ

(α)δ, since the main contribution toM is provided by the elevator.

With these considerations in mind and using thechange of coordinates ζ = � − 1/2π , the system(16) may be expressed as

ζ = −g cos (z + 1/2π)

V+ Clαα

mV

α = g cos (z + 1/2π)

V− Clαα

mV+ q

q = 1

IyyCmδ

δ (28)

Equation 28 is now in feed forward form for back-stepping procedure. For notational simplifica-tion, let

x = f (x) + ξ1

ξ1 = f1(x, ξ1) + ξ2

ξ2 = f2 + g2(ξ1)u (29)

with

x = mV�

Clα; f (x) = − g

Vcos

(Clα xmV

)

ξ1 = α; f1(x, ξ1) = gV

cos

(Clα xmV

)− Clα ξ1

mV

ξ2 = q; f2 = 0

u = δ; g2(ξ1) = 1

JyCmδ

(30)

Defining the following error states as

e � x − xdes

e1 � ξ1 − ξ1,des (31)

e2 � ξ2 − ξ2,des

Now, following the backstepping procedure dif-ferentiating the first equation in Eq. 31 yields

e = f (x) + ξ1,des + e1 − xdes (32)

where ξ1,des is viewed as a virtual control forthe last equation, choosing as ξ1,des = − f (x) −k1e + xdes. Then substituting this virtual control inEq. 32 we have that

e = −ke + e1 (33)

Repeating the same procedure, differentiating e1

yields

e1 = f1(x, ξ1) + e2 + ξ2,des − ξ1,des (34)

Let ξ2,des = − f1(x, ξ1) − e − k1e1 + ξ1,des so that

e1 = −e − k1e1 + e2 (35)

As a last step, now the real control signal is ob-tained in similar way. Differentiating e2 yields

e2 = f2 + g2(ξ1)u − ξ2,des (36)

Let

u = 1

g2(ξ1)

[− f2 − e1 − k2e2 + ξ2,des]

= u (...z d, zd, zd, zd, e, e1, e2) (37)

so that

e2 = −e1 − k2e2 (38)

It is important to ensure that g2(ξ1) �= 0, whichoccurs only with big enough negative values ofα. These values are assumed to be impossible toachieve in standard operation of the airplane, soavoiding division by zero. Equations 33, 35, and38 expressed in vectorial form

e = −Ke + Se (39)

S = −ST satisfies eT Se = 0, ∀e, so that with theLyapunov-candidate-function V(e) = 1

2 eTe, andthe time derivative evaluated in the trajectoriesyields

V(e) = eT(−Ke + Se) = −eT Ke < 0, ∀e (40)

This proves that the above differential equation,is asymptotically stable about the origin.


Fig. 9 Position andattitude of the vehicleunder disturbancecondition

0 500 10001

2

3

4

5

time[ms]

x po

sitio

n [m

]

xreference

0 500 1000−8

−5

−2

1

time[ms]

z po

sitio

n [m

]

zreference

0 500 1000−0.2

0

0.2

0.4

time[ms]

θ [r

ad]

← disturbance

θreference

6 Simulation Results

6.1 HF

The performance of the nonlinear controllerpresented in the previous section is evaluated on

the dynamic model (18) in MATLAB/Simulink.We started the Quad-plane at the position(x0, z0, θ0) = (2, 0, π

8 ) and (x, z, θ ) = (0, 0, 0).The aircraft had the task of performing hoverflight at (xd, zd, θd) = (4, −7, 0). Figures 9 and10 show the evolution and convergence of the

Fig. 10 Derivatives of theposition and attitude ofthe vehicle underdisturbance condition

0 500 1000−1

0

1

time[ms]

x ve

loci

ty [m

/s]

x velocityreference

0 500 1000

−4

−2

0

time[ms]

z ve

loci

ty [m

/s]

z velocityreference

0 500 1000−3

−2

−1

0

1

time[ms]

θ ve

loci

ty [

rad/

s]

θ velocityreference


Table 1 Parameters Parameter Value

Mass (m) 0.8 kg

Gravity (g) 9.8ms2

C 0.2 ml1 0.25 mWing span 1.15 m

states (x, x, z, z, θ, θ ) to the desired referenceswith the initial conditions mentioned above.It is important to note that position and anglereferences are tracked with negligible steady stateerrors. The controller is robust in the presence ofa perturbation in t = 600 ms with a magnitude of1/8π radians, as seen in Figs. 9 and 10. Table 1shows the real parameters for simulation analysis.

The control inputs are depicted in the Fig. 11,which shows the reaction to the disturbance.

6.2 FFF

After the vehicle experiments the transition-flight,its behavior is like an airplane. We have consid-ered the next initial conditions for purposes ofsimulation: �0 = 5, α0 = 5 and θ0 = 10. The air-craft had the task of tracking a trajectory shown inthe first part of Fig. 12. This figure shows the evo-lution and tracking trajectory of the states (�, α, θ)

to the desired reference, with the initial conditionsmentioned above. It is important to note thatangle references are tracked with negligible steadystate errors (Fig. 13).

7 Experimental Setup

The goal of this section is to present an experi-mental autonomous hover flight to evaluate notonly the performance and reliability of the pro-posed concept but also the efficacy of the pro-posed control algorithm. We have programmed aground station in MATLAB/Simulink for on-linevariable monitoring/adjusting.

7.1 Onboard Flight System (OFS)

1. Experimental prototype: The vehicle’s fuse-lage and the H-form structure are built of carbonfiber and balsa wood (Fig. 1). The wing wasbuilt with depron. Four counter rotating andtilting brushless motors provide the thrust,while the tilting mechanism of the engines iscontrolled through two analog servomotors.

2. Flight control CPU: The attitude control al-gorithm is implemented on the TMS320F2808

Fig. 11 UAV’s controlinputs and response todisturbance

0 500 10001.5

2.5

3.5

4.5

5.5

time[ms]

Thr

ust

↓response to disturbance

T1,2

T3,4

0 500 1000−1

−0.5

0

0.5

time[ms]

u x, d(u

x)/dt

↑response to disturbance

ux

d(ux)/dt


Fig. 12 Trajectorytracking

0 10 20 30 40−6

0

6

12

time[s]

Γ [d

eg]

Γreference

0 10 20 30 40−15−10

−505

10

time[s]

α [d

eg]

α

0 10 20 30 40−8

−4

−0

4

8

time[s]

θ [d

eg]

θ

digital signal processor (DSP) (Fig. 14).It has a high-Performance 32-Bit CPU at100 Mhz and 128 K × 16 of embeddedflash memory. This DSP is notable for itsrich set of on-chip peripherals including three32-bit CPU-Timers, two event-manager mod-ules (EVA, EVB), PWM, capture,enhancedanalog-to-digital converter (ADC) module,

I2C module, serial communications inter-face modules (SCI-A, SCI-B), serial periph-eral interface (SPI) module, digital I/O andshared pin functions and watchdog. The I2Cis used to control the four rotors via YGE30ibrushless controller and to read the mag-netic compass CMPS03, two PWM outputsare used to control the tilting mechanism,

Fig. 13 Control and errordefined by e = � − �d

0 10 20 30 40−50

−25

0

25

50

time[s]

u [d

eg]

u

0 10 20 30 40−0.5

0

0.5

time[s]

e(t)

[deg

]

Tracking error


Fig. 14 Homemade IMU,DSP-based embeddedflight system and workingprinciple of theQuad-plane UAV system

Fig. 15 Roll behavior inthe automatic hoveringflight test

100 200 300 400 500 600 700−1

0

1

time[s]

φ [r

ad]

100 200 300 400 500 600 700−10

0

10

time[s]φ ve

loci

ty [r

ad/s

]

100 200 300 400 500 600 700−100

0100

time[s]

φ co

ntro

l

disturbance disturbance

Fig. 16 Pitch behavior inthe automatic hoveringflight test

100 200 300 400 500 600 700−1

0

1

time[s]

θ [r

ad]

100 200 300 400 500 600 700−10

0

10

time[s]θ ve

loci

ty [r

ad/s

]

100 200 300 400 500 600 700−50

0

50

time[s]

θ co

ntro

l

disturbance disturbance


Fig. 17 Yaw behavior inthe automatic hoveringflight test

100 200 300 400 500 600 700−10

0

10

time[s]

Ψ [r

ad]

100 200 300 400 500 600 700−10

0

10

time[s]Ψ v

eloc

ity [r

ad/s

]

100 200 300 400 500 600 700−50

0

50

time[s]

Ψ c

ontr

ol

the (ADC) module is used to communi-cate the Homemade IMU with the DSP.The wireless communication between Quad-plane and the ground station is performedthrough a wireless serial protocol (two X-beepro modems). With the fast response of thecombination YGE30i brushless controller andthe Robbe Roxxy motor, we can set the exe-cution time for each iteration loop at 2 ms.

3. Homemade IMU: The homemade inertialmeasurement unit (IMU) (Fig. 14) is com-posed of three accelerometers and three gy-roscopes, measuring the angular position andrate along the three axis of the inertial frame.The comunnication between the homemadeIMU and the DSP is with the ADC moduleof the DSP.

7.2 Experimental Results

The Figs. 15, 16 and 17, shows the experimentalattitude performance of the vehicle during thevertical flight. As we can see in the pictures,the vehicle was perturbed, and the states remainsbounded.

8 Concluding Remarks and Future Work

This paper describes an experimental convertibleaircraft that is under development at the CompiègneUniversity. The longitudinal dynamics of this air-craft including its aerodynamics are derived atthe hover and forward flight operating mode.

The proposed control strategies were evaluated,at simulation level, for the nonlinear dynamicmodel, obtaining satisfactory results. The angu-lar position and velocity are obtained throughan onboard IMU. A DSP-based embedded flightsystem was designed and built to implement anattitude controller law. The proposed control al-gorithm is based on an inner-outer loop schemesince it is suitable for implementation purposes.An experimental setup (prototype and EFCS)was designed to perform an autonomous attitude-stabilized flight in hover regime showing a rele-vant performance in presence of external distur-bances. Future work includes the transition flightbetween cruise and hover flight modes (transi-tion flight) to evaluate the accuracy of the modeland to validate the control algorithm. For energy-saving purposes during forward flight (airplanemode), it is proposed that the vehicle can leadits orientation towards wind velocity vector. Toachieve this objective, the vehicle could easilyrotate its orientation (yaw movement in helicoptermode) and once addressed the wind vector, switchto airplane mode. In the proposed configuration,this process could be quite simple, since the vehi-cle is always maintained with the roll and pitch an-gles close to zero, which is not possible in the caseof a tail-sitter configuration since within verticalmode the wing surface is highly vulnerable to windgusts. It is possible to asses with a gyro-stabilizedcamera in order to record and send images andvideo of the inspection area without loss of thetarget to be captured. Again, this would be morecomplex for a tail-sitter configuration, due to the


difference of 90 degrees between the two flightmodes.

References

1. Stone, R.H.: Control architecture for a tail-sitter un-manned air vehicle. In: 5th Asian Control Conference,Melbourne, Australia, 23–25 July 2004

2. Escareño, J., Stone, H.R., Sanchez, A., Lozano, R.:Modeling and control strategy for the transition of aconvertible UAV. In: European Control Conference(ECC07), Kos, Greece (2007)

3. Stone, H.: Aerodynamic modeling of a wing-in-slipstream tail-sitter UAV. In: Biennial InternationalPowered Lift Conference and Exhibit, Williamsburg,Virginia, 5–7 November 2002

4. Green, W.E., Oh, P.Y.: Autonomous hovering of afixed-wing micro air vehicle. In: International Confer-ence on Robotics and Automation, Orlando, Florida,USA (2006)

5. Escareno, J., Salazar, S., Lozano, R.: Modeling andcontrol of a convertible VTOL aircraft. In: 45th IEEEConference on Decision and Control, San Diego,California, 13–15 December 2006

6. Etkin, B., Reid, L.: Dynamics of Flight. Wiley,New York (1991)

7. Stevens, B.L., Lewis, F.L.: Aircraft Control and Simu-lation, 2nd edn. Wiley, New York (2003)

8. Snyder, D.: The quad tiltrotor: its beginning and evo-lution. In: Proceedings of the 56th Annual Forum.American Helicopter Society, Virginia Beach, Virginia(2000)

9. Nonami, K.: Prospect and recent research and devel-opment for civil use autonomous unmanned aircraftas UAV and MAV. J. Syst. Des. Dyn. 1(2), 120–128(2007). Special issue on new trends of motion and vi-bration control

10. Oner, K.T., Cetinsoy, E., Unel, M., Aksit, M.F.,Kandemir, I., Gulez, K.: Dynamic model and control ofa new quadrotor unmanned aerial vehicle with tilt-wingmechanism. In: World Academy of Science, Engineer-ing and Technology, vol. 45 (2008)

11. Kokotovic, P.V., O’Reilly, J., Khalil, H.K.: SingularPerturbation Methods in Control: Analysis and Design.Academic, New York (1986)

12. Stengel, R.: Flight Dynamics. Princeton UniversityPress, Princeton (2004)

13. Stevens, B.L., Lewis, F.L.: Aircraft Control and Simu-lation. Wiley, New York (1992)

14. Mates, D., Hagstrom, M.: Nonlinear analysis and syn-thesis techniques for aircraft control. In: Lecture Notesin Control and Information Sciences, vol. 365. Springer(2007)

15. Khalil, H.K.: Nonlinear Systems, 2nd edn. PrenticeHall (2002)

Quad-Tilting Rotor Convertible MAV: Modeling and Real-Time Hover Flight Control

Documents

Transcript of Quad-Tilting Rotor Convertible MAV: Modeling and Real-Time Hover Flight Control