Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 213–216___________________________________________________________________________________________________________Modeling and Simulation for a Quadrotor Vehicle With Adaptive Wing
Qunpo Liu

School of Electrical Engineering and Automation, Henan Polytechnic University, 2001 Century Avenue
Jiaozuo (454003), Henan, P.R. China
Hongqi Wang

School of Electrical Engineering and Automation, Henan Polytechnic University, 2001 Century Avenue
Jiaozuo (454003), Henan, P.R. China
Fuzhong Wang

School of Electrical Engineering and Automation, Henan Polytechnic University, 2001 Century Avenue
Jiaozuo (454003), Henan, P.R. China
Jikai Si

School of Electrical Engineering and Automation, Henan Polytechnic University, 2001 Century Avenue
Jiaozuo (454003), Henan, P.R. China
Naohiko Hanajima

College of Information and Systems, Muroran Institute of Technology, 27-1 Mizumoto-cho,Hokkaido
Muroran-shi, Hokkaido (050-8585), Japan
E-mail: lqpny@hpu.edu.cn; wangfzh@hpu.edu.cn, sijikai527@126.com, hana@mondo.mech.muroran-it.ac.jp
www.hpu.edu.cn, www.muroran-it.ac.jp

Abstract
Aiming at developing high power efficiency system for quadrotor vehicle during height keeping and long distance
flight, a quadrotor vehicle with adaptive wing is proposed. Angle of the wing respect to flying direction can be
adjusted adaptively according to flying speed, to reduce energy expenditure of motor. The dynamic model was built
up. Rotor lift were analyzed based on the mechanical structure and its flight principle. The simulation is carried out
to verify the effectiveness of high power efficiency.
Keywords: Modeling, Quadrotor vehicle, Simulation, Wing.

helicopter. Compared to conventional helicopters, withthe large main rotor and tail rotor, the quadrotor iseasier to fly, does not have the complex swash platemechanism and is easier to model and control. The
quadrotor has a promising application as commercial,military and academic platforms.
Much research has focused on the Dynamic
modeling[1][5], simulation, optimization, controller
design[2], and control algorithm[3][4][5] for quadrotor

1. Introduction
Because of distinct features, such as vertical take-off
and landing(VTOL), sharp maneuvering, low cost,
simple mechanism, UAVs have attracted more and moreinterests in a wide range involving rescues, security,
inspection, surveillance, aerial photography, mapping,etc. Each individual rotor has a smaller diameter andless kinetic energy than the equivalent single-rotor

Copyright © 2017, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 213–216___________________________________________________________________________________________________________vehicle. However, there are still some problems inpractical use, such as energy expenditure during longdistance forward flight. By now, lithium battery is usedfor power supply for quadrotor vehicle. But the weightof the batteries increases with the capacity. At the sametime, the energy expenditure is also increases forincreased weight and dimension. Due to the conflict
between the weight of the batteries (capacity) and flight
distance, flight distance is subject to the restriction.
However, there are relatively fewer contributions on theenergy expenditure during long distance forward flightfor a quadrotor. Therefore, how to reduce the energy
expenditure during long weight is a problem to solve forthe application of quadrotor vehicle.
A quadrotor vehicle with adaptive underbelly wingis proposed. The underbelly wing at certain angles isexpected to obtain a horizontal direction of thrust.
Advantageously, this may result in a reduction of dip
angle for quadrotor body and also can resulting in lower
airflow resistance and lower downward force on
quadrotor body. And finally, it can eventually reduceenergy expenditure during long distance forward flight.

T2

T1

yb
xb

T4

T3

zb

Fig.1 The main structure of a quadrotor

Fig.2 Force modeling of the quadrotor2. Dynamic modelingbetween the wing and the horizontal flying direction
which marked by a line in green. mg is the weight of thequadrotor. All the analysis is on the assumption ofsteady volume of air flow situation.
The rotor speed is ωi and the thrust force is an
upward vector

This section presents a simple model of the quadrotor
dynamics according to reference [5] and [6].
As shown in Fig.1, the quadrotor possesses a simple
and symmetrical structure with four rotors and can becontrolled by the rotational speed of the four rotors.
For the sake of convenience, T1 is denoted as thehead of the rotorcraft. Meanwhile rotor T3 is the tail.
i.e., T1 , T2, T3 and T4 is named front, right, rear, left
rotor respectively. Define the following body coordinate
system xb, yb, zb: the original point(Ob ) is the center ofgravity; xb is from b Ob the head of the quadrotor; yb isfrom Ob to the right side of the quadrotor; and zb follows
the law of right hand.
The notation for the quadrotor model is shown inFig. 2. Define the following inputs to model thequadrotor: FThrust is the thrust generated by four motors;
FZ is the the vertical upward thrust force on thequadrotor body; Fbf is the air resistance on the body; Fwa
is the left force on the wing; FWf is the air resistance onthe wing; θ is the pitch of the quadrotor body; α is theangle between the xb and the wing; γ is the angle of4

FThrust = ∑ bωi2(1)i =1in the vehicle’s negative z-direction, where b > 0 is thelift constant that depends on the air density, the cube of
the rotor blade radius, the number of blades, and thechord length of the blade.
When the quadrotor is flying in a certain speed on
certain height, the vertical upward thrust force on thequadrotor body should be remained unchanged.

and214

Fz = FThrust cos θ + Fwa − mg

(2)1
Fwα = C y ρ ∞V∞ S cos(α + θ )2(3)Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 213–216___________________________________________________________________________________________________________

where, Cy is wing section lift coefficient; S is the areaof the wing; ρ∞ is the air density; V∞ is the steadyspeed.
Fwa is perpendicular to the direction of air flow.

Define that

δ=Deviation of the direction of air flow caused bywash velocity can be ignored for low speed.
The force F’wf on the quadrotor body generated by
the air resistance on the wing Fwf isFwf′ = Fwf + Fwf cos(− θ )× dTherefore, Eq. (11) can be simplified as

FThrust = δmg

(4)

(13)

From Eq.(13), it can be draw that the energy
expenditure would be deceased if 0 ≤ δ < 1 .
3. Simulation results
To verify whether there are same cases meetrequirements, analysis is carried out based on MATLAB
platform.
In the Eq.(12), there are two parameters Cy and C’y.
Normally, Lift-drag ratio k is used instead. Lift-dragratio k is relate to wing's angle of attack and can bemeasured from wind tunnel test:(5)

where, C’y is wing resistance coefficient.
When the quadrotor is fly on same height, the force
on the body in vertical direction isFz = FThrust cos θ + Fwa − mg = 0

C ′y cos θ sin(α + θ ) − C y sin θ cos(α + θ )(12)And it can be counteracted by increasing of ω3 andreducing of ω1.
The air resistance FWf on the wing is1
Fwf = C ′y ρ ∞V∞ S sin(α + θ )2C ′y sin(α + θ )

(6)

k=

Therefore, the equation can be obtained using Eq. (3)and (5)

CyC ′y(14)The lift-drag ratio k is simulated by wind tunnel test
data in reference [7], as shown in Fig.3. And it is usedin the conclusion of δ.

1mg − FThρust cos θ = C y ρ ∞V∞ S cos(α + θ ) (7)2During the flying, the force on the moving direction isFx = FThrust sin θ − Fwf = ma x(8)where, ax is acceration of quadrotor on the moving
direction.
When the speed is stable, ax=0,1FThρust sin θ = − C ′y ρ ∞V∞ S sin(α + θ ) (9)2In the situation without wing of quadrotor,

FThrust cos θ = mg

(10)

Fig.3 Lift-drag ratio k

In the situation with a wing of quadrotor, the following
equation can be deduced from Eq. (7) and (9)∴F Thrust =In the area marked A1, the results are not valid
because it falls outside the allowable range (α+θ) ≤ 0.
In the area marked A3, the value of δ is bigger than1, which is means more energy needed than quadrotor
without wing.

mgC ′y sin(α + θ )C ′y cos θ sin(α + θ ) − C y sin θ cos(α + θ )
(11)

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 3 (December 2017) 213–216___________________________________________________________________________________________________________

Eq.(6). The FThrust will decrease if the flying velocity V
remains constant. Considering Eq.(8), the force on xdirection isAs shown in Fig.4 and Fig.5, in the area (A2) withcolor changing from dark blue to dark violet in middleof the figure, the value of δ is 0 ≤ δ ≤1. It means thethrust force is smaller than the gravity of guardrotor.
Especially in same point, the thrust force is zero in idea
situation. And it also can be draw from the simulation
results that the thrust force will increase with (α+θ)
increasing. Expecially when α+θ ≻ π/6 (the line asshown in Fig.5), value of δ increase dramatically, whichis due to decrease of the lift-drag ratio k. In this casehowever, δ and the thrust force FThrust will increase verymuch even δ is small in the time.

1FThρust sin θ < − C ′y ρ ∞V∞ S sin(α + θ )2
Therefore, the flying velocity V should decrease until a
new stable equilibrium is reached.
4.

In this paper, a quadrotor vehicle with adaptive
underbelly wing is introduced. A simplified mathematic
model is studied firstly. The force modeling wasanalyzed. Simulation results show that the proposed
quadrotor vehicle with adaptive underbelly wing canreduce energy expenditure by arranging the attitudeangle of wing within limited range.

A3A1

Conclusions

A2

Acknowledgements
Supported by Innovation Scientists and Technicians
Troop Construction Projects of Henan Province(Grant No. CXTD2016054)

Fig.4 D view of simulation results of δα+θ = π/6

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A2

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A1
A3

Fig.5 Top view of simulation results of δTherefore, the best to reduce energy expenditure ison situation of 0 < α+θ < π/6. In this case, the thrustforce FThrust will be stable invariable when (α+θ) does
not change. If θ decreases under influence of air flow,
the value of α should increase to keep stable of FThrust .
In this case, FThrus*tcosθ will increase according to216