Journal of Robotics, Networking and Artificial Life
Vol. 7(2); September (2020), pp. 91–97
DOI: https://doi.org/10.2991/jrnal.k.200528.004; ISSN 2405-9021; eISSN 2352-6386
https://www.atlantis-press.com/journals/jrnal

Research Article

Effects of Variable Arm Length on UAV Control Systems
M. Rizon1,*, C.K. Ang1, Mahmud Iwan Solihin1, Zuradzman Mohamad Razlan2, Hazy Desa2,
Shahriman A. Bakar2, Wan Khairunizam2, Zunaidi Ibrahim3
Faculty of Engineering, Technology and Built Environment, UCSI University, Cheras, Kuala Lumpur 56000, Malaysia
School of Mechatronic, University Malaysia Perlis (UniMAP), Arau, Perlis 02600, Malaysia
3
Faculty of Technology, University of Sunderland, St Peter’s Campus, Sunderland SR6 0DD, UK
1
2

ARTICLE INFOABSTRACT

Article History

Quadrotor is a type of unmanned aerial vehicle that has been widely used in many applications, such as, policing, surveillance,
aerial photography and agriculture. Conventionally, the control of quadrotor flight direction is accomplished by varying
speeds of rotors or manipulating torques. In this paper, a novel mechanism is proposed. The mechanism uses stepper rotors tocontrol the arm length for changing flight directions, while maintaining rotors’ speed at constant. This can be achieved using amathematical analysis of relation between quadrotor arm length and moment of bending of various position of rotor. Analysis
and simulation results have shown the change in arm length required to produce moment of bending for hovering, roll and pitch
motion. Experimental results have shown that the new mechanism is able to carry more payloads which the rotor speed can beutilized fully at 100% while the flight direction is been controlled by changing of the arm length compared to conventional flightcontrol mechanisms.

Received 04 November 2019
Accepted 16 April 2020
Keywords
UAV
quadrotor
moment of bendingarm length© 2020 The Authors. Published by Atlantis Press SARL.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
UAV is a short name for “Unmanned Aerial Vehicle” defined as
aircrafts without the onboard presence of pilots [1]. UAV is commonly used in military and police forces in situations where therisk in sending a human piloted air craft is unacceptable. In many
developed countries, UAV is also used to perform tasks, for example intelligence, surveillance, and reconnaissance missions. Small
UAVs can also be used for entertainment industry, such as, aerial
filming, aerial photography and others. Most of the UAVs are madein quadrotor due to its easy to design, small rotors, and excellent
manoeuvrability [2]. The study requires analyzing the relationshipbetween UAV’s rotor support bar length and the UAV control systems. Quadrotor is a type of UAV that is lifted and propel by four
rotors. The propellers are connected with two pairs of support bars.
The flight direction of quadrotor can be controlled by increasingor decreasing the speed of rotors [3,4]. Predicting the motion ofmanipulators are based on an artificial neural network [5–10].
Larger rotor required quite high current, which are difficult to control using current or voltage regulating circuitry. Also, power usageof the UAV systems is a major problem to withstand the desired
endurance of flight time. A study to manage the power usage isimportant and a study from fluid mechanic’s point of view is muchneeded. Besides that, flight movement of quadrotor limits thepower of rotor. Quadrotor rotors cannot operate in 100% power
because of another 30% of power is reserved to control for flight
direction. Furthermore it is difficult to control the stability andCorresponding author. Email: MohdRizon@ucsiuniversity.edu.my*

precision of flight movement of quadrotor that powered by fuel orpetrol [11,12].
Therefore, the theory is implied to control the quadrotor’s directionof flight by increasing or decreasing the length of the support bar.
The length of support bar helps in balancing and stabilizing the UAV.
The study focus on relation between support bar length and momentof bending of various position of rotor. Thus, this study shall be thebasis to run the dynamic analysis at the UAV’s rotor support bar
length control systems and also to enhance the UAV’s mathematicalmodelling by using (SOLIDWORKS® software, Dassault Systèmes),
computer-aided design (CAD) and computer-­aided engineering(CAE) systems [13].

2. QUADROTOR DYNAMIC MODEL
Quadrotor is an UAV that consist of four rotors located at the endof the cross configuration. Each of the rotor consists of propellerthat generate thrust force for lifting the quadrotor [12]. The front
and rear rotor rotate counter-clockwise, while the left and the rightrotor rotate clockwise [14]. The rotations allow to nearly canceling the gyroscopic effects and aerodynamic torques in trimmed
flight [15]. The quadrotor is able to move in yaw, roll, pitch andhover direction with the change of thrust outputs of each propeller.
In Figure 1a, hover movement is obtained when the net thrust of
all the rotors is equal to zero. In order to achieve zero net thrust
for all rotors, the direction of rotation of rotor 1 and 3 must bein the opposite direction of rotor 2 and 4. Besides that, all therotors are operated in equal speed. When the speed of rotor (1–4)

M. Rizon et al. / Journal of Robotics, Networking and Artificial Life 7(2) 91–97

92

a

b

c

d

frame to earth frame. Applying the Newton–Euler method for rigid
body as:T

propeller		   mx = FR + [00 - mg ] - Fa 

(6)		   rw = w ´ rw + t (7)x represents the linear acceleration vector, F is the thrust that
produced by the rotors, Fa indicates the frictional force, τ is thecontrol torque produced by rotors, m is the mass of the body.
Thus, from Equations (6) and (7), quadrotor dynamic equation
is derived as:

Figure 1 | Movement of the quadrotor due to propeller rotation.

mx = u1(cos f sinq cosy + sin f siny ) - k1xmy = u1(cos f sinq cosy - sin f siny ) - k 2 ymz = u1(cosq cos f ) - mg - k3z	    + u3 - k 5f
I f = (I - I )fy
Figure 2 | Free body diagram of the quadrotor [11].

are increased equally as shown in Figure 1, the quadrotor flies invertical motion along z-axis according to the thrust output produce due to the propeller rotation. In Figure 1b, pitch movement
is obtained when the torque of rotor 3 is increase/decrease and thetorque of rotor 1 is decrease/increase and keeping constant torqueof rotor 2 and 4. The quadrotor will pitch forward or backward. In
Figure 1c, roll movement is obtained when the torque of rotor 4
is increase/decrease and the torque of rotor 2 is decrease/increase
and keeping constant torque of rotor 1 and 3. The quadrotor willroll right or roll left. In Figure 1d, yaw movement is obtained when
the torque of rotor 2 and 4 is increase while decrease the torqueof the rotor 1 and 3 to move left and vice versa for the right direction.
The quadrotor will rotate clockwise or counter-clockwise.
Quadrotor is non-linear system with six degree of freedom andcontains only four rotors input [15]. Figure 2 represents the freebody diagram and axes of the quadrotor. In Figure 2, l is the distance of each rotor toward the center of the pivot. ϕ, θ and ψ arerepresenting the Euler angles about the body axes x, y, z. F1, F2, F3
and F4 are the thrust force produce by the propeller.

y

z

x

x

x

z

(8)

I zy = (I x - I y )q f + u 4 - k 6y  + u2 - k 4q
I q = (I - I )qy
where I is the moment of inertia. The thrust induced variation the
speed of the rotors is the input vector and stated as:
U = [u1 u2 u3 u 4]T 
		 

(9)

Thus, the input vectors are defined as:
u1 = b(w12 + w 22 + w 32 + w 42 )		u2 = bl(w 32 - w12 )u3 = bl(w 42 - w 22 )



(10)

u 4 = d(w 22 + w 42 - w12 - w 32 )where, w is the rotor speed, b and d are thrust and drag coefficient.
The lift force to hover the quadrotor is defined as u1, u2, u3, andu4 are the input torques that locate the quadrotor to the pitch, rolland yaw attitude. In Equation (10), the increasing and decreasingof rotor speed produce the input torque that oriented toward pitch,roll or yaw attitude.

The position and velocity vectors in Earth frame stated as
			 x = [ x y z ] (1)			 x = [ x y z ] 

(2)

T
T

The pitch, roll and yaw angle in body frame are stated as			 q = [q fy ] (3) ] 
			 q = [q fy

(4)

T

T

Then, R indicates the rotational matrix from body to earth frame asæ cy cq   R = ç sy cf
çè - sq- sy c f + cy sq sf
cy cq + sq sf sy
cq sf

cf cy sq + sq sy ö
cf sq sy - cy sf ÷ 
÷
cq cf
ø

(5)

In Equation (5), c indicates cos() and s indicates sin().
The thrust force and control torque act on the body and producedby the propeller rotation. The vector of thrust moves from body

3. VARYING ARM LENGTH
Figure 3a indicates the pitch movement that is produced by thedecreasing the arm length l1 and increasing the arm length l3
and keeping both arm length l2 and l4 length unchanged. Figure 3b
shows the pitch movement produced when the arm length l1
is increased and the arm length l3 is decreased and kept constant length in both arm length l2 and l4. Figure 3c illustrates
the roll movement that is obtained when the arm length l2 isdecreased and the arm length l4 is increased while keeping thelength of both l1 and l3 fixed. Figure 3d shows the roll movement that is obtained when the arm length l2 is increased andthe arm length l4 is increased while keeping the length of bothl1 and l3 fixed. In Figure 3e, the yaw movement is accomplished byincreasing the arm length l2, l4 and decreasing the arm length l1,l3. Thus, the quadrotor tilted in counter-clockwise direction.
Figure 3f indicates the yaw movement in clockwise direction
produced by decreasing the arm length l1, l3 and increasing thearm length l2, l4. Equation (10) that stated earlier explains theM. Rizon et al. / Journal of Robotics, Networking and Artificial Life 7(2) 91–97

input torque produced by the increasing and decreasing therotor speed. According to torque law:			 t = fil (11)2
			 fi = bwi (12)version for its suitable propeller size and voltage. Rotor version
that suited well with 18.5″ diameter and 6.3 mm pitch propeller
is KDE5215XF-435 (435 KV). The data consists of amperage, power
input, thrust output, RPM and efficiency for different throttle
range between 25% and 100%. The data is obtained from the experiments conducted by the KDE Company.

The input torque is derived as:
u1 = b(w12 + w 22 + w 32 + w 42 )		u2 = bwi 2 (l 3 - l1)

u3 = bwi 2 (l 4 - l 2)

5. DETERMINING MOMENT OF BENDINGFOR EVERY ROTOR SPEED (RPM)(13)

Figure 4 shows the free body diagram of the quadrotor. In order toproduce hover movement, the equivalent net torque of the quadrotor
is equal to zero and all rotor spinning in equal speeds. Moment ofbending acting on quadrotor arm can be calculated using the formula as shown in Equation (14).

u 4 = dwi 2 (l 2 + l 4 - l 3 - l1)
Therefore, the pitch, yaw, roll movement of the quadrotor can becontrolled by increasing or decreasing arm length to generate thecertain input torque. The rotor speed is kept at constant where
wi = w1 = w2 = w3 = w4.

			 M i = Ti ´ L The analysis is conducted by referring KDE data performance
Table 1. KDEdirect.com provides data performance of specific rotor
b

c

d

e

f

(14)

M is the moment of force, T is the force or thrust output produce
by the propeller rotation and L is the quadrotor arm length, andI = 1, 2, 3, 4, 5, 6, 7. In the first step of the analysis, there are
two variables, a fixed variable and a manipulated variable. The
fixed variable is the length of the quadrotor arm, L. The manipulated variable is the thrust output produced from variation rotor
speeds. The length of the quadrotor arm is 400 mm suitable for18.5″ propeller. Quadrotor hover in vertical direction, when the all
four-­rotor spinning in equal speed, produces the same amount ofthrust. Higher speed produces more thrust so that the quadrotor
flies higher and vice versa for lower speed. Therefore, the moment

4. MATHEMATICAL ANALYSIS OFQUADROTOR ARM LENGTHa93

Figure 3 | Pitch, roll, yaw moment respect to arm length.

Figure 4 | Free body diagram respect to moment thrust and length.

Table 1 | KDE data performance
Voltage[V]

Propeller
size

Throttle
range

Amperage[A](Lower is
better)

KDE5215XF435 (435 KV) 14.8 V(4S)KDEXF16.8 V
UAS75HVCMAX
S.R.ENABLED

18.5″ × 6.3
KDECF185DP DUAL
BLADE

25.00%
37.50%
50.00%
62.50%
75.00%
87.50%
100.00%

2.1
4.6
8.3
13.6
20.6
29.7
39.3

Rotor
versionPower input[W]  [hp](Higher isbetter)Thrust output[g]   [N]  [lb](Higher is better)

31
68
122
201
304
439
581

430
860
1390
2010
2710
3510
4420

0.04
0.09
0.16
0.27
0.41
0.59
0.78

4.22
8.43
13.63
19.71
26.58
34.42
43.35

0.95
1.9
3.06
4.43
5.97
7.74
9.74

RPM
[Rev/Min](Higher isbetter)
1980
2820
3600
4320
4980
5640
6240

Efficiency[g/W]   [lb/hp](Higher is better)
13.87
12.65
11.39
10
8.91
8
7.61

22.8
20.79
18.73
16.44
14.66
13.14
12.51

M. Rizon et al. / Journal of Robotics, Networking and Artificial Life 7(2) 91–97

94

of bending can be calculated for every speed of rotor provided fromKDE data performance.

6. DETERMINING THE CHANGE INQUADROTOR ARM LENGTH
Finding arm length needed to produce a required moment fromprevious data using thrust output produce from three rotor speedsof 3600, 4320 and 4980 RPM (Figure 5). The constant variable now
is change to thrust output produced from a fixed rotor speed andthe manipulated variable is the moment of bending, Mi. Their relationship is shown in Equation (15).
			 Linew = M i / T (15)where i = 1, 2, 3, 4, 5, 6, 7 and M is the moment of force, T is thethrust output.

8. RESULTS
Figure 7 shows the relation of moment of bending against thethrust output. In the diagram, we can see that the moment ofbending is increased directly that is proportional to the thrust
output. Thrust output produced by the rotation of the propeller
is also related to the speed of rotor Table 2. The increased inrotor speed results in higher thrust generated. The minimum
value of moment of bending is 1.69 N.m acting on 0.4 m quadrotor arm length, with the thrust output of 4.22 N. The momentof bending increases until it reaches to the maximum value of
17.34 N.m with the thrust output of 43.35 N.

9. RESULT OF ARM LENGTH FORREQUIRED MOMENT OF BENDING
Figure 8 shows the arm length against moment of bending for threedifferent rotor speeds 3600, 4320 and 4980 RPM. In the graph,

7. ASSEMBLY DESIGN OF THE
QUADROTOR ARM
The design requires a stepper rotor, a fixed arm, a moving arm,
4 × 18.5″ propellers and a brushless DC rotor (Figure 6).

Figure 7 | Graph moment of bending against thrust output.
Figure 5 | Free body diagram for one arm.

Figure 8 | Graph arm length against moment of bending.

Figure 6 | Assembly design of the quadrotor arm.
Table 2 | Data moment of bending due to various rotor speed
Rotorversion
KDE5215XF435 (435 KV)KDEXFUAS75HVC
S.R.ENABLED

Propeller
size

Throttlerange

RPM [Rev/Min](Higher is better)

18.5″× 6.3
KDE-CF185-DP
DUAL-BLADE

25.00%
37.50%
50.00%
62.50%
75.00%
87.50%
100.00%

1980
2820
3600
4320
4980
5640
6240

Thrust output[g]   [N]    [lb](Higher is better)
430
860
1390
2010
2710
3510
4420

4.22
8.43
13.63
19.71
26.58
34.42
43.35

0.95
1.9
3.06
4.43
5.97
7.74
9.74

Arm length(m)

Momentof bending
(N.m)

0.4
0.4
0.4
0.4
0.4
0.4
0.4

1.69
3.37
5.54
7.88
10.63
13.77
17.34

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95

Table 3 | Data of arm length for required moment of bending (3600 RPM)
Rotor version
KDE5215XF-435(435 KV)KDEXF-UAS75HVC
S.R.ENABLE

Voltage [V]14.8 V (4S)
16.8 V (MAX)

Propeller size

Thrust [N]

RPM [Rev/Min]

Moment [N.m]

Lnew [m]18.5″ × 6.3
KDE-CF185-DP
DUAL-BLADE

13.63
13.63
13.63
13.63
13.63
13.63
13.63

3600
3600
3600
3600
3600
3600
3600

1.69
3.37
5.45
7.88
10.63
13.77
17.34

0.12
0.25
0.40
0.58
0.78
1.01
1.27

Propeller size

Thrust [N]

RPM [Rev/Min]

Moment [N.m]

Lnew [M]18.5″ × 6.3
KDE-CF185-DP
DUAL-BLADE

19.71
19.71
19.71
19.71
19.71
19.71
19.71

4320
4320
4320
4320
4320
4320
4320

1.69
3.37
5.45
7.88
10.63
13.77
17.34

0.09
0.17
0.28
0.40
0.54
0.70
0.88

Propeller size

Thrust [N]

RPM [Rev/Min]

Moment [N.m]

Lnew [m]18.5″ × 6.3
KDE-CF185-DP
DUAL-BLADE

26.58
26.58
26.58
26.58
26.58
26.58
26.58

4980
4980
4980
4980
4980
4980
4980

1.69
3.37
5.45
7.88
10.63
13.77
17.34

0.06
0.13
0.21
0.30
0.40
0.52
0.65

Table 4 | Data of arm length for required moment of bending (4320 RPM)
Rotor version

KDE5215XF-435 (435 KV)KDEXF-UAS75HVC
S.R.ENABLE

Voltage [V]14.8 V (4S)
16.8 V (MAX)

Table 5 | Data of arm length for required moment of bending (4980 RPM)
Rotor version

KDE5215XF-435 (435 KV)KDEXF-UAS75HVC
S.R.ENABLE

Voltage [V]14.8 V (4S)
16.8 V (MAX)

we can see that the arm length is proportional to the moment ofbending. Additionally, the slope showing in the graphs differs fromeach other. The slope of the rotor speed of 3600 RPM is highest
compared to two other rotor speeds, 4320 and 4980 RPM. Rotor
speeds of 3600, 4320 and 4980 RPM generate thrust output of
13.63, 19.71 and 26.58 N respectively Tables 3–5.
In order to generate moment of bending of 1.69–17.34 N.m withrotor speed of 3600 RPM, we need to increase the arm length from
0.12 to 1.7 m. For 4320 RPM rotor speed, the arm length needs to
be increased from 0.09 to 0.88 m. For rotor speed of 4980 RPM,
the arm lengths needs to be increased from 0.06 to 0.65 m in orderto generate moment of bending of 1.69–17.34 N.m. It shows thatlower thrust output or lower rotor speed requires longer arms to
produce sufficient moment.

Figure 9 | Arm moves inside the fixed arm.

10. RESULT OF SOLIDWORKS MOTIONSIMULATION
Figure 9 shows the moving arm moving inside the fixed arm.
This occurs when the stepper rotor rotates counter-clockwise thus
the moving arm moves in negative x-direction. Figure 10 shows

Figure 10 | Arm move outside the fixed arm.

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M. Rizon et al. / Journal of Robotics, Networking and Artificial Life 7(2) 91–97

that the moving arm is move outside the fixed arm. This motion
occurred when the stepper rotor rotates clockwise and achieved
positive linear motion (forward motion).

11. CONCLUSION
By using the mathematical analysis, the varying in arm lengths
affects the moment of bending of the quadrotor. Increasing thearm length changes the moment of bending of the quadrotor toincrease or decrease the arm length will decrease the moment ofbending. The speed of rotor is kept at constant so that the thrustgenerated by the propeller rotation is at constant. The analysis
also proves that the change in mechanism of the existing UAV’s
quadrotor that is the quadrotor flight direction can be obtain byincreasing or decreasing rotors speed. The existing methods havebeen extended to varying the speed of the rotor, the quadrotor
flight direction can be controlled by varying the length of thequadrotor’s arms.

CONFLICTS OF INTEREST
The authors declare they have no conflicts of interest.

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AUTHORS INTRODUCTION
Dr. M. Rizon

Dr. C.K. Ang

He graduated Doctor of Engineering at
Department of Computer Science andIntelligence System in Oita University,
Japan. He was a Professor of Biomedical
Technology in King Saud University,
Saudi Arabia in 2010. He served at
MIEC, Fuzhou University, China in 2019.
Currently, he is a Professor of Department
of Electrical and Electronics, UCSI University, Malaysia. MIET,MIEM member.

He received his Bachelor of Engineering
Degree with First Class Honors in
Mechatronic Engineering from Universityof UCSI, Malaysia in year 2010. In end ofyear 2010, He was attached with Universiti
Putra Malaysia for his PhD in Mechanicaland Manufacturing Engineering andgraduated in year 2014. Currently, heis the Dean for Faculty of Engineering
Technology and Built Environment, UCSI University. He isinterested in artificial intelligence, soft computing, robotics, andmechatronics. He has published many papers which related tothe application of Artificial Intelligence in recent years.

M. Rizon et al. / Journal of Robotics, Networking and Artificial Life 7(2) 91–97

Dr. Mahmud Iwan Solihin

Dr. Shahriman A. Bakar

He is an assistant professor in mechatronics engineering department, specialized
in applications of artificial intelligence/machine learning, optimizations, control systems, robotics and automation.
His current research interest is mainly on
applications of AI (artificial intelligence)and optimization algorithms in various
filed including robotics, control systems,
spectroscopy applications, sensor networks, etc., toward sustainable engineering development in the future.

cycle for MITI.

Dr. Zuradzman Mohamad Razlan

Dr. Wan Khairunizam

He received his PhD in Energy Mechanical
System Engineering from Mie University,
Japan in 2012. He is currently an Associate
Professor of Mechanical Engineering
Department at School of Mechatronic
Engineering, University Malaysia Perlis,
Malaysia. He has 11 years experiences inindustrial research and development of air
conditioning system and registered as Professional Engineer.

97

He received his B. Eng., M. Eng., and PhD
degrees in Mechanical engineering fromMie University, Mie, Japan. His PhD
research on human and robot collaborative tasks. He is currently an Associate
Professor in UniMAP Malaysia researching in system design for automotive andtransportation system and currently he isleading Motorsport Technology Centreof Excellence to develop hybrid motor-

He received his B. Eng. degree in Electrical& Electronic Eng. from Yamaguchi
University and PhD in Mechatronic Eng.
from Kagawa University, in 1999 and 2009,
respectively. He is currently an Assoc.
Professor for Mechatronic Engineering,
University Malaysia Perlis, Malaysia.

Dr. Hazy Desa

Dr. Zunaidi Ibrahim

He received his Bachelor of MechanicalEngineering from Tokushima University,
Japan. He was a Senior Design MechanicalEngineer in R&D Sony Technology
Malaysia in 1997. In 2001, he was
employed by Tamura Electronics Malaysia.
He pursued his PhD at the Artificial Lifeand Robotics Laboratory, Oita University,
Japan in 2003. He is a Professor, Director ofCenter of Excellence for Unmanned Aerial System at Universityof Perlis. IEEE, IET member.

He received his B.Eng., M.Eng. and PhD
degrees in Mechanical Engineering fromMie Univ, Japan in 1997, 2003 and 2006,
respectively. Currently, he is leading a
Sustainable Advanced Manufacturing
research group at University Sunderland,to support TRL5-8 for SMEs company in the UK. His research interest
is in machine learning in the area of abio-medical robotic application for asustainable manufacturing environment.