Effect of Discrete Yaw Direction Setting for 4 Roter Helicopter Control: Computer Simulation and AR. Drone Model Implementation

International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2763
Issue 07, Volume 3 (July 2016) www.ijirae.com
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Effect of Discrete Yaw Direction Setting for 4 Roter
Helicopter Control: Computer Simulation and AR. Drone
Model Implementation
Hideki Toda*
Hiroaki Takano
University of Toyama University of Toyama
Abstract—In this paper, the effectiveness of discrete yaw direction setting in 4 rotor helicopter control was evaluated
by simple computer simulation and Parrot AR. Drone 4 rotor helicopter in horizontal plane automatic position fixing
control. For 4 rotor system, it is necessary to control the attitude of the drone and the position in the space
simultaneously in order to realize stable flight of the system. The attitude control can be realized by the internal acc /
gyro sensors with high sampling rate (near 1 kHz), on the contrary, the position control in the outdoor situation is
necessary to realize by the external 3D position measurement method with relatively low sampling rate techniques
(lower than 100 Hz) such as GPS. The low sampling rate reduces the positional control stability, and it is causing the
control problem such applications of inspection work at high height and long distance. Our attempt is to evaluate the
effect of adding discrete yaw direction setting while normal 4 rotor helicopter roll and pitch control in horizontal
plane movement by a simple computer simulation and model implementation. By adding the discrete yaw direction
setting to the target direction, the fixed position movement control performance of the 4 rotor system could increase
comparing with without the yaw direction setting of the 4 rotor system. The proposed method would be useful to
improve the 4 rotor system control performance under the relatively low sampling rate positional information
acquired situation.
Keywords— Discrete yaw direction control, degree of freedom of yaw axis, AR. Drone, 4 rotor system, automatic
position stop control.
I. INTRODUCTION
In this paper, the effectiveness of discrete yaw direction setting for 4-rotor helicopter control was evaluated by simple
computer simulation and AR. Drone 4 rotor helicopter control in horizontal plane. In order to apply the 4 rotor system in
real difficult wind flow environments (outdoor, tunnel, bridge site inspections and so on), there are large demands to
improve a positional movement control performance of the 4 rotor system [1-3]. Our attempt is to evaluate the effect of
adding "discrete" yaw direction setting in horizontal plane movement by a simple computer simulation and 4 rotor model
implementation. By adding the discrete yaw direction setting to the general 4 rotor horizontal positional control, the
positional control performance would increase even though the relatively low sampling rate position control commands.
Fig. 1 Effect of roll and pitch controllers with discrete yaw direction setting (solid line) and comparison with normal roll and pitch controllers without
yaw direction setting (dotted line). The yaw direction setting is performed discretely in the star mark points. Figure shows there is a difference of the
reaching movement trajectories between the two control methods.
(B) Normal roll and pitch
independent controllers
without yaw direction
change
(A) Roll and pitch independent controllers
with discrete yaw direction setting
Timing of discrete
yaw direction set
Target
Start

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This paper shows the evaluation of the adding discrete yaw direction setting from two sides - (1) computer simulation, (2)
AR. Drone model implementation. In our previous study, it has been discussed and examined [4,5], however, the basic
mechanism has been unknown.. The aim of this paper is to show one of the reason of the flight control performance
increasing by using the discrete yaw direction setting. Fig.1 illustrate the example trajectory of roll and pitch controllers
with the discrete yaw direction setting (solid black line, Fig.1A, the drone direction is changed in the timing of the star
marks to the target direction) and the normal control procedure of the roll and pitch controls without yaw direction
setting (dotted line, Fig.1B, the drone nose direction is fixed). Key point of the proposed method is the timing of the yaw
direction setting of the drone to the target direction, and the timing of the yaw direction setting (or control) is executed
discretely such as 100 msec period as shown in the star mark of Fig.1A. Generally, the yaw (spin) movement of the drone
is not directly related to the position movement control in the 3D space and it is only used to control the direction of the
camera or the drone body (e.g. Nonami et al. [6,7]). Our method is to use the yaw direction setting discretely while the
drone movement, and it could realize the effective drone movement comparing with normal roll and pitch controls
without yaw direction change strategy.
A. Previous studies
Attitude estimation control [6,8-20] and autonomous flight control [1,6,21-27] are important topics in the study field
of the 4 rotor drone system. The attitude control, generally, is realized by the internal acceleration and gyro sensors with
high sampling rate (near 1 kHz). On the other hand, the positional control especially in outdoor situation is necessary to
be realized by the external 3D position measurement method with relatively low sampling rate techniques (lower than
100 Hz, normally, 10-30 Hz range) such as GPS or camera. The low sampling rate reduces the positional control stability,
and it causes the instability control such applications of inspection work at high height and long distance places (bridge
site, tunnel for example) [1-3]. In the situation, a positional control stability or an improvement control method have been
required especially in the low sampling rate situation. In our previous study, we have discussed and examined about the
effect of improvement of 4 rotor control performance by using fast speed yaw and roll control switching in the timing of
the roll control [4,5]. However, the basic mechanism has been unknown. The aim of this paper is to show one of the
reason of the flight control performance increasing by using the discrete yaw direction setting.
B. Outline
Section 2 describes a simple mathematical model of the drone movement in the 2D space under the two conditions of
(roll) and (pitch) controllers with the discrete yaw direction setting condition and and controllers without yaw
direction change condition. In addition, the proposed roll and pitch controls with discrete yaw setting method was
implemented to the AR. Drone model helicopter. Section 3 and 4 shows the experimental setup and the result of the two
computer simulation conditions of the drone in 2D space and AR. Drone model implementation of the proposed method.
And the discussion and the conclusion is described in section 5 and 6 respectively.
II. METHOD
A. Mathematical model of the computer simulation
First of all, the simple mathematical model of a drone as = and = (nose direction is fixed) independent one
mass point model is developed,
̈ = − ̇ + 1.0(0 − ) − − ̇
̈ = − ̇ + 1.0(0 − ) − − ̇ (1)
where , , and are mass, friction coefficient, the two feedback parameters by setting of LQR respectively. The
direction of the nose is assumed to north direction (0,1) in the and axis 2D map ( = and = axis). The final
position set as (0,0). The mathematical model is confirmed by using computer simulation such a method of our previous
studies [28,29]. Eq.1 represents the case of normal 4 rotor system positional control method using the pitch and roll
simultaneously in 2D space (conventional, Fig.1B).
Next, the pitch and roll axis equation of motion is shown below,
̈ = − ̇
̈ = − ̇ + 1.0(0 − ) − − ̇ (2)
where r, are the roll and pitch axis. The , position (and velocity) on the 2D plane and the , was always able to
convert each other by using rotation matrix (− ). ( , ) = (− )( , ). The direction of the nose was calculated
from = / . This direction change of the was "discretely" determined such a timing of once in 100 cycles of the
computer simulation. This discrete nose direction change process is important. If the nose direction will be calculated
in each computer simulation cycle, there will be no residual error about the axis of . In this case, the will be calculated
as = 0 anytime.

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By using above the equation of motion, the effectiveness of the nose direction change in the experiment 1 is able to be
confirmed. Eq.2, on the contrary, represents the case of proposed 4 rotor system positional control method using roll and
pitch control with discrete yaw direction setting in 2D space (proposed, Fig.1A).
Above all computer simulation, the rotational moment of inertia of the drone does not take into account in order to
simplify the mathematical model. In addition, ( , ) of Eq.2 was calculated on the and axis space, and the feedback
force / velocity and the rotational factor depending on the nose direction was converted it to and axis factors by the
rotation matrix (− ) in order to simplify the computer simulation of the equation of motion Eq.2.
B. AR. Drone 4 rotor as the model implementation
The effect of the proposed roll and pitch control with discrete yaw direction setting was performed by AR. Drone
version 1.0, 4 rotor hobby-class helicopter and it is realized by using only the built-in camera in the front (QVGA
320x240 image with 30 Hz frame rate). In Fig.2, the aircraft is positioned at the center of the room (5x3.5 m square,
room height is 2.4 m) and it flows automatically with the height of 80 cm from the ground. In order to control the
movement of the aircraft, AR. Drone library for Processing named ARDroneForP5 as developed by S. Yoshida [38] was
used and it was connected to a PC1 with Wi-Fi network.
Fig. 2 Experimental setup of AR. Drone helicopter movement control in a room. PC1 controls the aircraft via Wi-Fi network and PC2 is measuring the
aircraft position from the camera on the ceiling.
Fig.3 shows the implementation method of the proposed the roll and pitch control with discrete yaw direction setting
to AR. Drone system. (a) Normal roll and pitch control experimental condition (Ex.2a). (b) Proposed roll and pitch
control with discrete yaw direction setting case (Ex.2b). Since AR. Drone architecture is not possible to execute two
commands at the same time, it is realized by changing the yaw and roll (in addition, yaw control) commands with short
time period (50 msec bin). The drone's movement roll and pitch speed commands , and the yaw (spin) control
command are determined,
= (160 − ) = ( − ) (3)
= ( − )
Fig. 3 Implementation method of the proposed the roll and pitch control with discrete yaw direction setting to AR.Drone system. (a) Normal roll and
pitch roll control (without yaw control). (b) Proposed roll and pitch control with discrete yaw direction setting. Each control bin are executed serially
with 50 msec bin.
Target
Control PC1
Measurement PC2
3.5 m
5 m
2.4 m
(2.5m, 55cm)
USB camera
cm)))))))))))))) Drone
(b) Proposed roll and pitch control with
discrete yaw direction setting method
yaw
50msec 50msec
(a) Normal roll and pitch movement
Time
Time
roll
pitch
roll
pitch yaw
roll
pitch
pitch
50msec 50msec
roll
pitch
roll

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where , and , are constant. is the yaw angle, is the original yaw angle when the take-off, is constant. The
QVGA (320x240) camera that is attached in the front of the AR. Drone aircraft is used for real time position information
measurement and performs the control based on the position and area of the target object (red cylinder) in the camera
image. When the center of the gravity of the red target object is ( , ) and the area is , simple proportional feedback
terms (160 − ) as right-left axis and ( − ) as forward-backward axis where is initial target area when the
drone take off (Eq.3) was used. This method is a kind of visual servo system [10,25,26,32-37].
Above three commands were used to switch serially in each 50 msec bin. In the experiment 2a, and were
exchanged serially with 50 msec bin and it realizes general 4 rotor's positional movement control. This control condition
corresponds to normal roll and pitch controllers with fixed nose direction. In the experiment 2b, , and were
exchanged serially with 50 msec bin and it realizes the proposed roll and pitch control with discrete yaw direction setting.
As a result, there is about 150 msec duration of in the experiment 2b. It was assumed to realize the discrete yaw
direction setting denoted in the computer simulation of the experiment 1.
III.EXPERIMENT
A. Experiment 1: Mathematical model simulation
Eq.1 and Eq.2 were used as the equation of motion of the drone in the 2D ( , ) space. In the simulation, = 10,
= 5 were set as constant values, and the feedback parameters and was calculated by LQR method. Computer
simulation time step was ∆ = 0.01. From the equation of Eq.1, the evaluation function was determined as below,
⃗̇ = ⃗ + ⃗ = ⃗ ⃗ + ⃗ ⃗
(4)
where is system matrix and it expresses Eq.1, ⃗ = ( , ) is state vector, ⃗ is controller input. By using the LQR
method, the feedback parameter are calculated , = (1.32,1.47) as minimize the . In this experiment, three
experimental conditions were considered, (1) normal 4 rotor's roll and pitch controls in 2D space (Eq.1), (2) proposed
(there is no control term about axis) and axis movement with discretely yaw direction setting (Eq.2), (3) (there is
control term about axis) and axis movement with discretely yaw direction setting as Eq.5.
̈ = − ̇ + 50.0(0 − ) − − ̇
(5)
B. Experiment 2
Fig. 2 shows the experimental setup (5x3.5x2.4 m) in performing the 30 sec automatic position stop in the center of
the room. The USB camera that is installed on a ceiling used to trace the drone position (there is a red board on the top of
the drone) while the experiment by using PC2 (position discrimination is about 2 mm). The tracing drone position is
evaluated by the center of the gravity and the standard deviation (S.D. , ) of the trace positions. It is necessary to
note that the tracing drone position is not used in PC1's the drone control.
Normal drone movement control method that use roll and pitch controls is performed (Ex.2a). The command of the
pitch and the roll is continuously exchanged by 50 msec period. The feedback parameters , are determined by
continuously measured 30 sec flight control experiments (N=over 100) in order to minimize the S.D. , .
Proposed discrete yaw control in the timing of the roll control method is performed (Ex.2b). The command of the yaw,
the roll and the pitch is continuously exchanged by 50 msec period. In this experiment, feedback parameter is
determined by continuously measured 30 sec flight control experiments (N=over 100) in order to minimize the S.D.
, .
IV.RESULT
A. Result of experiment 1

_________________________________________________________________________________________________
Fig. 4 The computer simulation result of (1) normal 4 rotor's roll and pitch controls without yaw direction change in 2D space (Eq.1) and (2) proposed
r (there is no control term about r axis) and p axis movement with discretely yaw direction setting (Eq.2).
Fig.4 shows the computer simulation result of (1) normal 4 rotor's roll and pitch controls without yaw direction control
in 2D space (Eq.1), and (2) proposed (there is no control term about axis) and axis movement with discretely yaw
direction setting (Eq.2). In this simulation, the initial velocity was set as ⃗ = (10,10) in order to give it a slight slide
factor that is difficult to recover the trajectory, and the initial and the final position are (40, −40), (0,0) respectively. The
result of (1) trajectory was settled to the final position (0,0) with slight overshoot. On the other hand, the result of (2)
only axis control with discrete yaw direction setting (once yaw direction set in 100 cycles) has a large overshoot and a
damping around the final position (0,0). Important point of this experiment is discrete yaw direction set. If the yaw
direction set would be executed in every computer simulation cycle, there would be no trajectory difference (within
calculation error) between trajectory (1) and (2). When the yaw direction set is executed in every computer simulation
cycle, the calculation of is anytime 0.
Fig. 5 The computer simulation result of (1) normal 4 rotor's r and p controls (without yaw direction setting) in 2D space (Eq.1) and (3) r (there is
control term about r axis) and p axis movement with discretely yaw direction setting as Eq.5.
Fig.5 shows the computer simulation result of (1) normal 4 rotor's = and = axis controls in 2D space (Eq.1),
and (3) (there is control term about axis) and axis movement with discretely yaw direction setting as Eq.5. In this
condition (3), a feedback gain 50.0 of axis was set. The discrete yaw direction set was executed once in 100 cycles. The
trajectory of (3) was close to the straight line from the initial (40, −40) to the final point (0,0) comparing with the
trajectory of (1). It is main result of proposing the meaning of the yaw direction set with the discrete fashion. Total
necessary energy = ∫ are calculated = 1200886 (condition(1)), = 2363732 (condition(2)), =
1186518 (condition(3)). The ratio is = 0.998 < 1 and the total energy cost will decrease in the condition (3)
comparing with the condition (1) of the LQR calculation result.
-20 -10 10
20
10
-10
-20
-30
-40
20 30 40 50
Initial position (40,-40)
Final position (0,0)
+ Discrete Yaw direction set
calculated PD gain by LQR
+
p
p
p
y
y
x
x
Condition (1)
Condition (2)
+
+
10
10 20
-10
30 40
-20
-30
-40
Pitch and Roll
Two PD controllers
+
Diccrete Yaw
direction set
X and Y-axis
Two PD controllers
+ Discrete Yaw direction set
calculated PD gain
by LQR
+
+
y
p
r
p
r
x
y
x
Condition (1)
Condition (3)
y
x
+
+

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Above result is one of the example condition of the LQR and it is not guaranteed by any parameter conditions
including LQR calculation parameters so far. There is a tendency that the ratio / is decreased lower than 1.0 when
the initial velocity ⃗ is not zero and the discrete yaw direction set is not too slow such as once in 1000 cycles.
Fig. 6 The computer simulation result of the initial velocity is (a) ⃗ = (20,20) and (b) ⃗ = (50,50) in the condition (1) and (3).
Fig.6 shows the trajectory movement of the initial velocity is (a) ⃗ = (20,20) and (b) ⃗ = (50,50) in the condition
(1) and (3) respectively. The trajectory of condition (1) is expanded by the ⃗ factor, on the other hand, proposed method
of condition (3) converges to the trajectory to the final position as soon as possible. Firstly, the axis residual error
occurs by the discretely setting the yaw direction to the final position (if the yaw direction set to the target direction is
executed in every computational cycle, the axis residual error equals to 0 anytime) and it is assumed that the axis
feedback realizes the minute trajectory correction against the translation component by the inertial motion. Generally, if
the nose direction would be locked to the final position anytime, the possibility of lost site of the final position would be
decreased and it is an important function of the yaw direction change. In addition, a new function of the yaw direction
change by the computer simulation was found in the limited conditions by this experiment even though it is a slight effect.
B. Result of experiment 2
Fig. 7 (a) Normal drone movement control that use the pitch and the roll simultaneously without yaw direction control (Ex. 2a). (b) Proposed roll and
pitch control with discrete yaw control method (Ex. 2b).
p
r
p
r
y
x
y
x
y
x
y
x
0
-10
-20
-30
-40
10 20 30 40-10
0 10 20 30 40-10
-10
-20
-30
-40
a)
b)
condition(1)
condition(3)
condition(3)
condition(1)

_________________________________________________________________________________________________
Fig.7a shows the result of normal drone movement control that use the pitch and roll simultaneously without yaw
direction control (Ex. 2a). The oscillating motion of and axis were measured around the initial position. S.D.
=24.9 cm and =15.0 cm were measured. Fig.7b shows the result of proposed roll and pitch control with discrete
yaw direction control (Ex. 2b). S.D. =10.1 cm and =13.5 cm were measured and the both S.D. are decreased
comparing with experiment 1. The reducing rate of the , are 10.1/24.9=40.6%, 13.5/15.0=90.0% realized
respectively. From the result of experiment 2a and 2b, the roll and pitch control with discrete yaw control method
improves the stability of the positional control and it was assumed that the above results were affected by the nose
direction (yaw) change as previously shown in the computer simulation experiment 1.
V. DISCUSSION
Generally, the yaw movement of the drone is not directly related to the position movement in the 3D space and it is
usually used to control the direction of the camera or the drone body. The mathematical or theoretical meanings of the
nose direction change have been studied, however, there are few discussion of theoretical analysis of the nose direction
change so far [7,31]. Actually, many UAV systems do not use the nose direction change to control the position in the vast
3D space for the ease of the operation. On the other hand, such as aircraft human board, birds and insects use the nose
direction change. The turning ways of the aircraft human board movement control is called as "horizontal turn". As one
assumption, there is a possibility that the proposed method is related to the horizontal turn control. Horizontal turn is
used to operate general airplane's turn direction in the air flow turbulence and unpredictable wind flow [30]. The basic
mechanism is to suppress the vibration and the change of the airplane's nose direction induced by the external
unpredictable wind flows by tilting the airplane's wing. The tilting airplane's wing changes the lift force to move the
airplane body to go to the turn direction and it is effective in changing and maintaining the airplane's nose direction
stably. Same with the airplane's horizontal turn control, it is considered that the drone's nose direction change (yaw
control) with tilting (roll control) make an effective role. It had been discussed by experimental data in previous our
study [4,5]. As an another hypothesis, there is a possibility to increase the controllability by adding degree of the freedom
of the yaw direction. It is, however, just a hypothesis and more precise analysis and experimental confirmation would be
necessary.
VI.CONCLUSION
In this paper, the discrete yaw control in the timing of the roll control method was confirmed by a simple computer
simulation and it was also confirmed by AR. Drone 4 rotor helicopter for automatic position stop. In general, 4 rotor
drone's rotational axis (yaw) is the degree of the freedom for controlling and only a few techniques have been studied for
the use of the degree of freedom. In this study, the computer simulation result shows that the discretely yaw direction
setting to the target direction affect the movement trajectory for the automatic fixed position movement and there is a
slight performance improvement comparing with normal x and y axis controllers method. In addition, the AR. Drone
experiment shows S.D. of x and y axis were reduced to 40.6% and 90.0% respectively for 30 sec automatic stop position
control by using the proposed control strategy. Proposed method have robustness for automatic stop position control and
it will be useful for inexpensive RC type 4-rotor controller having not good unstable wireless system, especially
accepting one command at a time communicating structure.
ACKNOWLEDGMENT
This work was supported by JSPS KAKENHI Grant Number 15K12598.
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