effect of discrete yaw direction setting for 4 roter helicopter control: computer simulation and ar....

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




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

푟(roll) and 푝(pitch) controllers with the discrete yaw direction setting condition and 푟 and 푝 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 푟 = 푥 and 푝 = 푦 (nose direction is fixed) independent one mass point model is developed,

푚푥̈ = −푘푥̇ + 1.0(0 − 푥) −퐾 푥 − 퐾 푥̇푚푦̈ = −푘푦̇ + 1.0(0− 푦)− 퐾 푦 −퐾 푦̇

(1)

where 푚, 푘, 퐾 and 퐾 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 푥 and 푦 axis 2D map (푟 = 푥 and 푝 = 푦 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, 푚푟̈ = −푘푟̇

푚푝̈ = −푘푝̇ + 1.0(0− 푝)−퐾 푝 −퐾 푝̇

(2)

where r, 푝 are the roll and pitch axis. The 푥, 푦 position (and velocity) on the 2D plane and the 푟, 푝 was always able to convert each other by using rotation matrix 푅(−휃). (푟, 푝) = 푅(−휃)(푥,푦). The direction of the nose 휃 was calculated from 푡푎푛휃 = 푥/푦. This direction change of the 휃 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 휃 will be calculated in each computer simulation cycle, there will be no residual error about the axis of 푟. In this case, the 푟 will be calculated as 푟 = 0 anytime.




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, (푟,푝) of Eq.2 was calculated on the 푥 and 푦 axis space, and the feedback force / velocity and the rotational factor depending on the nose direction 휃 was converted it to 푥 and 푦 axis factors by the rotation matrix 푅(−휃) 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 푉 , 푉 and the yaw (spin) control command 푉 are determined,

푉 = 훾 (160− 퐺 )푉 = 훾 (퐴 − 퐴) (3)

푉 = 훾 (휃 − 휃)

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

yaw50msec 50msec

(a) Normal roll and pitch movement

Time

Time

roll

pitch

roll

pitch yaw

roll

pitch

pitch50msec 50msec

roll

pitch

roll




where 훾 , 훾 and 퐴 , 퐴 are constant. 휃is the yaw angle, 휃 is the original yaw angle when the take-off, 훾 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 (퐺 ,퐺 ) and the area is 퐴, simple proportional feedback terms 훾 (160 −퐺 ) as right-left axis and훾 (퐴 − 퐴) as forward-backward axis where 퐴 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, 푉 and 푉 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, 푉 , 푉 and 푉 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 푉 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 (푥,푦) space. In the simulation, 푚 = 10,

푘 = 5 were set as constant values, and the feedback parameters 퐾 and 퐾 was calculated by LQR method. Computer simulation time step was ∆푡 = 0.01. From the equation of Eq.1, the evaluation function 퐽 was determined as below,

푥̇⃗ = 퐴푥⃗ + 퐵푢⃗퐽 = 푥⃗ 푄푥⃗ + 푢⃗ 푅푢⃗푑푡 (4)

where 퐴 is system matrix and it expresses Eq.1, 푥⃗ = (푥,푣) is state vector, 푢⃗ is controller input. By using the LQR method, the feedback parameter are calculated 퐾 ,퐾 = (1.32,1.47) as minimize the 퐽 . In this experiment, three experimental conditions were considered, (1) normal 4 rotor's roll and pitch controls in 2D space (Eq.1), (2) proposed 푟 (there is no control term about 푟 axis) and 푝 axis movement with discretely yaw direction setting (Eq.2), (3) 푟 (there is control term about 푟 axis) and 푝 axis movement with discretely yaw direction setting as Eq.5.

푚푟̈ = −푘푟̇ + 50.0(0− 푟)−퐾 푟 −퐾 푟̇

(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. 휎 ,휎 ) 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 훾 , 훾 are determined by continuously measured 30 sec flight control experiments (N=over 100) in order to minimize the S.D. 휎 ,휎 .

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 훾 is determined by continuously measured 30 sec flight control experiments (N=over 100) in order to minimize the S.D. 휎 ,휎 .

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 푟 (there is no control term about 푟 axis) and 푝 axis movement with discretely yaw direction setting (Eq.2). In this simulation, the initial velocity was set as 푣⃗ = (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 푝 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 푟 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 푥 = 푟 and 푦 = 푝 axis controls in 2D space (Eq.1), and (3) 푟 (there is control term about 푟 axis) and 푝 axis movement with discretely yaw direction setting as Eq.5. In this condition (3), a feedback gain 50.0 of 푟 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 퐸 = ∫ 푚푣 푑푡 are calculated 퐸 = 1200886 (condition(1)), 퐸 = 2363732 (condition(2)), 퐸 =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

py

y

x

x

Condition (1)

Condition (2)

+

+

10

10 20

-10

30 40

-20

-30

-40

Pitch and RollTwo PD controllers+Diccrete Yaw direction set


Final position (0,0)

X and Y-axisTwo 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

+

+




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 퐸 /퐸 is decreased lower than 1.0 when the initial velocity 푣⃗ 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) 푣⃗ = (20,20) and (b) 푣⃗ = (50,50) in the condition (1) and (3).

Fig.6 shows the trajectory movement of the initial velocity is (a) 푣⃗ = (20,20) and (b) 푣⃗ = (50,50) in the condition (1) and (3) respectively. The trajectory of condition (1) is expanded by the 푣⃗ factor, on the other hand, proposed method of condition (3) converges to the trajectory to the final position as soon as possible. Firstly, the 푟 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 푟 axis residual error equals to 0 anytime) and it is assumed that the 푟 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

-40Initial position (40,-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 푥 and 푦 axis were measured around the initial position. S.D. 휎 =24.9 cm and 휎 =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. 휎 =10.1 cm and 휎 =13.5 cm were measured and the both S.D. are decreased comparing with experiment 1. The reducing rate of the 휎 , 휎 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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