intelligent controller design for quad-rotor...

Research ArticleIntelligent Controller Design for Quad-Rotor Stabilization inPresence of Parameter Variations

Oualid Doukhi, Abdur Razzaq Fayjie, and Deok Jin Lee

Smart Autonomous System Laboratory, Kunsan National University, Jeollabuk, Republic of Korea

Correspondence should be addressed to Deok Jin Lee; [email protected]

Received 24 March 2017; Accepted 5 June 2017; Published 18 July 2017

Academic Editor: Guizhen Yu

Copyright © 2017 Oualid Doukhi et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Thepaper presents themathematicalmodel of a quadrotor unmanned aerial vehicle (UAV) and the design of robust Self-Tuning PIDcontroller based on fuzzy logic, which offers several advantages over certain types of conventional control methods, specifically indealing with highly nonlinear systems and parameter uncertainty.The proposed controller is applied to the inner and outer loop forheading and position trajectory tracking control to handle the external disturbances caused by the variation in the payload weightduring the flight period. The results of the numerical simulation using gazebo physics engine simulator and real-time experimentusingAR drone 2.0 test bed demonstrate the effectiveness of this intelligent control strategy which can improve the robustness of thewhole system and achieve accurate trajectory tracking control, comparing it with the conventional proportional integral derivative(PID).

1. Introduction

The payload variation has been playing an important role inthe field of transportation. The control for the unmannedaerial vehicles (UAV) becomes more challenging when itinvolves the payload variation over time. With the increasingpopularity of autonomous UAVs in the field of militaryand civilian such as surveillance, disaster monitoring, rescuemission, firefighting, and package delivery [1], where carryingand transporting external payload is essential to complete themission successfully, the safe and fast transportation of fragileor dangerous payloads by UAVs has become an interestingand important topic for the recent researchers in the field.Thecontrol of such UAVs requires the UAV stability and constantperformance with the changing payload weight during theflight. But these UAVs are inherently unstable, nonlinear, andmultivariable with complex and highly coupled dynamics [2].It is also very sensitive to unmolding dynamics, parametricuncertainties, and external disturbances. Thus, it makes thecontrol design for UAVs with payload variation very critical.The critical design of such controllers leads the field of controltheory to introduce new intelligent types of controllers [3].

Recent researches on the same field show different con-trol methodologies. Bouabdallah and Siegwart present the

real-time tests with an integral backstepping controller foran autonomous vehicle [4] and Boudjedir et al. mentionedan Adaptive Neural Control technique at the presence ofsinusoidal disturbance [5] which is tested only in a simulationenvironment. Even though there exists another controllerdepicting the adaptive nature using sliding mode, controlin the presence of external disturbances is described in [6],but it holds the simulation environment only. The work in[7] describes a Fuzzy PID for quadrotor with space fixed-point position control in a real-time flight test. Kim and Leeextend their control idea to nonlinear attitude stabilizationand tracking control for an autonomous hexarotor vehicle[8]. A new approach is taken in the field of control by thedesign of an Intelligent controller for unmanned quadrotor[9] which seems to be promising. But the discussed workslack the analysis of the payload weight variation effects andthe performance of the UAV in presence of such variationson the weight. This phenomenon is an integral part of theenvironments like mountains or unstructured areas for realUAV applications where UAV needs to drop the payloadgradually without landing. The most practical example toview the importance of such system is the application infirefighting.Other applications like package delivery andmaildelivery involve maximizing the number of delivery within

HindawiJournal of Advanced TransportationVolume 2017, Article ID 4683912, 10 pageshttps://doi.org/10.1155/2017/4683912

https://doi.org/10.1155/2017/4683912

2 Journal of Advanced Transportation

an area where package or mail drop from air helps to makedelivery easier. In hazard situations like fire control, suchsystem can be used as continuous spray ofwater or fire controlgases. The application also extends to the field of agriculturewith medicine spray in a crop field.

It is extremely painful that there exists a few successfulresearch focused on payload weight variation and its effecton the UAV performance. These studies include a fixedwing UAV that has been used for payload dropping mission[10]. It lacks the stationary flight capability which leads theresearcher to focus onVertical Take-Off andLanding (VTOL)vehicles such as quadrotor UAV which offers the ability tofly in any direction and even to stop their movement stayinghovering above a specific target.

In [11] a robust adaptive control is designed for quadrotorpayload add and drop applications in simulation environ-ment. Another research presented a payload drop applicationof unmanned quadrotor helicopter using Gain-ScheduledPID and model predictive control techniques in real-timeexperiment [12] but the work analyzes the effect only inaltitude. Muhammad presented the simulation work with thePID controller for payload drop of a quadrotor UAV [13]. Tohandle such complex UAV systems to unload package or todrop payload without landing, a robust flight controller isneeded which must be intelligent enough to keep the UAVstable in different circumstances. The intelligent controllermust adapt itself in a short duration of time with the suddenchanges in the payloadwhich enable theUAV to be stabilized.The design of such controllers aims to avoid the damageof the system and guarantees the safety operation for thesurrounding environment and people present.

This work studies the effects of payload weight variationand analyzes the behavior of the UAV in a 3-dimensionalspace (𝑥, 𝑦, 𝑧) along with the attitude (roll, pitch, and yawangles) instead of the single axis 𝑧 (altitude) considerationof most of the present works. The work contributes to thedesign of a robust intelligent self-tuning PID controller basedon fuzzy logic to ensure the trajectory tracking performancein the presence of payload weight variations. The proposedcontrol idea is tested both in the simulation as well as in real-time environment.

The paper introduces the existing research works whichare similar to the topic of the paper, the pros and cons ofsuch control ideas, the problem definitions, and the proposedidea in Section 1. The next part describes the dynamic modelof the quadrotor in Section 2 and the controls developmentis presented in Section 3. Section 4 presents the simulationenvironment and asymptotic tracking results obtained inthat environment which is further extended to real-timeenvironment and the real flight test results are presented inSection 5. Finally, the paper concludes with the promisingresult and uses of proposed idea in near future to handlepayload variation on a UAV effectively.

2. Description and Dynamics of the Quadrotor

The work uses a quadrotor, AR Drone 2.0, that was unveiledat CES Las Vegas 2012. It comes with 720p camera andthe onboard sensors (like ultrasonic altimeter and 3-axis

F1

F2

F3

F4

X Y

Z

Rm

Rb𝜃𝜙

𝜓

x y

z

Figure 1: Quadrotor configuration frame scheme with body-fixedand inertia frames.

gyroscope, along with a 3-axis accelerometer and magne-tometer) which allow the quadrotor for greater control. Thewifi communication with 802.11n standard provides bettercommunication with the ground station. The rotors arepowered by 15 watts and brushless motors are powered by an11.1 Volt lithiumpolymer battery.This provides approximately12 minutes of flight time at a speed of 5m/s (11mph). Inorder to design a flight controller, one must first understandthe quadrotormovements, its dynamics, and consequently itsdynamic equations. This understanding is necessary not justfor the design of the controller, but also to ensure that thesimulations of the vehicle behavior are closer to the realitywhen the command is applied.

The quadrotor is classified in the category of the mostcomplex flying systems given the number of physical effectsthat affect its dynamics, namely, aerodynamic effects, gravity,gyroscopic effects, friction, and moment of inertia. Theschematic configuration of a quadrotor we adopted in thisstudy is shown in Figure 1. Four rotors are usually placedat the ends of two orthogonal axes. The rotation for twopropellers needed to be in a clockwise direction while theother two are in a counterclockwise direction. The modelingof flying robots is a delicate task as the dynamics of thesystem are strongly nonlinear and fully coupled. In order tounderstand the model dynamics developed in this work, theworking hypotheses are given below [14]:

(1) The structure of the quadrotor is assumed to be rigidand symmetric.

(2) The propellers are rigid.(3) Thrust and drag forces are proportional to the square

of the rotors speed.(4) The center of mass and origin of the coordinate

system related to the quadrotor structure coincide.

To evaluate the mathematical model of the quadrotor, weuse two reference frames, a fixed frame linked to the groundcalled inertial frameRb and anothermobile frameRm with its

Journal of Advanced Transportation 3

Table 1: Quadrotor parameters.

Symbol Quantity Value𝑘1 Thrust factor 8.048 × 10−6N⋅S2𝑘2 Drag coefficient 2.43 × 10−7 N⋅m⋅s2𝐼𝑥𝑥 Moment of inertia along 𝑥 direction 0.002237568 kg⋅m2𝐼𝑦𝑦 Moment of inertia along 𝑦 direction 0.002985236 kg⋅m2𝐼𝑧𝑧 Moment of inertia along 𝑧 direction 0.00480374 kg⋅m2𝑙 Center distance between the gravity of quadrotor and each propeller 0.1785m𝑚 Total mass of the quadrotor 0.450 kg𝐽𝑟 Rotor inertia 2.029585 × 10−5 kg⋅m2𝑔 Gravity 9.81m/s2

origin at the center of mass of the quadrotor. By varying therotor speeds, the thrust forces Fi=1⋅⋅⋅ 4 can be changed whichresults in the six principal motions as follows:

(1) Roll rotation 𝜙 followed by translation along 𝑂𝑦(2) Pitch rotation 𝜃 followed by translation along 𝑂𝑥(3) Yaw rotation 𝜓(4) Translation along 𝑂𝑧 (the altitude).

Let 𝑞 = [𝑃, 𝑟]𝑇 ∈ 𝑅6 be the generalized coordinates for thequadrotor where 𝑃 = [𝑥, 𝑦, 𝑧]𝑇 denotes the absolute positionin the inertial frame Rb, and 𝑟 = [𝜙, 𝜃, 𝜓]𝑇 is the vectorconsists of three Euler angles 𝜙, 𝜃 and 𝜓. 𝜗 = [Ω1, Ω2, Ω3]𝑇denotes the vector containing angular velocities of roll, pitch,and yaw with respect to the body-fixed frame Rm. Therotation matrix from body frame to earth frame can beobtained as follows:

𝑅 = [[[

𝑐𝜙𝑐𝜃 𝑠𝜙𝑠𝜃𝑐𝜓 − 𝑠𝜓𝑐𝜙 𝑐𝜙𝑠𝜃𝑐𝜓 + 𝑠𝜓𝑠𝜙𝑠𝜙𝑐𝜃 𝑠𝜙𝑠𝜃𝑠𝜓 + 𝑐𝜓𝑐𝜃 𝑐𝜙𝑠𝜃𝑠𝜓 − 𝑠𝜙𝑐𝜓−𝑠𝜃 𝑠𝜙𝑐𝜃 𝑐𝜙𝑐𝜃

]]], (1)

where 𝑠(⋅) and 𝑐(⋅) are abbreviations for sin(⋅) and cos(⋅)functions, respectively.

Using the Newton-Euler formulation, the rotational andtranslational dynamics are written in the following equationwith the corresponding parameters presented in Table 1:

�̈� = (𝑐𝜙𝑠𝜃𝑐𝜓 + 𝑠𝜙𝑠𝜓) 1𝑚𝑈1,̈𝑦 = (𝑐𝜙𝑠𝜃𝑠𝜓 − 𝑠𝜙𝑐𝜓) 1𝑚𝑈1,

�̈� = −𝑔 + (𝑐𝜙𝑐𝜃) 1𝑚𝑈1,̈𝜙 = ̇𝜃�̇� (𝐼𝑦𝑦 − 𝐼𝑧z𝐼𝑥𝑥 ) − 𝐽𝑟𝐼𝑥𝑥 ̇𝜃Ω𝑑 + 1𝐼𝑥𝑥𝑈2,̈𝜃 = ̇𝜙�̇� (𝐼𝑧𝑧 − 𝐼𝑥𝑥𝐼𝑦𝑦 ) + 𝐽𝑟𝐼𝑦𝑦 ̇𝜙Ω𝑑 + 1𝐼𝑦𝑦𝑈3,

�̈� = ̇𝜃 ̇𝜙 (𝐼𝑥𝑥 − 𝐼𝑦𝑦𝐼𝑧𝑧 ) + 1𝐼𝑧𝑧𝑈4,

(2)

altitudecontroller

PID

altitudecontroller

PID

Quadrotordynamics

PIDposition

controller

𝜃des

𝜙des

𝜓des

xdes

ydes

zdes

z

u1

u2

u3

u4

[x, y]

[𝜃, 𝜙, 𝜓]

Figure 2: PID controller structure.

where

Ω𝑑 = 𝜔2 + 𝜔4 − 𝜔1 − 𝜔4 (3)

and 𝑈𝑖 (𝑖 = 1, 2, 3, 4) is the virtual control input defined asfollows:

[[[[[[

𝑈1𝑈2𝑈3𝑈4

]]]]]]

=[[[[[[

𝐾1 𝐾1 𝐾1 𝐾10 −𝑙𝐾1 0 𝑙𝐾1

−𝑙𝐾1 0 𝑙𝐾1 0𝐾2 −𝐾2 𝐾2 −𝐾2

]]]]]]

[[[[[[[

𝜔21𝜔22𝜔23𝜔24

]]]]]]]. (4)

3. Control Development

The work develops a self-tuning PID controller for positionand heading trajectory tracking control to deal with the massvariance of the quadrotor when the payload is graduallychanged.

3.1. Design of PID Controller. The proportional integralderivative (PID) controller is designed to ensure the tra-jectory tracking capability of {𝜓} and {𝑥, 𝑦, 𝑧} along thedesired yaw angle trajectory {𝜓𝑑} and {𝑥𝑑, 𝑦𝑑, 𝑧𝑑, } positionas illustrated in Figure 2.


The based control laws of PID controller for position andheading take the following form:

𝑈4 = 𝐾𝑝𝜓 ⋅ 𝑒𝜓 + 𝐾𝑑𝜓 ⋅ ̇𝑒𝜓 + 𝐾𝑖𝜓 ⋅ ∫ 𝑒𝜓 ⋅ 𝑑𝑡,𝑈1𝑥 = 𝐾𝑝𝑥 ⋅ 𝑒𝑥 + 𝐾𝑑𝑥 ⋅ ̇𝑒𝑥 + 𝐾𝑖𝑥 ⋅ ∫ 𝑒𝑥 ⋅ 𝑑𝑡,𝑈1𝑦 = 𝐾𝑝𝑦 ⋅ 𝑒𝑦 + 𝐾𝑑𝑦 ⋅ ̇𝑒𝑦 + 𝐾𝑖𝑦 ⋅ ∫ 𝑒𝑦 ⋅ 𝑑𝑡,𝑈1 = 𝐾𝑝𝑧 ⋅ 𝑒𝑧 + 𝐾𝑑𝑧 ⋅ ̇𝑒𝑧 + 𝐾𝑖𝑧 ⋅ ∫ 𝑒𝑧 ⋅ 𝑑𝑡,

(5)

where𝑒𝜓 = 𝜓des − 𝜓,𝑒𝑥 = 𝑥des − 𝑥,𝑒𝑦 = 𝑦des − 𝑦,𝑒𝑧 = 𝑧des − 𝑧

(6)

and 𝐾𝑝., 𝐾𝑑., 𝐾𝑖. are parameters tuned without payloadonboard. 𝑈1𝑥 and 𝑈1𝑦 are virtual control inputs used togenerate the desired roll 𝜙𝑑 and pitch 𝜃𝑑 angles as illustratedin Figure 2:

𝜙𝑑 = 1𝑔 (𝑈1𝑥 sin𝜓des − 𝑈1𝑦 cos𝜓des) ,𝜃𝑑 = 1𝑔 (𝑈1𝑥 cos𝜓des − 𝑈1𝑦 sin𝜓des) .

(7)

3.2. Fuzzy Logic for Self-Tuning of PID. Fuzzy logic is a toolfor reasoning propositions that can be manipulated withmathematical precepts. It has been suggested by researchersthat measurements, process modeling, and control can neverbe exact for real and complex processes. Also, there are uncer-tainties such as incompleteness, randomness, and ignoranceof data in the process model [15].

The seminal work of Zadeh introduced the concept offuzzy logic to model human reasoning from imprecise andincomplete information by giving definitions to vague termsand allowing construction of a rule base (Zadeh, 1965, 1973).Fuzzy logic can incorporate human experiential knowledgeand give it an engineering flavor to model and control suchill-defined systems with nonlinearity and uncertainty. Thefuzzy logic methodology usually deals with reasoning andinference on a higher level, such as semantic or linguistic.Fuzzy logic requires knowledge in order to reason which isprovided by a person who knows the process or machine(the expert). One of the most important components of fuzzylogic is membership function. Membership functions groupinput data into sets, such as temperatures that are too cold,motor speeds that are acceptable, and distances that are toofar. The fuzzy controller (see Figure 4) assigns the input dataa grade between 0 and 1 based on how well it fits into eachmembership function [16].

Mathematically a fuzzy set is described as a set 𝐴 in 𝑋.The set 𝐴 is characterized by a membership function 𝜇𝐴(𝑥)

associated with each point in 𝑥, a real number in the interval[0, 1], with the values of 𝜇𝐴(𝑥) at 𝑥 representing the grade ofmembership of 𝑥 in 𝐴.

The function that characterizes the fuzziness of a fuzzy set𝐴 in 𝑋, which associates each point in 𝑋 with a real numberin the interval [0, 1], is known as membership function.

Fuzzification and Defuzzification. The process that allowsconverting a numeric value into a fuzzy input is calledfuzzification.

Defuzzification is the reverse process of fuzzification.Mathematically, the defuzzification of a fuzzy set is theprocess of conversion of a fuzzy quantity into a crisp value.This is necessary when a crisp value is to be provided from afuzzy system to the user.

InferenceMechanism. Inference is the process of formulating anonlinear mapping from a given input space to output space.The mapping then provides a basis from which decisionscan be made. The process of fuzzy inference involves all themembership functions, operators, and if-then rules [16].

3.3. Self-Tuning of the Designed PID Controller. TraditionalPID designed in Section 3.1 comes with a lot of limitations.For example, its three parameters are tuned for a specificoperating condition such as with constant payload or withoutpayload. Therefore, such mass uncertainty may significantlyaffect the fly control performance. To solve this problemof designed PID, a self-tuning mechanism based on fuzzylogic is developed which has the capability of adjustingthe parameters of designed PID online which enables thepreviously developed PID to handle the sudden or gradualchange of the payload weight. We know that the weightchange practically has a big and inevitable effect not only inthe altitude stability of the quadrotor but also in 𝑥-𝑦 position.More specifically, in the hovering condition, a quadrotor withits onboard load is seen as a heavy body [13], thus requiringmore upward thrust to attain the desired altitude. Once thepayload is dropped or gradually changed, the quadrotor willreach a higher altitude, thus, producing overshooting onits desired height. The self-tuning intelligent PID controllermustmonitor this overshoot and quickly compensates for thisand return the quadrotor to its desired altitude by loweringthe upward thrust by slowing the speed of the brushless DCmotor (BLDC) or in the opposite way when the payload isadded to compensate the undershoot.

The self-tuning mechanism is designed for automatic-tuning of each of PID controller parameters so that thesystem becomes robust to the mass uncertainty. The inputsto the fuzzy mechanism are error and change in the error. Itproduces the output of the PID parameters “𝐾𝑝”, “𝐾𝑖”, “𝐾𝑑”as presented in Figure 3.

3.4.Design ofMembership Function (MF). Theworkdesignedfive triangular membership functions nl, ns, ze, ps, andpl which represent negative large, negative simple, zero,positive simple, and positive large for each input variable (seeFigure 5) and seven triangular membership functions pvs,


−

−

−

−

+

+

+

+Desiredposition

Desiredheading

Desiredaltitude

Guidance

Positioncontroller

Attitudecontroller

Altitudecontroller

Fuzzy logicmechanism 1

Scalingfactor


Scalingfactor


Scalingfactor

e

e

e

Quadrotor controlallocation Quadrotor dynamics

𝜓des

d/dt

d/dt

d/dtzdes z

𝜓

u1

u2

u3

u4

[x, y]

[𝜃, 𝜙]

w1

w2

w3

w4

[xdes, ydes]

[𝜃des, 𝜙des]

Figure 3: Overall structure for the developed control mechanism.

Rule Base

Fuzzification

Inference

DefuzzificationCrispinputs

Crispoutput

Rule base

Fuzzification Defuzzification

Figure 4: Fuzzy structure.

ps, pms, pm, pml, pl, and pvl for each output variables (seeFigures 6–8). Based on experience, 25 fuzzy rules are definedfor all possible combinations of the inputs. The “centroidmethod” is used for defuzzification. The three-dimensionalsurface of chosen fuzzy rules for the controller design isshown in Figures 9–11. Fuzzy controller is made of “if-then”rules.The selected rules for the quadrotor control process areshown in Tables 2–4. The equation for the control algorithmis given as

𝑈 (𝑡) = 𝑈 (𝑡)SP + 𝑈 (𝑡)Sd + 𝑈 (𝑡)SI , (8)

where the control signals self-tuning proportional, self-tuning Integral, and self-tuning derivative are

𝑈 (𝑡)SP = 𝑆𝑘𝑃𝐹𝑃𝑒 (𝑡) ,𝑈 (𝑡)Sd = 𝑆𝑘𝑑𝐹𝑑𝑒 (𝑡) ,𝑈 (𝑡)SI = 𝑆𝑘𝑖𝐹𝑖𝑒 (𝑡) ,

(9)

nl ns ze ps pl

0

0.2

0.4

0.6

0.8

1

Deg

ree o

f mem

bers

hip

−5−10 5 100Error/error rate

Figure 5: Membership functions designed for the inputs.

where 𝐹𝑃, 𝐹𝑑 and 𝐹𝑖 are scaling factors; hence, three fuzzycontroller outputs are

𝑆𝑘𝑝 = 𝑓𝑝 (𝑒, 𝑑𝑒𝑝𝑑𝑡 ) ,

𝑆𝑘𝑑 = 𝑓𝑑 (𝑒, 𝑑𝑒𝑑𝑑𝑡 ) ,

𝑆𝑘𝑖 = 𝑓𝑖 (𝑒, 𝑑𝑒𝑖𝑑𝑡 ) .

(10)


pvs ps pms pm pml pl pvl

0

0.2

0.4

0.6

0.8

1

Deg

ree o

f mem

bers

hip

1 1.5 2 2.5 30.5Kp

Figure 6: Membership functions designed for the output 𝑘𝑝.


0

0.2

0.4

0.6

0.8

1

Deg

ree o

f mem

bers

hip

1 1.5 2 2.5 30.5Kd

Figure 7: Membership functions designed for the output 𝑘𝑑.


0

0.2

0.4

0.6

0.8

1

Deg

ree o

f mem

bers

hip

1 1.5 2 2.50.5Ki

Figure 8: Membership functions designed for the output 𝑘𝑖.

05

100

510

ErrorError rate −5

−10

−5

−10

Kd

2.5

2

1.5

1

Figure 9: Error and derivative error for the output 𝑘𝑑.

05

100

510

Error

Error rate −5−10

−5−10

Ki

1.3

1.2

1.1

1

0.9

0.8

0.7

Figure 10: Error and derivative error for the output 𝑘𝑖.

05

100

510

ErrorError rate

Kp

2.6

2.4

2.2

2

1.8

1.6

−5−10

−5−10

Figure 11: Error and derivative error for the output 𝑘𝑝.

Therefore, the self-tuning control input can be written as

𝑈 (𝑡) = 𝑓𝑝 (𝑒, 𝑑𝑒𝑝𝑑𝑡 )𝐹𝑃𝑒 (𝑡) + 𝑓𝑑 (𝑒, 𝑑𝑒𝑑𝑑𝑡 )𝐹𝑑𝑒 (𝑡)+ 𝑓𝑖 (𝑒, 𝑑𝑒𝑖𝑑𝑡 )𝐹𝑖𝑒 (𝑡) .

(11)


Subscriber

The proposed control algorithm

Publisher

Sensors measurement (position + orientation)

Motor speed command

Master

Quadrotor system

Figure 12: Simulation environment configuration.

DesiredReal

DesiredPIDSelf-tuning

10 20 30 40 50 600Time (s)

DesiredReal

10 20 30 40 50 600Time (s)

10 20 30 40 50 600Time (s)

−20

020

𝜙(d

eg)

−20

020

𝜃(d

eg)

−2

02

𝜓(d

eg)

Figure 13: Response curves of quadrotor UAV attitude (𝜙, 𝜃, 𝜓).

4. Simulation Setup and Results

Simulations have been conducted using robot operatingsystem (ROS) interfaced with Matlab/Simulink and gazebophysic engine simulator as illustrated in Figure 12, in orderto verify the efficiency of the proposed self-tuning PIDcontroller for heading and position control and benchmarkwith a regular PID.


10 20 30 40 50 600Time (s)


10 20 30 40 50 600Time (s)


10 20 30 40 50 600Time (s)

0

1

2

3

X(m

)

0123

Y(m

)

0

1

2

Z(m

)

Figure 14: Response curves of quadrotor UAV position (𝑥, 𝑦, 𝑧).

01

23

01

230

0.5


Z(m

)

Y (m)X (m)

−1−1

1.5

1

Figure 15: Three-dimensional response curves of quadrotor UAVposition (𝑥, 𝑦, 𝑧).

Firstly PID parameters are tuned in normal case quadro-tor without payload; from Figures 13–15, we can see that theproposed self-tuning controller gives us very good result interms of trajectory tracking performances. In the next sectionto demonstrate the effectiveness of the proposed controlleragainst adverse condition, like payload weight variation, we


Ctrl_Input

Measurements

Ground station

Place dedicated for external payload

Figure 16: Experimental environment setup.

Table 2: Fuzzy rule for 𝑘𝑝.de/e NL NS ZE PS PLNL PVL PVL PVL PVL PVLNS PML PML PML PL PVLZE PVS PVS PS PMS PMSPS PML PML PML PL PVLPL PVL PVL PVL PVL PVL

Desired

PIDSelf-tuning

10 20 30 40 500Time (s)

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

X(m

)

Figure 17: Quadrotor 𝑥 position under payload with variableweight.

need to do some experimental tests; we change the weightgradually and then we analyze the effect of this change inthe position tracking performance and we compare it withconventional PID.

5. Experiment Setup and Results

In this section to validate the position and heading trajectorytracking performance experiment tests (the experimental

Desired

PIDSelf-tuning

5 10 15 20 25 30 35 40 45 500Time (s)

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Y(m

)

Figure 18: Quadrotor 𝑌 position under payload with variableweight.

video is available at the URL https://www.youtube.com/channel/UC6eedfqCWGpj1YqANGdzfIg) are implementedon the Ardrone 2.0 testbed as presented in Figure 16. Firstlythe quadrotor is on the ground with initial payload of20 g onboard; after takeoff the quadrotor was ordered tofollow square trajectory, and then during the fly maneuverwe change gradually the weight by adding external loadtill we reach the maximum load supported by our systemwhich is about 60 g; from Figures 17–21 we can see thatthe the self-tuning PID algorithm based on fuzzy logic thatautomatically adjust the parameter gain within rage 𝑘𝑝, 𝐾𝑑 ∈[0.4 3], 𝐾𝑖 ∈ [0.1 2.5] is able to make the quadrotorreach the desired trajectory, without overshoot and with

https://www.youtube.com/channel/UC6eedfqCWGpj1YqANGdzfIg

https://www.youtube.com/channel/UC6eedfqCWGpj1YqANGdzfIg


Table 3: Fuzzy rule for 𝑘𝑑.de/e NL NS ZE PS PLNL PVS PML PM PL PVLNS PMS PML PL PVL PVLZE PM PL PL PVL PVLPS PML PVL PVL PVL PVLPL PVL PVL PVL PVL PVL

Table 4: Fuzzy rule for 𝑘𝑖.de/e NL NS ZE PS PLNL PM PM PM PM PMNS PMS PMS PMS PMS PMSZE PS PS PVS PS PSPS PMS PMS PMS PMS PMSPL PM PM PM PM PM

Desired

PIDSelf-tuning

10 20 30 40 500Time (s)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Z(m

)

Figure 19: Quadrotor 𝑧 position under payload with variableweight.

slightly oscillatingmotion compared to the conventional PIDcontroller system which presents about 19 cm of overshootin the altitude and position, because the control parameters𝑘𝑝 = 1.5 𝐾𝑑 = 0.8 𝐾𝑖 = 0.3 are tuned in the initial case withconstant payload.

6. Conclusion

This paper presents a self-tuning PID control algorithm toachieve quadrotor aerial vehicle’s performancewith a variablepayload. The comparison between the conventional PID andself-tuning PID base on fuzzy logic has been conducted; theresult shows that both control methodologies are acceptablein the case of no variation in the payload weight, experi-mental results demonstrate the superiority of the proposedself-tuning PID comparing to the PID in case of variable

DesiredReal

DesiredSelf-tuningPID

5 10 15 20 25 30 35 40 45 500Time (s)

DesiredReal

5 10 15 20 25 30 35 40 45 500Time (s)

5 10 15 20 25 30 35 40 45 500Time (s)

150160170180190

Yaw

(deg

)−10

010

Roll

(deg

)

−10

010

Pitc

h (d

eg)

Figure 20: Response curves of quadrotor UAV attitude (𝜙, 𝜃, 𝜓).payload weight, and it provides good performance in termsof disturbance reduction and trajectory tracking.

Conflicts of Interest

The received funding did not lead to any conflicts of interestregarding the publication of this manuscript.

Acknowledgments

This research was supported by Unmanned VehiclesAdvanced Core Technology Research and Development


1.21

0.80.6

0.40.2

0−0.2

1.210.8

0.60.4

0.20−0.2

Y (m)X (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Z(m

)

DesiredSelf-tuningPID

Figure 21: Three-dimensional response curves of quadrotor UAVposition (𝑥, 𝑦, 𝑧) with variable payload weight.

Program through theNational Research Foundation of Korea(NRF) and Unmanned Vehicle Advanced Research Center(UVARC) funded by theMinistry of Science, ICT and FuturePlanning, Republic of Korea (NRF-2016M1B3A1A01937245),and was also supported by the Human Resource TrainingProgram for Regional Innovation and Creativity through theMinistry of Education and National Research Foundation ofKorea (no. 2014H1C1A10166733).

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