This document is a thesis submitted by Kalpitkumar Thakar to the University of Wollongong for the degree of Master of Professional Engineering in Electrical Engineering. The thesis investigates controlling a 2 DOF robotic arm using fuzzy logic control. The robotic arm has 2 revolute joints connected by cylindrical rods. The arm is interfaced to a PC through USB and can operate in position, velocity and torque modes. The thesis aims to model the arm, develop a fuzzy logic controller to control the 2 DOF motion, and test the controller in simulation and experiments. Literature on robotic arm control and fuzzy logic control is reviewed. The kinematics and dynamics of the 2 DOF arm are also derived and explained.

1. 1
Trajectory control of a DYNAMIXEL PRO Make H42-20-S300-R
model (2 DOF Robot arm) using Fuzzy logic control (FLC)
A thesis submitted in partial fulfilment of the
requirements for the award of the degree
Masters of Professional Engineering
(Major in Electrical Engineering)
From
University of Wollongong
By
Kalpitkumar Thakar (4709354)
School of Electrical, Computer and
Telecommunications Engineering
November, 2016
Supervisor: Prof. Fazel Naghdy

2. 2
Abstract
Control Engineering is a vast and fascinating field of Engineering, but at the same time, many of
control engineering students are having different sorts of problems in understanding the practical
aspects of control techniques for a robotic arm. In the era of inventions, there are many control
techniques are developed to control a robotic arm. In this particular project, I will control and
monitor the results of DYNAMIXEL PRO Make H42-20-S300-R model (2 DOF Robot arm) using
MATLAB and FLC (Fuzzy logic control) because FLC enables design engineers to model very
complex systems more swiftly and effectively than traditional approaches and methods. The aim
of this project is to help control engineering students to understand how to control robotic arm
using MATLAB and FLC (fuzzy logic control). The DYNAMIXEL PRO Make H42-20-S300-R (2-DOF
robot arm) has 2 revolute joints, and both joints are connected to each other with cylindrical rods
in order to make 2-DOF robot arm. Both revolute joints revolve with the help of the connected
servo system and move in the same plane (trajectory).
Here, the DYNAMIXEL PRO Make H42-20-S300-R (2-DOF robot arm) has been controlled using
different control environments: the first control technique was done by using “ROBOPLUS
(Dynamixel Wizard)” standard software, which is created by hardware manufacturer. The second
control technique is “MATLAB” software, and the third and final control technique approach was
done using “FLC (fuzzy logic controller)”.
The first control environment was successfully done by “ROBOPLUS (Dynamixel Wizard)”, the
results of this control technique showed, it was not very friendly for users and most of the time, it
needed modification in the program, which was not an easy task for any user to include feedback
and further develop PID control due to aforementioned reason a “MATLAB” based control
technique was developed, and it (2-DOF robot arm) connected with “MATLAB” software. In this
case, experimental results showed that the goal positions and the goal accelerations of this Robot
arm could be controlled, and most importantly the goal accelerations of the 2-DOF robot arm can
be controlled while changing its goal position.
In the end, I will explain about future recommendations for the possible use of integrating with
various other softwares such as LABVIEW, C, C++, JAVA, Visual Basic, Python and so on.

3. 3
Acknowledgement
I would like to express my sincere thank to Professor Fazel Naghdy, My supervisor, who gave me
this chance to do this project. He has been very generous with guidance, constant support and
valuable time throughout this task.
Last, but not the least, I am also grateful to all, who have helped, motivated and encouraged me to
complete this project.

4. 4
Statement of Originality
I, Kalpitkumar Thakar, declare that this thesis, submitted as part of the requirements for the award
of Master of Engineering, in the School of Electrical, Computer and Telecommunications
Engineering, University of Wollongong, is wholly my own work unless otherwise referenced or
acknowledged. The document has not been submitted for qualifications or assessment at any other
academic institution. As author of this thesis, I also hereby grant, subject to any prior confidentially
agreements, SECTE permission, to use, distribute, publish, exhibit, record, digitize broadcast,
reproduce and archive this work for the purposes of further research and teaching.
Signature:
Name: Kalpitkumar Thakar
Student ID: 4709354
Date:

5. 5
Table of content
Topic Pg. No.
Abstract 2
Acknowledgement 4
Statement of Originality 5
Table of Content 6
List of Figures 8
List of Tables 9
Notation 10
Chapter – 1 Introduction
1.1 Overview
1.2 Importance of Project
1.3 Objectives
11
Chapter – 2
2.1 Literature Review
2.2 Kinematics & dynamics of a 2-DOF robot arm
13
Chapter – 3 Experimental design
3.1 Hardware
3.2 Software
3.3 Block Diagram & specification
3.4 Connection & Set up for experiment
3.5 Operating Modes of 2-DOF robot arm
19
Chapter – 4 Modelling
4.1 MATLAB modelling
4.2 Simulink modelling
29

6. 6
4.3 FLC Modelling
Chapter – 5 Results & Conclusion
5.1 Results
5.2 Conclusion
5.3 Future work
43
References 46
Appendix A 47
Appendix B 50
Appendix C 51

7. 7
List of Figures
Topic Pg. No.
Figure 2.1: Estimated worldwide annual supply of industrial robots 13
Figure 2.2: Overview of Control Structure of 2DOF robotic arm 15
Figure 2.3: Schematic representation of a 2-DOF robot arm manipulator 16
Figure 3.1: DYNAMIXEL PRO Make H42-20-S300-R model 19
Figure 3.2: Dynamixel Pro Power supply circuit board 19
Figure 3.3: Dynamixel Pro USB2DXL dongle 20
Figure 3.4: Lists of softwares can be used to control dynamixel Pro 21
Figure 3.5: RoboPlus software 21
Figure 3.6: Block representation of Fuzzy Logic Controller 22
Figure 3.7: Block diagram of the project 24
Figure 3.8: Two Dynamixel pro servo motors connection with USB dongle 25
Figure 3.9: 4-pin connection and servomotor connection points 26
Figure 3.10: Dynamixel PRO goal angle and goal position relation 27
Figure 4.1: Figure 4.1: Dynamixel Wizard window for COM Port connection 28
Figure 4.2: Dynamixel Wizard Parameter Window 29
Figure 4.3: Result of the servomotor-1 to an angular position of 1 radian 31
Figure 4.4: Result of the servo motor-2 to an angular position of 1 radian 32
Figure 4.5: Simulink model for each servo individually 33
Figure 4.5.1: Function Block Parameters 33
Figure 4.6: Simulink model for both servos at a same time 34

8. 8
Figure 4.6.1: Function Block Parameters 35
Figure 4.6.2: Function Block Parameters 35
Figure 4.7: Fuzzy Logic Schematic for the 2-DOF robot arm control system 36
Figure 5.1: Result of the servo motor-1 at -1 and servo motor-2 at -1 42
Figure 5.2: Result of the servo motor-1 at -0.5 and servo motor-2 at -0.5 43
Figure 5.3: Result of the servo motor-1 at 0 and servo motor-2 at 0 43
Figure 5.4: Result of the servo motor-1 at 0.5 and servo motor-2 at 0.5 44
Figure 5.5: Result of the servo motor-1 at 1 and servo motor-2 at 1 44
Figure 5.6: Dynamixel Pro control methods 45

9. 9
List of Tables
Topic Pg. No.
Table 3.1: Table for Fuzzy logic mathematical operations 23
Table 3.2: Specification table of Dynamixel pro 24
Table 3.3: Table for Fuzzy logic operation modes 27
Table 4.1: FLC computational steps 36

10. 10
Notation
Symbols
I – Current
V – Voltage
1ϕ – Single phase
θ – Displacement
g – Gravity
τ – Torque
μ – Membership function
Abbreviations
DOF – Degree of Freedom
Dynamixel Pro – Dynamixel make H42-20-S300-R (2-DOF robot arm)
PC – Personal Computer
FLC – Fuzzy Logic Control
USB2DXL – USB to Dynamixel PRO Dongle
Goal Position – Angular position
Goal Acceleration – Speed/Velocity
AC – Alternating Current
DC – Direct Current
RPM – Rotations per minute
PID – Proportional Integral derivative
PD - Proportional derivative
IJC – Independent Joint Control

11. 11
Chapter 1 - Introduction
1.1 Overview
The aim of the project is to study, control and monitor the results of the given 2-DOF Robot arm
using MATLAB and FLC. The robot has 2 revolute joints, and both joints are connected to each other
with cylindrical rods in order to make 2-DOF robot arm. Both revolute joints revolve with the help
of the connected servo system and move in the same plane (trajectory). The robot arm is interfaced
to a PC through USB2DXL, a Serial communication (RS 485). The robot can operate in three modes,
which are Position mode, Velocity mode, and torque mode. In this project, the robot arm will be
controlled in each mode individually. For example, I will run the given robot arm at various
velocities in this mode robot arm can rotate at desired velocity and I will check its results. Similarly,
the given robot arm will run in various joint modes, which controls velocity and the positions of the
robot arm. In this given robot, the position ranges between 180 degrees (151875) to -180 degrees (-
151875) and the joint mode results will be monitored. The robot arm can move to the desired
position at the desired velocity. Finally, I will operate a robot arm at various torque. This mode can
control the output torque and the performance of the robot arm will be measured.
1.2 Importance of Project
The project is very important in the field of control engineering and it will give the idea about
applying FLC to the given robot arm. The project will also cover various aspects of robot arm
control with a fuzzy logic control such as velocity control, torque control and position control of a
robot arm.
Today, many industries accept and welcome robot arm technologies to increase productivity and
accuracy and meet their desired requirements. Hence, programming the robot arm with FLC is
very important because this is one of the unique and effective ways to control of the given robot
arm. This project will help control engineering students to gain knowledge about robot arm
control with FLC.

12. 12
1.3 Objectives
The main aim of the project is to study and understand the control of the 2-DOF robot arm using
FLC. The following objectives will be pursued:
[1] A better understanding of the application of the FLC to the given robot arm will be developed.
[2] The robot arm will be analytically modelled,
[3] A FLC will be developed to control the 2 - DOF planar robot.

13. 13
Chapter 2 – Literature Review
2.1 Literature Review
Flexible Automation is playing a significant role in the modern manufacturing industry around the
globe. Especially, robotic arm technology has become an increasingly common in many industries
because of its high precision; improve productivity, reliability and very little supervision. All
industrial robotic arms have two basic elements, one is the manipulator arm and another is the
controller of this robotic arm. It is also one of the popular illustrations of trajectory-following
electromechanical system; it presents various challenges in control because of its nonlinearities &
strong couplings represent in the dynamics of the robot manipulator [Mahmoud M. Othman,
Abdel Badie Sharkawy, and Abouel Makarem A. Khalil, January, 2010].
Since last decade, the Robotic arm control system has come out rapidly as an active area of
research.
[International Federation of Robotics, 2015]
Figure 2.1 Estimated worldwide annual supply of industrial robots

14. 14
Robotic arms are becoming popular in several applications such as pick and place, grinding,
welding, painting, mechanical handling, assembling and other industrial applications. Many of
robotic arm controls, industrial and commercial approach deals with the joints of robotic arm
created of servomechanism with PID, PD and IJC [Osman, 1991]. Most of current industrial
approaches to the robotic arm control design to treat each joint of the manipulator as a simple
linear servomechanism with simple controller like independent Joint Control (IJC), Proportional
Derivative (PD), or Proportional Integral Derivative (PID) controllers.
There is a long history of the control design of robotic arm; it provides control engineer a good
opportunity to learn intelligent control based techniques such as computed torque method,
optimal control, Variable Structure Control (VSC), Neural Networks (NNs), Fuzzy system [Reham H.
Mohammed, Fahmy Bendary Benha, Kamel Elserafi, 2013]. The Dynamixel servo motors (Dynamixel
Pro) are used widely in many developments and research projects around the world. The biggest
advantage of dynamixel servos are robust, fast, and they are easy to program, therefore they
become a smart actuators for precision control [Ahmad Zahid Rao, 2013].
Popularity of the Fuzzy logic control (FLC) has increased in the last couple of years.
FLC design follows the linguistic structure and it gives us a very good
performance for all non-linear systems.
However, in Fuzzy logic control (FLC) we need to include parameters such as linguistic
control rules and limits and membership functions for a given system. A major
disadvantage is its tuning process becomes more and more difficult for control
engineers and moreover it is very time consuming as well. Especially, when system
inputs and outputs are increased [Zafer Bingul, Ogzuhan Karahan, 2010].
Lastly, below figure is a representation of an overview of the control structure of 2
DOF robot arm and here, in this project, I am using a non-model based Fuzzy logic
control to control 2-DOF robotic arm manipulator.

15. 15
Figure 2.2: Overview of Control Structure of 2 DOF robotic arm
Nonetheless, when linkages of the robotic arm are moving at high speed and at a same time, the
nonlinear coupling of the robot arm and the interaction forces between the links of robotic arm will
be responsible to decrease the overall performance of the system and it improves the performance
of the tracking error. The disturbances and uncertainties like as the variable payload in a task cycle
can be one reason for the poor tracking performance of the robotic arm system [Osman, 1991].
Literature review also includes the kinematics & dynamics of the given 2 DOF robot arm. It is
explained in numerical analysis as below further.
2.2 Kinematics & dynamics of a 2-DOF robot arm
For developing a control strategy for the positioning of a 2-DOF robot manipulator, an
understanding of the kinematics and further dynamics of the manipulator need to be examined.

16. 16
Figure 2.3: Schematic representation of a 2-DOF robot arm manipulator
A 2-DOF robot arm is shown in Figure 2.3; Robotic arm kinematics and dynamics calculation can be
done as follow:
𝑥₁ = 𝑙₁𝑠𝑖𝑛𝜃1 (E.1)
𝑦₁ = 𝑙₁𝑐𝑜𝑠𝜃1 (E.2)
𝑥₂ = 𝑙₁𝑠𝑖𝑛𝜃1 + 𝑙₂sin⁡( 𝜃1 + 𝜃2) (E.3)
𝑦₂ = 𝑙₁𝑐𝑜𝑠𝜃1 + 𝑙₂cos(𝜃1 + 𝜃2) (E.4)
Where, 𝑙₁ - Length of link 1.
𝑙₂ - Length of link 2.
𝜃1 - Angle between link-1 and positive y axis.
𝜃2 - Angle between link-2 and positive y axis.
g - Gravitational constant to include the effects of inertia and self weight of robot linkages.
Now, we can use Lagrangian formulation to find the overall energy contributions of the system
𝛤 = 𝐾𝑖𝑛𝑒𝑡𝑖𝑐⁡𝑒𝑛𝑒𝑟𝑔𝑦⁡𝑜𝑓⁡𝑡ℎ𝑒⁡𝑠𝑦𝑠𝑡𝑒𝑚 − 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙⁡𝑒𝑛𝑒𝑟𝑔𝑦 Of the system (E.5)
Therefore, the kinetic energy can be formed as below
𝐾𝑖𝑛𝑒𝑡𝑖𝑐⁡𝑒𝑛𝑒𝑟𝑔𝑦⁡ = ⁡0.5⁡(m₁x1̇ 2
+ ⁡m₁y1̇ 2
+ m₂x2̇ 2
+ my2̇ 2
) (E.6)

17. 17
Overall kinetic energy can be calculated as
𝐾𝑖𝑛𝑒𝑡𝑖𝑐⁡𝑒𝑛𝑒𝑟𝑔𝑦⁡ = ⁡0.5((𝑚₁ + 𝑚₂)𝐿1
2
𝜃1
̇ + 𝑚₂𝐿2
2
𝜃1
̇ + 𝑚₂𝐿2
2
𝜃2
̇ 𝜃2⁡)̇ + 𝑚₂𝐿2
2
𝜃2
̇ 𝜃1
̇ +
𝑚₂𝐿1 𝐿2 𝑐𝑜𝑠𝜃2(𝜃1
̇ 𝜃2
̇ + 𝜃1
̇ 𝜃1
̇ ) (E.7)
Same as above, the potential energy of the 2-DOF robotic arm can be represented as
𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙⁡𝑒𝑛𝑒𝑟𝑔𝑦 = 𝑚₁𝑔𝑙₁𝑐𝑜𝑠𝜃1 + 𝑚₂𝑔𝑙₁𝑐𝑜𝑠𝜃1 + 𝑚2
𝑔𝑙₂ cos(𝜃1 + 𝜃2) (E.8)
Substitute equations (E.7) and (E.8) into the equation (E.5) the Lagrangian formulation of the
system in Figure 1 can be calculated as
⁡0.5((𝑚₁ + 𝑚₂)𝑙₁²𝜃1
̇ + 𝑚₂𝑙₂²𝜃1
̇ + 𝑚₂𝑙₂²𝜃2
̇ 𝜃2)̇ + 𝑚₂𝑙₂²𝜃2
̇ 𝜃1
̇ +̇ 𝑚₂𝑙₁𝑙₂𝑐𝑜𝑠𝜃2(𝜃1
̇ 𝜃2
̇ + 𝜃1
̇ 𝜃1
̇ ) −
𝑚₁𝑔𝑙₁𝑐𝑜𝑠𝜃1 − (𝑚₂𝑔𝑙₁𝑐𝑜𝑠𝜃1 + 𝑚₂𝑔𝑙₂ cos(𝜃1 + 𝜃2))⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡(E.9)
We can use (E.9) the dynamic equations of motion can be expressed using Lagrange’s first principle
𝐹𝜃1,2
= 𝑑/𝑑𝑡 [
𝜕Γ
𝜕𝜃1,2
̇ ] −
𝜕Γ
𝜕𝜃1,2
(E.10)
Each respective operator substitute into equation (E.10) in the equations of motion for a 2-DOF
robot arm calculated as above
((𝑚₁ + 𝑚₂)𝑙₁² + 𝑚₂𝑙₂² + 2𝑚₂𝑙₁𝑙₂𝑐𝑜𝑠𝜃2)𝜃1
̈ + (𝑚₂𝑙₂² + 𝑚₂𝑙₁𝑙₂𝑐𝑜𝑠𝜃2)𝜃2
̈ − 𝑚₂𝑙₁𝑙₂𝑠𝑖𝑛𝜃2(2𝜃1
̇ 𝜃2
̇ +
𝜃2
2̇ ) − (𝑚₁𝑔𝑙₁𝑠𝑖𝑛𝜃1 + 𝑚₂𝑔𝑙₁𝑠𝑖𝑛𝜃1) − ⁡𝑚₂𝑔𝑙₂𝑠𝑖𝑛⁡( 𝜃1 + 𝜃2) = ⁡𝐹𝜃₁⁡⁡⁡ (E.11)
𝑚₂𝑙₂²𝜃1
̈ + 𝑚₂𝑙₁𝑙₂𝑐𝑜𝑠𝜃2 𝜃1
̈ + 𝑚₂𝑙₂²𝜃2
̈ − 𝑚₂𝑙₁𝑙₂𝑠𝑖𝑛𝜃2 𝜃1
̇ 𝜃2
̇ − 𝑚₂𝑔𝑙₂𝑠𝑖𝑛𝜃₁ + 𝑚₂𝑔𝑙₂𝑠𝑖𝑛𝜃2) = ⁡𝐹𝜃₂
(E.11)
For a 2-DOF robot arm equations (E.10) and (E.11) can be arranged and put into the matrice with
the system equation
𝐵𝑞̈ + 𝐶𝑞̇ + 𝐺𝑞 = 𝐹 (E.12)
Here,
𝑞 =⁡[
𝜃1
𝜃2
]

18. 18
𝐵 =⁡[
((𝑚₁ + 𝑚₂)𝑙₁² + 𝑚₂𝑙₂² + 2𝑚₂𝑙₁𝑙₂𝑐𝑜𝑠𝜃2) 𝑚₂𝑙₂² + 𝑚₂𝑙₁𝑙₂𝑐𝑜𝑠𝜃2
(𝑚₂𝑙₂² + 𝑚2𝑙₁𝑙₂𝑐𝑜𝑠𝜃2) 𝑚₂𝑙₂²
]
𝐶 =⁡[
𝑚₂𝑙₁𝑙₂𝑠𝑖𝑛𝜃2(2𝜃1
̇ 𝜃2
̇ + 𝜃2
2̇ )
𝑚₂𝑙₁𝑙₂𝑠𝑖𝑛𝜃2 𝜃1
̇ 𝜃2
̇
]⁡
𝐺 =⁡[
−(𝑚₁ + 𝑚₂)𝑔𝑙₁𝑠𝑖𝑛𝜃1 − 𝑚₂𝑔𝑙₂𝑠𝑖𝑛⁡( 𝜃1 + 𝜃2)
𝑚₂𝑔𝑙₂𝑠𝑖𝑛⁡( 𝜃1 + 𝜃2)
]
𝐹 = [
𝑓𝜃1
𝑓𝜃2
]
[shahab, Masoud,2008].

19. 19
Chapter 3 – Experimental Design
3.1 Hardware
Hardware requirements are as below for the given 2-DOF robotic arm,
[1] DYNAMIXEL PRO Make H42-20-S300-R model 2 DOF Robot arm System.
Figure 3.1: DYNAMIXEL PRO Make H42-20-S300-R model
[2] 24VDC Power Supply for a DYNAMIXEL PRO Make H42-20-S300-R model 2 DOF Robot System.

20. 20
Figure 3.2: Dynamixel Pro Power supply circuit board
[3] USB2DXL dongle for Serial communication with PC.
It uses the RS-485 communication protocol. Here, we are required to position the switch from USB-
to-Dynamixel dongle to RS485. [Quick Start for Dynamixel Pro v1.00b, “User Manual”].
Figure 3.3: Dynamixel Pro USB2DXL dongle
Latency Time can be done as below.
Under Windows Device Manager -> Port -> USB Serial Port (right mouse click) -> properties -> Port
Setting -> Advanced -> Latency Timer (msec) -> set to 1msec.
[4] PC (Personal Computer) with MATLAB software.
3.2 Software
Lists of below softwares can be used to control 2-DOF robot arm such as C, C++, Visual basic, Java,
Labview, Python, MATLAB and so on. In this project, we use MATLAB-Simulink and Fuzzy logic
control.

21. 21
Figure 3.4: Lists of softwares can be used to control dynamixel Pro
[nodna.de/Dynamixel-Pro-H42-20-S300-R_1]
[1] RoboPlus – It is a standard software, which is designed by Dynamixel Pro manufacturer to
control the given 2-DOF robotic arm.
Figure 3.5: RoboPlus software

22. 22
[2] MATLAB – It is the basic platform on which we will run all the programs for the given project.
[2.1] Simulink – Whole task of the given project is developed on the Simulink model. In Simulink,
We can develop the logic by using the Simulink blocks for simulink library and it is an easy way to
develop the program.
Some advantages of Simulink:
1. Simulink has a simulink library. Where, we can find various logic blocks to make simulink
model.
2. We can use Graphical Interface to design and analyse the logic.
3. Simulink has an error detection tool inside.
4. Simulink allow us to use other MATLAB tools for the given project.
[2.2] Fuzzy Logic Toolbox – It is a part of MATLAB software. Most of “FLC” are consisted of closed-
loop system (feedback system). It (FLC) gives an input to the process by gathering information of
required output. “FLC” have a number of parameters and all of them are needed to configure prior
to start program, such as input membership functions, fuzzification method, output membership
functions, rule base, premises connective, inference method and defuzzification.
Figure 3.6: Block representation of Fuzzy Logic Controller

23. 23
Where, r (t) is kwon as the reference signal
u (t) as the input signal
and y (t) as the output signal
In above figure, we can see that there are 4 major process components of the FLC. First one is
fuzzification, it switches the crisp signal in to fuzzy signal. Second one is Rule-base, it is for making
rules, it helps in decision making process and, Inference mechanism can be able to take its decision
by using information from reference signal, output signal and Rule-base. Third one is a De-
fuzzification, It switches the fuzzy signal back to crisp signal.
Mainly, the crisp signal is like a real number, it also follows the math rules but, on the other hand,
fuzzy signal is completely different from crisp signal. Here, we can’t apply basic math operations to
it because its calculations are done by fuzzy-logic sets.
Fuzzy-logic sets
All the Math operations and calculations can’t be applicable to the fuzzy-logic. For making the
mathematical operation happen in the FLC, we need to make fuzzy-logic sets, which are based on
its Membership functions. Where, all the crisp inputs and crisp outputs are categorizing into
different sets on the basis of its Linguistic Variables and, it is known as Fuzzy-logic sets. The math
operations, which are applicable are AND, OR and NOT.
Fuzzy Intersection (AND operation) A1∩A2 = min { µA1, µA2 }
Fuzzy Union (OR operation) A1∪A2 = max { µA1, µA2 }
Fuzzy Subset µA1 ≤ µA2 ; Where, A1 is the subset of A2
Fuzzy Complement (NOT operation) µA2 = 1 - µA1 ; Where, A1 is the complement of A2
[Kevin M. Passino, Stephen Yurkovich, 1998]
Table 3.1: Table for Fuzzy logic mathematical operations
3.3 Block diagram & Specification
Block diagram of the given the 2-DOF robotic arm system in shown in figure 3.9.

24. 24
Figure 3.7: Block diagram of the project
Specifications of the Dynamixel Pro make H42-20-S300-R
Specifications Data Unit
Rated Voltage 24 V
No load current 0.57 A
No load speed 32.7 RPM
Continuous operation
Current 1.5 A
Speed 29.8 RPM
Torque 6.3 N.M
Resolution 303800 Step/turn
Gear ratio 304 -
Backlash 3.8 Arc/min
Interface RS485
Operating temperature 5 to 55 Degree C
Weight 20 W
Dimensions 42*42*84 mm
Table 3.2: Specification table of Dynamixel pro
[trossenrobotics.com/c/dynamixel-pro”,2016, & Quick Start “User Manual”]

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3.4 Features of 2-DOF robotic arm of Dynamixel Pro
[1] It has an electrical current sensing based control.
[2] It also has an internal temperature sensing capabilities.
[3] Position, speed and torque based command.
[4] Detachable reduction gear, future available options are Straight, Right Angle, and Belt.
[5] RS-485 communication physical layer, it also supports CAN, TTL, Ethercat as well.
3.5 Connection & Set up for the experiment
In this section, I will explain overall system setup including wiring, computer software package and
operating modes required to run the given 2-DOF robot manipulator. The given 2-DOF robot arm
mechanism has two servomotors connected with cylindrical rods and they make H-series dynamixel
“H42-20-S300-R” type 2–DOF robotic arm. It requires 24VDC power supply to operate. USB2DXL
can be connected to a PC through a USB dongle; now, these two servo motors are controlled
through the USB dongle as shown in below Figure, The PC and servo motors are communicated
through a serial communication (RS485 Protocol).

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Figure 1.8: Two Dynamixel pro servo motors connection with USB dongle
[Quick Start for Dynamixel Pro v1.00b. “User Manual”]
Here, the connection between USB and Dynamixel PRO Servo motors was successfully done
through a 4-pin cable (shown in below figure 3.9) with a 24VDC power supply to power the
servomotors as shown in Figure 4.
Figure 3.9: 4-pin connection and servomotor connection points
[Quick Start for Dynamixel Pro v1.00b. “User Manual”]
These two Dynamixel servo motors are connected in series connection. The control software of it is
called “Dynamixel Wizard” and it is used for the open loop control of the servo motor angle
position for two servomotors individually. In “Dynamixel Wizard” the servo motors goal angle is
defined by the goal position value according to below formula
𝐺𝑜𝑎𝑙⁡𝑎𝑛𝑔𝑙𝑒⁡(𝑖𝑛⁡𝑑𝑒𝑔𝑟𝑒𝑒𝑠) = 𝐺𝑜𝑎𝑙⁡𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛⁡𝑉𝑎𝑙𝑢𝑒 ∗⁡
180
151875
(18)
[Quick Start for Dynamixel Pro v1.00b. “User Manual”]
It means that the servo motor revolves -180 to 180° and its respective pulses requirements are -
151875 to 151875 as shown in below figure.

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Figure 3.10: Dynamixel PRO goal angle and goal position relation
On the other hand, the relationship between current and the goal torque value represented below
𝐶𝑢𝑟𝑟𝑒𝑛𝑡⁡𝑖𝑛⁡𝑚𝐴 = 𝑣𝑎𝑙𝑢𝑒⁡𝑜𝑓⁡𝑔𝑜𝑎𝑙⁡𝑡𝑜𝑟𝑞𝑢𝑒 ∗⁡
8250
2048
[Quick Start for Dynamixel Pro v1.00b. “User Manual”].
3.5 Operation modes of 2-DOF robot arm
The given 2-DOF robotic arm can be operated in 3 different operation modes. These three
operating modes are mentioned in table below.
Operation Mode Specification
Position Mode Achieve the desired position of servomotor1 and servomotor2.
Velocity Mode Achieve the desired velocity of the servomotor1 and servomotor2.
Torque Mode Controls the output torque of the servomotor1 and servomotor2.
Table 3.3: Table for Fuzzy logic operation modes

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Chapter 4 - Modelling
4.1 RoboPlus modelling
RoboPlus is software developed by Dynamixel Pro manufacturer. It is one of the traditional and
easiest way to control and monitor the given 2-DOF robotic arm. Following steps explain further,
Step – 1: Connect 24VDC Power supply to Dynamixel Pro.
Step – 2: Connect USB2DXL dongle to PC.
Step – 3: Open RoboPlus in your PC.
Step – 4: Assigned COM Port to it in Device Manager of your PC.
Step – 5: Follow the Latency Time procedure path as given below,
Under Windows Device Manager -> Port -> USB Serial Port (right mouse click) -> properties -> Port
Setting -> Advanced -> Latency Timer (msec) -> set to 1msec. [Quick Start for Dynamixel Pro v1.00b.
“User Manual”].
Step – 6: Open “Dynamixel Wizard” and connect it with the desired BaudRate. Once the COM port
connection get successful, select ‘DXL 2.0’ , ‘57600,’ and ‘1000000’ and, click ‘Start Searching.’
[Quick Start for Dynamixel Pro v1.00b. “User Manual”].
Figure 4.1: Dynamixel Wizard window for COM Port connection

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Step – 7: Successful communication will allow you to open Parameters for both servo motors in
“Dynamixel Wizzard”.
[ID:001] Parameter window for servo motor 1.
[ID:002] Parameter window for servo motor 2.
Figure 4.2: Dynamixel Wizard Parameter Window
Step – 8: Use the mentioned parameters below to operate given 2-DOF robotic arm.
[1] Parameter – 11: Operating Mode – Operating mode can be change by using parameter 11.
[2] Parameter – 562: Torque Enable – Must apply 1 to be activated and apply 0 when changing
parameters
[3] Parameter – 600: Goal Velocity
[4] Parameter – 596: Goal Position

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[5] Parameters – 563,564 & 565 – For LED.
4.2 MATLAB modelling
The control and monitor of the given 2-DOF robotic arm using MATLAB software will be valuable
work for all control engineering students to learn this control technique.
Here, MATLAB can control the goal angle and goal acceleration of the servomotor at both joints.
Step – 1: Open the MATLAB in PC.
Step – 2: Connect 24VDC power supply to Power circuit of the given robotic arm.
Step – 3: Connect USB2DXL to PC.
Step – 4: Assigned COM Port and Latency time as below,
Under Windows Device Manager -> Port -> USB Serial Port (right mouse click) -> properties -> Port
Setting -> Advanced -> Latency Timer (msec) -> set to 1msec.
Step – 5: Do serial communication between MATLAB and dynamixel Pro (2-DOF robot arm) as
below coding,
s = serial('COM1');
set(s,'Baudrate',1000000);
set(s,'StopBits',1);
set(s,'DataBits',8);
set(s,'Parity','none');
fopen(s);
Step – 6: Use MATLAB m-files dynamixelm1.m and dynamixelm2.m for servo 1 and servo 2
respectively.
Where, dynamixelm1.m and dynamixelm2.m m-files are given in appendix C.
Step – 6: We can change values for goal position and goal acceleration by changing its value in the
given m-files. This is the how; we can operate given robotic arm in speed and position modes.
Step -7: MATLAB can change goal acceleration of the given 2-DOF robotic arm as below coding,

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servo_ID = 1;
goal_accel = 5;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_ACCEL,goal_accel,BYTES_GOAL_ACCEL,s);
dec2hex(Instruction_Packet)
Step -8: MATLAB can change goal angle of the given 2-DOF robotic arm as below coding,
servo_ID = 1;
goal_angle = 1;
goal_pos = goal_angle*RAD2POS;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_POS,goal_pos,BYTES_GOAL_POS,s);
dec2hex(Instruction_Packet)
Figure 4.3: Result of the servomotor-1 to an angular position at 1 radian
Step - 9: For servo ID-2 and goal angle 1 radian.

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Figure 4.4: Result of the servo motor-2 to an angular position of 1 radian
Step – 10: COM Port disconnection can be done by below command,
fclose(s);
4.2 Simulink modelling
The control and monitoring of the given 2-DOF robotic arm using Simulink model.
We can control the goal angle and goal acceleration of the servomotor at both joints.
Case-1: Run each servo motor individually using below simulink model.

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Figure 4.5: Simulink model for each servo individually
Figure 4.5.1: Function Block Parameters

34. 34
Here, dynamixelm2 is a dynamixelm2.m (MATLAB m-file). Dynamixelm2.m is given in appendix C.
Similarly, for dynamixelm1 can be put in MATLAB function in simulink model. Dynamixelm1.m is
also given in appendix C.
Case-2: Run both servo motor at a same time using below simulink model.
Figure 4.6: Simulink model for both servos at a same time.

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Figure 4.6.1: Function Block Parameters
Figure 4.6.2: Function Block Parameters
Where, dynamixelm1 and dynamixel2 are MATLAB m-files and their coding is given in appendix C.

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4.2 FLC modelling
Now, I am going to control the given robotic arm using Fuzzy logic control because Popularity of
the FLC has increased in the last couple of years. FLC design follows the linguistic
structure and it gives us a very good performance for all non-linear systems.
More importantly, it follows f i v e s t e p s ,
1 I n p u t s
2 F u z z i f i c a t i o n o f t h e I / P v a r i a b l e s
3 R u l e b a s e I n f e r e n c e
4 D e f u z z i f i c a t i o n o f t h e O / P v a r i a b l e s
5 O u t p u t s
Table 4.1: FLC computational steps
To control and monitor the given 2-DOF robotic arm using fuzzy logic control follow below steps,
Step – 1: Designed Fuzzy Inference System for 2-DOF robotic arm.
Figure 4.7: Fuzzy Logic Schematic for the 2-DOF robot arm control system

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Step – 1: Create FIS for the given 2-DOF robotic arm.
FIS
Step – 2: Create membership functions for the given 2-DOF robotic arm.
Membership
Functions
Target: defined between [-1 1] in radian as shown below:
Input 1: E (error)

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Input 2: CE (change in error)
Output 1: servo1

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Output 2: servo2

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Step – 3: Prepare rule base for the given 2-DOF robotic arm.
Rules

41. 41
Surface
Step – 4: For changing the position of both servo motors; change the constant values in figure 4.5.
Step – 5: For changing acceleration of both servo motors; change the acceleration values in m-files.
Step – 6: Repeat the steps for changing position and acceleration of both servo motors.

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Chapter 5 – Results & Conclusion
5.1 Results
This chapter includes the results & conclusion of 2 – DOF robot arm using Fuzzy logic control; as
desired position and acceleration. Results are documented as below,
Case – 1: Servo motor – 1 at -1 and Servo motor – 2 at -1.
Figure 5.1: Result of the servo motor-1 at -1 and servo motor-2 at -1
Case – 2: Servo motor – 1 at -0.5 and Servo motor – 2 at -0.5.

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Figure 5.2: Result of the servo motor-1 at -0.5 and servo motor-2 at -0.5
Case – 3: Servo motor – 1 at 0 and Servo motor – 2 at 0.
Figure 5.3: Result of the servo motor-1 at 0 and servo motor-2 at 0
Case – 4: Servo motor – 1 at 0.5 and Servo motor – 2 at 0.5.

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Figure 5.4: Result of the servo motor-1 at 0.5 and servo motor-2 at 0.5
Case – 5: Servo motor – 1 at 1 and Servo motor – 2 at 1.
Figure 5.5: Result of the servo motor-1 at 1 and servo motor-2 at 1

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5.2 Conclusion
In conclusion, both servo motors of the 2-DOF robot manipulator are network driven. They both
can be addressed with a unique ID dynamically. In this project, I have controlled and monitored 2 –
DOF robot arm using RoboPlus, MATLAB and FLC softwares. Out of all three control techniques, it is
clear that the Fuzzy logic control is quite convenient and more computationally efficient compare to
other two control techniques of the given 2-DOF robotic arm (Dynamixel PRO servomotors) but its
tuning process is difficult and time consuming. The results of this project show that we can control
its goal position and goal acceleration effectively.
5.3 Future work
In future, 2 - DOF robotic arm (DYNAMIXEL PRO) can be control through various control techniques
mentioned below and show in figure 5.1.
[1] Dynamixel PRO is controlled using various PC software’s such as LABVIEW, C, C++, JAVA, Visual
Basic,Python and so on.
[2] Dynamixel PRO is controlled using various exclusive controllers such as CM-700, CM-530.
Figure 5.6: Dynamixel Pro control methods
[http://en.robotis.com/index/product.php?cate_code=101010]

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References
[1] Quick Start for Dynamixel Pro v1.00b. “User Manual”.
[2] M. Shahab, A. Masoud, “2DOF Robotic Manipulator Control Design & Simulation”, 2008.
[3] K. M. Passino, S. Yurkovich, “Fuzzy Control”, 1997-1998.
[4] H. Elaydi, I. A. Hadrous, M. Al Ashi, “Trajectory Tracking Control of A 2-DOF Robot Arm Using
Neural Networks”, 2014.
[5] B. B. Reddy, I. S. Babu, G. V. SK. Rao, “Modelling and Control of 2-DOF Robotic Manipulator
Using BLDC Motor”, 2014.
[6] M. M. Othman, A. B. Sharkawy, A. A. Khalil, “FUZZY TRACKING CONTROL OF TWO DEGREES OF
FREEDOM ROBOTIC ARM”, 2010.
[7] Z. Bingul, O. Karahan, “A Fuzzy Logic Controller tuned with PSO for 2 DOF trajectory control”,
2011.
[8] Osman, “A PI Sliding Mode Tracking Controller with application to a 3 DOF Direct-Drive Robot
Manipulator”, 1991.
[9] “International Federation of Robotics”, 2015.
[10] “http://www.trossenrobotics.com/c/dynamixel-pro”, 2016.
[11] “https://nodna.de/Dynamixel-Pro-H42-20-S300-R_1”.
[12] “http://en.robotis.com/index/product.php?cate_code=101010”.

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Appendix - A
Name: Kalpitkumar Thakar
Student No: 4709354
Supervisor: Prof. Fazel Naghdy
Title of Project: Trajectory control of a DYNAMIXEL PRO Make H42-20-S300-R model
(2 DOF robot arm) using Fuzzy logic control (FLC)
Project Plan & Project Specification:
Aim: The aim of the project is to study & control a DYNAMIXEL PRO Make
H42-20-S300-R model (2 DOF Robot) arm with FLC (Fuzzy logic controller).
Requirements: A DYNAMIXEL PRO Make H42-20-S300-R model (2 DOF Robot) arm, MATLAB-
Simulink, USB2DXL for Serial communication with PC (RS 485).
Brief Procedure: Take a DYNAMIXEL PRO Make H42-20-S300-R model (2 DOF Robot) arm. Study the
given robot arm and Fuzzy logic control systems to control this robot arm. I have selected fuzzy
logic control to control this given robot arm because FLC provides advantage over traditional
processes, it gives edge to all designers to model complex systems swiftly and effectively.
Moreover, the given robot arm and the PC are connected to each other through USB2DXL serial
communication (RS485).
In the next step, fuzzy tool box in Simulink- MATLAB will be used to design a controller for the given
robot arm in it. This program is created to Control and monitor the robot arm by using Fuzzy logic
control.
For this given project, use MATLAB-Simulink software:
MATLAB – MATLAB is very basic platform and we will run all the programs for the project on
MATLAB.

48. 48
Simulink – The full project will be prepared on the Simulink, on which it is an easy process to
develop a logic by using the Simulink blocks.
Fuzzy Logic Toolbox – It is a internal part of MATLAB software and we are using it in this given
project.
USB2DXL– USB2DXL is a communication mode between robot and PC, which is RS485.
Reasons for adopting this Project Strategy:
The expansion of the robotics and FLC in modern industries demands to develop precise and
powerful control systems for robotic arm therefore it has become a biggest reason for adopting this
project.
The goal of this project is to control a DYNAMIXEL PRO Make H42-20-S300-R model (2 DOF Robot)
arm based on Fuzzy Logic techniques. This project involves FLC instruction set and analysing its
ability to control the given robot arm.
Validation of experiment results
The entire project is based on MATLAB-Simulink and Fuzzy logic system. Fuzzy logic control is a good
software for validating, controlling and monitoring the date of a DYNAMIXEL PRO Make H42-20-
S300-R model (2 DOF Robot) arm.

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Gantt chart for achieving objectives:
Read Literature
Read Robot Manual
Develop FLC for Robot
System Testing
Completing Experiment
Writing Thesis
Make A1 poster
Weeks 1 2 3 4 5 6 7 8 9 10 11 12 13
Intense task
Adequate task

50. 50
Appendix B: Logbook Summery sheet

51. 51
Appendix C
Modelling for servo 1 (dynamixelm1.m)
function yy = dynamixelm1(x)
if (x>=-1)&&(x<=1)
yy=x;
s = serial('COM1');
set(s,'Baudrate',1000000);
set(s,'StopBits',1);
set(s,'DataBits',8);
set(s,'Parity','none');
fopen(s);
run('Control_Table_Constants')
servo_ID = 1;
brightness = 255;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_RED_LED,brightness,BYTES_RED_LED,s);
dec2hex(Instruction_Packet)
servo_ID = 1;
goal_accel = 5;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_ACCEL,goal_accel,BYTES_GOAL_ACCEL,s);
dec2hex(Instruction_Packet)
servo_ID = 1;
enable = 1;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_TORQUE_ENABLE,enable,BYTES_TORQUE_ENABLE,s);
dec2hex(Instruction_Packet)
servo_ID = 1;
goal_angle = x;
goal_pos = goal_angle*RAD2POS;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_POS,goal_pos,BYTES_GOAL_POS,s);
dec2hex(Instruction_Packet)
fclose(s);
delete(s)
clear s
else
s = serial('COM1');
set(s,'Baudrate',1000000);

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set(s,'StopBits',1);
set(s,'DataBits',8);
set(s,'Parity','none');
fopen(s);
run('Control_Table_Constants')
servo_ID = 1;
goal_angle = 0;
goal_pos = goal_angle*RAD2POS;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_POS,goal_pos,BYTES_GOAL_POS,s);
dec2hex(Instruction_Packet)
fclose(s);
delete(s)
clear s
end
end
Modelling for servo 2 (dynamixelm2.m)
function yy = dynamixelm2(x)
if (x>=-1)&&(x<=1)
yy=x;
s = serial('COM1');
set(s,'Baudrate',1000000);
set(s,'StopBits',1);
set(s,'DataBits',8);
set(s,'Parity','none');
fopen(s);
run('Control_Table_Constants')
servo_ID = 2;
brightness = 255;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_RED_LED,brightness,BYTES_RED_LED,s);
dec2hex(Instruction_Packet)
servo_ID = 2;
goal_accel = 5;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_ACCEL,goal_accel,BYTES_GOAL_ACCEL,s);
dec2hex(Instruction_Packet)

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servo_ID = 2;
enable = 1;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_TORQUE_ENABLE,enable,BYTES_TORQUE_ENABLE,s);
dec2hex(Instruction_Packet)
servo_ID = 2;
goal_angle = x; %[rad]
goal_pos = goal_angle*RAD2POS;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_POS,goal_pos,BYTES_GOAL_POS,s);
dec2hex(Instruction_Packet)
fclose(s);
delete(s)
clear s
else
s = serial('COM1');
set(s,'Baudrate',1000000);
set(s,'StopBits',1);
set(s,'DataBits',8);
set(s,'Parity','none');
fopen(s);
run('Control_Table_Constants')
servo_ID = 2;
goal_angle = 0;
goal_pos = goal_angle*RAD2POS;
Instruction_Packet =
DynamixelPro_write(servo_ID,ADDRESS_GOAL_POS,goal_pos,BYTES_GOAL_POS,s);
dec2hex(Instruction_Packet)
fclose(s);
delete(s)
clear s
end
end