Development of a Segway-Type Wheelchair

by

Kittipong Pramotago

A thesis submitted in partial fulfillment of the requirements for the

degree of Master of Engineering in

Mechatronics

Examination Committee: Prof. Manukid Parnichkun (Chairperson)

Assoc. Prof. Erik L.J. Bohez

Dr. Mongkol Ekpanyapong

Nationality: Thai

Previous Degree: Bachelor of Engineering in Mechanical Engineering

Ubon Ratchathani University

Thailand

Scholarship Donor: Royal Thai Government Fellowship – AIT Fellowship

Asian Institute of Technology

School of Engineering and Technology

Thailand

May 2017

ii

ACKNOWLEDGEMENTS

Firstly, I would like to thanks to my thesis advisor, Prof. Manukid Parnichkun. He is a

lots of knowledge and other experiences in mechanical and control engineering system.

Moreover, he giving me a suggestion, interesting lecture and simulation throughout my

thesis.

Secondly, I also would like a special thanks to committee Assoc. Prof. Erik L.J. Bohez

and Dr. Mongkol Ekpanyapong for the recommendation provided during thesis work.

They are very important to help me about my thesis.

Thirdly, my special thanks go to my friend and my senior, Mr. Warawut Suwalai and Mr.

Surachat Chantarachit to supporting, suggestions and many techniques.

Fourthly, I would like to thankful to my family for support in every way. In addition,

Royal Thai Government Fellowship – AIT Fellowship provided me a great opportunity

for study in AIT.

Finally, my thesis cannot be finished if I do not have all of help form Mechatronics, senior

students, my friends and all staff. They have suggestion and special techniques for me.

Thank you so much.

iii

ABSTRACT

The difficult challenge in a Segway type wheelchair is to control the robot which can

balance two wheels in roll or pitch direction. There are many techniques to balance a

Segway type wheelchair. In about thesis, the inverse pendulum technique is applied to

balancing in the longitudinal direction. Many section in this thesis used balance such as

the fusion sensor (Gyroscope & accelerometer), the dynamic model and the control

algorithm. This thesis concerns about the control algorithm to control the robot. The PID

controller is applied to the simulation model and the real plant in order to observe the

response of the robot. Finally all thesis, the simulation and experiment result are presented

and discussion. The simulation result uses the Simulink in the Matlab program to simulate

form dynamic model.

Keywords: a Segway type wheelchair, Newton Euler method, PID controller,

Dynamic model

iv

TABLE OF CONTENTS (Cont’l)

CHAPTER TITLE PAGE

TITLE PAGE ACKNOWLEDGEMENTS ii

ABSTRACT iii

TABLE OF CONTENTS iv

LIST OF FIGURES vi

LIST OF TABLES vii

LIST OF SYMBOLS viii

1. INTRODUCTION 2

1.1 Background 2

1.2 Statement of the problems 3

1.3 Objectives 3

1.4 Scopes of works 3

1.5 Limitations 3

2. LITERATURE REVIEW 4

2.1 Introduction 4

2.2 Research on the balancing concept 4

2.3 State space control algorithm 7

2.4 PID control algorithm 8

2.5 Linear model of a direct current (DC) motor 10

3. METHODOLOGY 11

3.1 Methodology flow chart 11

3.2 Mechanical model 12

3.3 Physical model 14

3.4 Electrical hardware configurations 15

3.4.1 Microcontroller features 16

3.4.2 Driver DC motor board 16

3.4.3 BNO055 (Gyro and accelerometer) 17

3.4.4 Regulator 17

3.4.5 DC motor with encoder 18

3.4.6 DC power supply features 18

3.4.7 Encoder 19

3.5 Dynamic model of a Segway type wheelchair 20

3.6 The state space model 27

3.7 Parameter identification 29

3.8 Control algorithms of a Segway-type robot 30

3.9 Data of experiment 31

4. RESULTS AND DISCUSSION 32

4.1 Simulation result in Matlab software 32

4.2 Experiment result 34

v

5. CONCLUSIONS AND FUTURE WORKS 35

5.1 Conclusions 35

5.2 Future works 35

REFERENCES 36

APPENDIX 37

Appendix A: C code for control a segway-type wheelchair

vi

LIST OF FIGURES

FIGURE TITLE PAGE

Figure 2.1 The two wheel inverted pendulum model [2] 4

Figure 2.2 The prototype robot balancing two wheel [4] 5

Figure 2.3 The iBot. The main features are highlighted 6

Figure 2.4 The SEGFREE, a Segway Wheelchair 7

Figure 2.5 System inputs and outputs 7

Figure 2.6 PID controller block diagram 9

Figure 2.7 Diagram of a DC motor 10

Figure 3.1 Methodology of flow chart to study 11

Figure 3.2 Parts of wheelchair design in SolidWorks 12

Figure 3.3 All parts assembly of wheelchir robot 13

Figure 3.4 Model of a Segway type wheelchair 13

Figure 3.5 Physical model of a Segway type wheelchair 14

Figure 3.6 Electrical and electronic hardware 15

Figure 3.7 Microcontroller Arduino MEGA 2560 16

Figure 3.8 H-bridge driver dc motor 80A 16

Figure 3.9 BNO055 sensor 17

Figure 3.10 Regulator output 5 V 17

Figure 3.11 DC motor 24 V 18

Figure 3.12 Battery 12 V-7AH 18

Figure 3.13 Encoder for counter motor 19

Figure 3.14 Free body diagram of the left wheel and the right wheel 20

Figure 3.15 The dynamic model of the body robot 21

Figure 3.16 Pole of system 30

Figure 3.17 Data of experiment balancing robot 31

Figure 4.1 The PID simulation model 33

Figure 4.2 The PID simulation result for balancing 33

Figure 4.3 Real robot for balancing 34

Figure 4.4 The PID experiment result of balancing 34

vii

LIST OF TABLES

TABLE TITLE PAGE

Table 2.1 Summary of researches about balancing of robot 4

Table 2.2 Summary of researches about balancing of robot 6

Table 2.3 Effects of increasing a parameter 9

Table 3.1 DC motor parameters 18

Table 3.2 Battery specifications 19

Table 3.3 The table of constant parameter for balancing 29

viii

LIST OF SYMBOLS

V is the voltage input

𝐾𝑒 is the EMF constant

𝐾𝑡. is the torque constant

𝐾𝑑 is the transmission ration

R is the armature coil resistance

bm is the viscosity of the motor

Ib is the moment inertia of body

i is the armature current

Jm is the moment inertia of motor rotor

Mb is the mass of the body

Mw is the mass of the wheel

Jw is the moment inertia of the wheel

hb is the center of high of the body

x is the horizontal distance

f is the friction between wheel and ground

r is the radius of the wheel

R is horizontal reaction force

N1 is vertical reaction force from a ground to a wheel

N2 is vertical reaction force from a body to a wheel

τ is the torque input

∅ is longitudinal leaning angle

g is gravity acceleration

c is the viscosity friction of the wheel

α is the wheel angle

2

CHAPTER 1

INTRODUCTION

1.1 Background

Nowadays, there are many Segway-type wheelchair robots and balancing robot which

it can help many disable people. Overtime, many persons have developed each kind

of robots wheel. Many times, the disabled people encounter difficulties when they

want something that is high. Use hand for mandatory wheel of wheelchair, it may

dangerous to disabled people. However, this leads to a risk of injury for both the

disabled person and the assistants. In this thesis, there are four wheels of a Segway-

type wheelchair to motion.

The benefits of the segway-type wheelchair robot is to traveling in small and

complicate paths. Moreover, the segway-type wheelchair can help many people that

they cannot movement to travel to go other places. However, the control of Segway-

type wheelchair robots is difficult when comparing with multi-wheel robot. Several

research works on the dynamic model and balanced control algorithm of the Segway-

type wheelchair robot had been studied.

As a result, there are a number of researches to study about a Segway-type wheelchair

to help the disabled people. For example, to balance the robot in the lateral direction,

the balancing concept of inverse pendulum [1 2 3 4 5 6] and the effect of gyroscope

are utilized in order to produce the balancing torque.

In previous works, the five parameters which are important for control algorithm: roll

angle, pitch angle, the rate of change in roll and pitch angle, and the robot wheel's

speed were considered.

Therefore, this research is just to balance two wheels of a segway-type wheelchair.

Also, this research aims to use the effect of gyroscope and accelerometer which are

widely used for balancing robot applications. In this thesis, although there several

control algorithm which were proposed for balancing purpose, the PID control

algorithm will be applied for balance the platform in this thesis.

3

1.2 Statement of the problems

The problem of the people who are unable to walk because they have some problems

with their lower-limb part, for example, physical disabilities like polio, blindness,

paralysis, and other deficiencies which affect their legs, should be solved. Those

problems can as a result in to make this research. The segway-type wheelchair is

similar to an inverted pendulum. There are techniques of a segway-type wheelchair

balancing. For the nonlinear model of a segway-type wheelchair, the linearization

should be used to transformed the nonlinear model to linear system model before the

step of analysis and design for the control algorithm.

The concept to control only the torque or speed of two wheels is a best for controlling.

By using the controller PID

1.3 Objectives

To design a controller for balancing the segway-type wheelchair robot

1.4 Scopes of works

The scopes of this thesis are as following:

Balancing wheelchair two-wheel.

Design a new prototype hardware of a Segway-type wheelchair

Using Microcontroller Arduino MEGA 2560 discovery and Matlab Simulink

1.5 Limitations

The limitations of this thesis are as following:

Define the dynamics of segway-type wheelchair robot.

All Weight limit at 100 kg

4

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

In this literature review, there is research works to make the robot balanced itself and there

are many ways to balance out the robot which will be reviewed in the following topics: The

balancing concept of robot to control algorithms.

2.2 Research on the balancing concept

There are several concepts to perform a balancing the robot which were proposed. Some

of the research used inverted pendulum theory. In addition, there are the gyroscope and

accelerometer to effect on angle of body robot which can produce a stable system.

Moreover, the angular momentum theory can applied to torque dc motor.

Table 2.1 Summary of researches about balancing of robot

Ref Topic Control Results

[1] Robust Control Method Applied in

Self-Balancing Two-Wheeled Robot

SMC

technique

Simulation and

Experiment

[2] A Two-Wheeled Self-Balancing Robot

with the Fuzzy PD Control Method

Fuzzy PD Simulation and

Experiment

[3] Self-balancing two-wheeled robot LQR Simulation and

Experiment

[4] Balancing a Two-Wheeled

Autonomous Robot

PID and

LQR

Simulation and

Experiment

Figure 2.1 The two wheel inverted pendulum model [2]

5

In the researches on balancing control of two wheel robot [1 2 3 4], the SMC technique

were used to control a SBTWR system by HerTerng Yau et al. [1]. It consists of two major

steps. First, the stability dynamics must be confirmatory by switching surface. Second, the

hitting of the switching surfaces should be ensured from determination of a SMC in this

step.

Next, Junfeng Wu et al. [2] used the Fuzzy PD Controller. The robot structure is a

composition of a chassis carrying a DC motor coupled to a planetary gearbox. The digital

signal processing board was used to implement the control algorithm. The power

amplifiers were selected for the the motors. The necessary sensors are used to sense the

state of the robot. And the receiver for the radio control unit, as well as a vertical bar. The

two-wheel inverted pendulum model is in Figure 2.1.

The state feedback with used Linear Quadratic Regulator (LQR) was proposed by Brian

Bonafilia et al. [3]. Result of the simulation found that the Kalman Filter are using

the state estimated. The control system stability by using the gyroscope and

accelerometer sensor. The error angle using the LQR controller. There are three main

sensor: the accelerometer 3 axis, the gyroscope 1 axis and motor with encoders

were used to estimate the current state of the system.

Rich Chi Ooi [4] used Linear Quadratic Regulator (LQR) and PID controller. This is a

prototype robot balancing two wheel in Figure 2.2.

Figure 2.2 The prototype robot balancing two wheel [4]

6

Table 2.2 Summary of researches about balancing of robot

Ref Topics Control

[5] The iBot, a Segway wheelchair Keman bes-known

[6] The SEGFREE, a Segway Wheelchair Feedback control

Figure 2.3 The iBot. The main features are highlighted

(gizmodo.com/117720/ibot-mobility-system) [5]

This is a credit to its design. It is capable of tackling most terrains, rotating 360 degrees

at almost a zero radius, reaching the jar on the top shelf of a cupboard, and most

importantly climbing up and down stairs. This is the iBot in Figure 2.3. In doing so the

iBot user requires the assistant of a trained person. The ascent occurs in three stages:

1. The user approaches the step backwards. They then have to perform

several transitional functions on their electronic controller.

2. Once ready, the user is then required to grip the railing (so it is to your

disadvantage to be located towards the middle of the steps) and gently

pull themselves forward. When start up to stair, the user will need to

center gravity to move forward slowly the robot.

3. Moving up until the robot and you stay the top of the stairs.

7

Figure 2.4 The SEGFREE, a Segway Wheelchair

http://www.segfree.co.za/the-segfree.htm [6]

The Segfree [6] is the segway to balance two wheels to let the people ride. This Segway

robot is suitable for disabled people, the elderly or people walking legs. The Segfree

developed a Segway wheelchair. Robots used gyroscope to stabilize balancing. There are

to use feedback control. The main of the Segway to balance two wheels are left motor

and right motor which control the robot by gyroscope or accelerometer and two drive

motor which generated the robot forward, backward, turn left and turn right.

2.3 State space control algorithm

Before the design has to be mechanics model by using the state space equation to

stabilize balancing of the robot. The system consists of the A, B, C and D matrixes.

There are three parameter, inputs, state variable, and output. Thus, the state space provides

the dynamics with first-order differential equation.

Figure 2.5 System inputs and outputs

8

The properties of the system is the matrixes A and B which are determined by system

structure. The output matrixes C and D are determined by output variables. The standard

of state-space equation find dynamic system.

x(t)=Ax(t)+Bu(t)

y(t)=Cx(t)+Du(t)

Where:

x(t) : “state vector”

𝑦(𝑡) : “output vector”

u(t) : “input or control vector”

𝐴(𝑡) : “state or system matrix”

B(t) : “input matrix”

𝐶(𝑡) : “output matrix”

D(t) : “feed through”

And x(t)=d

dt x(t)

2.4 PID control algorithm

Type of feedback control algorithm is PID controller which PID is mean proportional, integral

and derivative. Normally PID controller basically used the error e(t) between the set

points and process variable. Therefore, a desire output given by the controller of the

error. The formula of PID shown as below. There are three terms of PID to calculate of total

gain.

u(t)= Kpe(t)+ Ki ∫ e(τ)dτ + Kd

d

dt

t

0

e(t

9

Where

u(t) : Input of system

Kp : The proportional gain

Ki : The integral gain

Kd : The derivative gain

e(t)=SP-PV(t) : The error of system

SP = set point and PV(t) = The process variable of system

t : Instantaneous times

e(τ) : Variable of the integration

Figure 2.6 PID controller block diagram

P gain is shown current values of the error I gain is shown previous values of the error

D gain is shown future values of the error

The adjusted value of gain, all of first is to set Ki and Kd to zero values. After that,

increase the Kp value until there is a loop oscillates system. Then adjust the Ki values to

increasing. On the other hand, if Ki value is very big, it will effect on unstable system.

Lastly, increasing Kd value until the system respond faster to reach. This is parameter for

setting to tuning method shown on table 2.3

Table 2.3 Effects of increasing a parameter

10

2.5 Linear model of a direct current (DC) motor

Figure 2.7 Diagram of a DC motor

For DC motor equation

V-Keω=Ldi

dt+Ri

τm-τL=Jmω+bmω

τm=KtKdi

ω=α

KtKdi-τL=Jmα+bmα

Where

V : the input of voltage

Ke : the constant of EMF

Kt. : the constant of torque

Kd : the ratio of transmission

τm : the torque of dc motor

τL : the load of torque

L : the coil inductance of armature

R : the coil resistance of armature

i : the current of armature

Jm : the moment inertia in dc motor

bm : the viscosity in dc motor

11

CHAPTER 3

METHODOLOGY

The methodology of a segway-type wheelchair give divided into three steps. The first of

all is to find the dynamic model of a Segway-type wheelchair robot system. The second

step is to design the physical and hardware of a segway-type wheelchair and create a new

prototype for the experiment. Moreover, there are electrical design also and are to design

controller. The last step is simulation in Matlab program and experiment real robot by

using PID controller.

3.1 Methodology flow chart

Figure 3.1 Methodology of flow chart to study

The methodology of this thesis have three steps to show in Figure 3.1. Firstly, there are

to find the dynamic equation of a Segway-type wheelchair robot by using the Newton

Euler method and state space representation, A, D, C and D matrixes. Second, I write

mechanical design in SolidWorks program. Then, there are physical model assembly and

hardware of a segway-type wheelchair. The last steps are to design a controller in order

to balance the Segway-type wheelchair robot by using the PID concept. Moreover, there

are simulation in Matlab and experiment real wheelchair robot.

12

3.2 Mechanical model

I designed the model a Segway type wheelchair itself. Figure 3.2 below. All parts of a

Segway type wheelchair has designed in SolidWorks program.

Figure 3.2 Parts of wheelchair design in SolidWorks

13

Then, all parts has designed of each part of a Segway-type wheelchair robot. Each parts

lead to assembly as the figure 3.3 which all assembly parts are importance for balancing

of a Segway-type wheelchair robot.

Figure 3.3 All part assembly of wheelchair robot

Therefore, this is of a Segway type wheelchair show on figure 3.4 as below. There are

there motor for control which left and right motor are balancing of control wheelchair

robot. Another motor is rotated of axis four wheels. A Segway type wheelchair has four

wheels because there are two function, balancing two wheels and up the stairs four

wheels.

Figure 3.4 Model of a Segway type wheelchair

14

3.3 Physical model

Real physical model of a Segway type wheelchair robot are importance to balancing.

There are many tools and equipment used doing wheelchair robot. All assembly of a

Segway type wheelchair are showing on figure 3.5 as below,

Figure 3.5 Physical model of a Segway type wheelchair

15

3.4 Electrical hardware configurations

The electrical and electronic circuit diagram of a Segway type wheelchair show on figure

3.6. The system of a Segway-type wheelchair robot consist of Microcontroller Arduino

MEGA 2560, three DC motor, three drive motor board, regular, three encoder, MPU6050

(Gyro & accelerometer fusion sensor) and two battery 12 V. All electrical and electronic

design are very importance to balance wheelchair robot.

Figure 3.6 Electrical and electronic hardware

16

3.4.1 Microcontroller features

Figure 3.7 Microcontroller Arduino MEGA 2560

Nowadays, there are many microcontroller for using to control robot balancing. However,

this thesis used the main of microcontroller Arduino MEGA 2560 board are given below.

There are 54 digital input/output pins. Moreover, PMW outputs can used 15 pin.

16 analog inputs, operation voltage 5V

4 UARATs (hardware serial ports), a USB connection, a power jack

I/O pin, current is 40 mA

3.3V pin, current is 50 mA

This microcontroller MEGA 2560 board can write program with the Arduino software

(IDE)

3.4.2 Driver DC motor board

Figure 3.8 H-bridge driver dc motor 80A

The main board are given below.

Output: DC supply 12-48V 80A and full-complementary power mosfet driver

Input: full opto-isollated input interface signals, 5V 8mA

Drive mode consist of on-off control, direction control and Speed control

Frequency of PWM = 400 Hz – 1000 Hz

17

3.4.3 BNO055 (Gyro and accelerometer)

Figure 3.9 BNO055 sensor

BNO055 sensor gives 9 DOF. Moreover, this sensor has fusion between accelerometer

with gyroscope. The main board are given below.

Power supply input = 3.3-5 V

The GND pin for power

Digital bidirectional I2C and UART interfaces

9-DOF

3.4.4 Regulator

Figure 3.10 Regulator output 5 V

There are IC7805 which it is a voltage regulator integrated circuit. IC7805 provides

+5V regulated power supply. The main board are given below,

The main board are given below,

Input 12 V

Output 5 V for supporting microcontroller Arduino MEGA 2560

18

3.4.5 DC Motor with encoder

Figure 3.11 DC motor 24 V

There are two dc motor for control balancing of robot and two encoder are counter push

of motor also. The main dc motor are given below,

Input DC ±24V

Output 100 rpm

Table 3.1 DC motor parameters

3.4.6 DC power supply features

Figure 3.12 Battery 12 V-7AH

This thesis, the robot used two battery for support Driver DC motor board ±24V.

19

Table 3.2 Battery specifications

3.4.7 Encoder

Figure 3.13 Encoder for counter motor

Encoders are used to measure cycle of rotating the motor. In order to know if the motor

rotates, encoder will be counter. This provided as below,

The output is an analog voltage such as 0-10V or ±5V

The output is an analog current such as a 4-20mA or 0-20 mA current loop.

The shaft shall be rotated at no load for a total of 20,000±1000 cycles, whereas 1

cycle is 360˚ rotation

20

+

3.5 Dynamic model of a Segway type wheelchair

For the wheel of the robot

Figure 3.14 Free body diagram of left wheel and the right wheel

Using Newton’s law

ΣFx = max

f-R = (M1+M2)α

f = (Mw1

+Mw2)α+R (3.1)

Forces around the center

Στ = Iα

τ-cα-fr = (Iw1+Iw2)α (3.2)

Then substitute equation (3.1) to equation (3.2)

τ-cα-((Mw1

+Mw2)x+R)r = (Iw1+Iw2)α

: For the left wheel

τ-cα-((Mw1

+Mw2)Lx+RL)r = (Iw1+Iw2)Lα (3.3)

: For the right wheel

τ-cα-((Mw1

+Mw2)Rx+RR)r = (Iw1+Iw2)Rα (3.4)

When

(Mw1

+Mw2)L = MwL

+

Note:

rL=rR=r

21

+

+

(Iw1+Iw2)L = IwL

(Mw1

+Mw2)R = MwR

(Iw1+Iw2)R = IwR

Then

τ-cα-rMwLx-rRL = IwLα (3.5)

τ-cα-rMwRx-rRR = IwRα (3.6)

Adding equation (3.5) and (3.6)

2τ-2cα-r(MwL

+MwR)x-r(RL+RR) = (IwL+IwR)α (3.7)

For the body of the robot

Figure 3.15 The dynamic model of the body robot

Using Newton’s law

ΣFx = max

RL+RR = Mb(x+∅hbcos∅-∅2hb sin ∅)

RL+RR=Mbx+Mb∅hbcos∅-Mb∅2hb sin ∅ (3.8)

ΣFy = may

N2L+N2R-Mbg = Mb(-∅hbsinθ-∅2hb cos ∅)

N2L+N2R = Mbg-Mb∅hbsin∅-Mb∅2hb cos ∅ (3.9)

∅2ℎ𝑏

∅ℎ𝑏

R

𝑁2

∅

𝑀𝑏g

ℎ𝑏

22

Στ = Iα

(N2L

+N2R)hbsin∅-(R

L+RR)h

bcos∅-2c∅ = Jb∅ (3.10)

Then, substitute (3.8) and (3.9) equation into (3.10) equation

(Mbg-Mb∅hbsinθ-Mb∅2hb cos ∅)hbsin∅-(Mbx+Mb∅hbcos∅-

Mb∅2hb sin ∅)hbcos∅-2c∅ = Ib∅

Mbghbsin∅-Mb∅(hb)2sin2∅-Mb∅

2hb cos ∅ hbsin∅-Mbxhbcos∅-

Mb∅(hb)2cos2∅+Mb∅

2hb sin ∅ hbcos∅-2c∅ = Ib∅

Mbghbsin∅-Mb∅(hb)2-M

bxhbcos∅-2c∅ = Ib∅

When x = αr

Mbghbsin∅-Mbαrhbcos∅-2c∅ = (Mb(hb)

2+Ib)∅

Then

∅ = 1

Mb(hb)2+Ib

(Mbghbsin∅-Mbαrhbcos∅-2c∅) (3.11)

Another, then substitute (3.8) equation into (3.7) equation

2τ-2cα-r(MwL

+MwR)x-r(Mbx+Mb∅hbcos∅-Mb∅2hb sin ∅) = (I

wL+IwR)α

2τ-2cα-r( MwL+MwR)x-Mbrx-Mb∅hbrcos∅+Mb∅

2hb rsin ∅ = (IwL

+IwR)α

When the x = αr

2τ-2cα-r( MwL+MwR)αr-Mbr2α-Mb∅hbrcos∅+Mb∅

2hb rsin ∅ = (IwL

+IwR)α

2τ-2cα-( MwLr2+MwRr2)α-Mbr2α-Mb∅hbrcosθ+Mb∅2hb rsin ∅ = (IwL+IwR)α

2τ-2cα-Mb∅hbrcosθ+Mb∅2hb rsin ∅ = ( MwLr2+MwRr2+Mbr2+I

wL+IwR)α

Then

α = 1

MwLr2+MwRr2+Mbr2+IwL+IwR(2τ-2cα-Mbθhbrcos∅+Mb∅

2hb rsin ∅) (3.12)

+

23

The process of linearization used to convert the unstable nonlinear model to linear model.

And θ ≈ 0

sin∅ ≈ θ

cos∅ ≈ 1

∅2𝜃 ≈ 0

The linearization is used in (3.11) and (3.12) equation

θ = 1

Mb(hb)2+Ib

(Mbghb∅-Mbαrhb-2c∅)

Where µ = Mb(hb)2+Ib

∅ = 1

µ(Mbghb∅-M

bαrhb-2c∅) (3.13)

Moreover

α = 1

MwLr2+MwRr2+Mbr2+IwL

+IwR

(2τ-2cα-Mb∅hbrcos∅+Mb∅2hb rsin ∅)

Where β = MwL

r2+MwRr2+Mbr2+IwL

+IwR

α = 1

β(2τ-2cα-Mb∅hbr) (3.14)

Substitute (3.14) equation into (3.13) equation

∅ =1

μ(Mbghb∅-M

brhb (

1

β(2τ-2cα-Mb∅hbr)) -2c∅)

∅ =1

μ(Mbghb∅- (

2τ Mbhbr

β-2cαMbhbr

β-(Mb)

2(hb)2r2∅

β) -2c∅)

∅ = (Mbghb

μ)∅- (

2Mbhbr

μβ) τ+ (

2Mbhbcr

μβ) α+ (

(Mb)2(hb)

2r2

μβ) ∅- (

2c

μ) ∅

(1-(Mb)

2(hb)2r2

μβ) ∅ = (

Mbghb

μ)∅- (

2Mbhbr

μβ) τ+ (

2Mbhbcr

μβ) α- (

2c

μ) ∅

24

Then

∅ = (βMbghb

μβ-(Mb)2(hb)2r2)∅- (

Mbhbr

μβ-(Mb)2(hb)2r2) τ+ (

2Mbhbcr

μβ-(Mb)2(hb)2r2) α-

(2βc

μβ-(Mb)2(hb)2r2) ∅

Where ρ = μβ-(Mb)2(hb)

2r2

∅ = (βMbghb

ρ)∅- (

2Mbhbr

ρ) τ+ (

2Mbhbcr

ρ) α- (

2βc

ρ) ∅ (3.15)

Substitute equation (3.13) into equation (3.14)

α =1

β(2τ-2cα-Mbhbr (

1

μ(Mbghb∅-M

bαrhb-2c∅)))

α =1

β(2τ-2cα-

(Mb)2(hb)

2gr∅

μ+

(Mb)2(hb)

2r2α

μ+

2Mbhbrc∅

μ)

α = (2

β) τ- (

2c

β) α- (

(Mb)2(hb)

2gr

μβ)∅+ (

(Mb)2(hb)

2r2

μβ) α+ (

2Mbhbrc

μβ) ∅

(1-(Mb)

2(hb)2r2

μβ) α = (

2

β) τ- (

2c

β) α- (

(Mb)2(hb)

2gr

μβ)∅+ (

2Mbhbrc

μβ) ∅

Then

α = (2μ

μβ-(Mb)2(hb)2r2) τ- (

2cμ

μβ-(Mb)2(hb)2r2) α-

((Mb)

2(hb)2gr

μβ-(Mb)2(hb)2r2)∅+ (

2Mbhbrc

μβ-(Mb)2(hb)2r2) ∅

When ρ = μβ-(Mb)2(hb)

2r2

α = (2μ

ρ) τ- (

2cμ

ρ) α- (

(Mb)2(hb)

2gr

ρ)∅+ (

2Mbhbrc

ρ) ∅ (3.16)

25

For the DC motor model is considered

From the motor equation

V-Keω=Ldi

dt+Ri

τm-τL=Jmω+bmω

τm=KtKdi

ω=α

KtKdi-τL=Jmα+bmα

Then

τL=τ=KtKdi-Jmα-bmα (3.17)

Substitute equation (3.17) to equation (3.16)

ρα =2μτ-2cμα-(Mb)2(hb)

2gr∅+Mbhbrc∅

ρα =2μ(KdKti-Jmα-bmα)-2cμα-(Mb)

2(hb)2gr∅+2Mbhbrc∅

(2μJm+ρ)α =2μKdKti-(2μb

m+2cμ)α-(Mb)

2(hb)2gr∅+2Mbhbrc∅

Then a new equation will be

α = 1

2μJm+ρ(2μKdK

ti-(2μb

m+2cμ)α-(Mb)

2(hb)2gr∅+2Mbhbrc∅) (3.18)

And substitute equation (3.17) to equation (3.15)

ρ∅ = βMbghb∅-2Mbhbr(KdKti-Jmα-bmα)+2Mbhbcrα-2βc∅

ρ∅ = βMbghb∅-2MbhbrKdKti+2MbhbrJ

mα+(2Mbhbrbm+2cMbhbr)α-2βc∅

26

For this term 2MbhbrJm

α

= 2MbhbrJm

(1

2μJm+ρ(2μKdK

ti-(2μb

m+2cμ)α-(Mb)

2(hb)2gr∅+2Mbhbrc∅))

= 4MbhbrJ

mμKdK

t

2μJm+ρi-

2MbhbrJm(2μb

m+2cμ)

2μJm+ρα-

2Jm(Mb)3(hb)

3gr2

2μJm+ρ∅+

4(Mb)2(hb)

2r2Jmc

2μJm+ρ∅

Then substitute back

ρ∅ = βMbghb∅-2MbhbrKdKti+

4MbhbrJm

μKdKt

2μJm+ρi-

2MbhbrJm(2μb

m+2cμ)

2μJm+ρα-

2Jm(Mb)3(hb)

3gr2

2μJm+ρ∅+

4(Mb)2(hb)

2r2Jmc

2μJm+ρ∅+(2Mbhbrbm+2cMbhbr)α-2βc∅

ρ∅ = (βMbghb-Jm(Mb)

3(hb)3gr2

2μJm+ρ)∅- ( 2MbhbrKdK

t+

4MbhbrJm

μKdKt

2μJm+ρ) i-

( 2MbhbrJ

m(2μb

m+2cμ)

2μJm+ρ+2Mbhbrbm+2cMbhbr) α+ (

4(Mb)2(hb)

2r2Jmc

2μJm+ρ-2βc) ∅

When A = Mbhbr

B = Jm

2μJm+ρ

ρ∅ = ( βAg

r-gMbhbA

2B)∅-(2AKdK

t+4ABμKdK

t)i-

(2AB(2μbm

+2cμ)+2Abm+2cA)α+(4A2Bc-2βc)∅

Then another equation will be

∅ = 1

ρ((

βAg

r-gMbhbA

2B)∅-(2AKdK

t+4ABμKdK

t)i-

(2AB(2μbm

+2cμ)+2Abm+2cA)α+(4A2Bc-2βc)∅) (3.19)

27

The motor model is

V-Keω = Ldi

dt+Ri

Inductance is less than resistance (L<<R).

V-Keω ≈ Ri

Then

i≈V-Keω

R ≈

V

R-

Ke

Rα (3.20)

Substitute equation (3.20) into equation (3.18)

α =1

2μJm+ρ(2μKdK

t(V

R-Ke

Rα) -(2μb

m+2cμ)α-(Mb)

2(hb)2gr∅+2Mbhbrc∅)

α=1

2μJm+ρ(

2μKdKt

RV- (2μb

m+2cμ+

2μKdKtKe

R) α-(Mb)

2(hb)2gr∅+2Mbhbrc∅) (3.21)

Moreover, substitute equation (3.20) into equation (3.19)

θ = 1

ρ((

βAg

r-gMbhbA

2B)∅-(2AKdK

t+4ABμKdK

t) (

V

R-Ke

Rα) -

(2AB(2μbm

+2cμ)+2Abm+2cA)α+(4A2Bc-2βc)∅)

∅ = 1

ρ((

βAg

r-gMbhbA

2B)∅- (

2AKdKt+4ABμKdKt

R) V+ ((

2AKdKtKe

R+

4ABμKdKtKe

R) -

(2AB(2μbm

+2cμ)+2Abm+2cA)) α+(4A2Bc-2βc)∅) (3.22)

3.6 The state space model

If equation of the mechanics of the system is complete, the state space representation are

shown inputs, outputs and state variables. The standard formula of state space shown as

below, y(t) shown by output, x(t) shown by state of the system.

28

State space model of the longitudinal will be

x=Ax+BV

x=[α α ∅ ∅] T

y=[α ∅] T

From equation (20) and (21) can write the matrix of state space representation as below

Then,

A=

[ 0 1 0 0

0 -1

2μJm+ρ(2μb

m+2cμ+

2μKdKtKe

R) -

1

2μJm+ρ((Mb)

2(hb)2gr)

1

2μJm+ρ(2Mbhbrc)

0 0 0 1

01

ρ(((

2AKdKtKe

R+

4ABμKdKtKe

R) -(2AB(2μb

m+2cμ)+2Abm+2cA)))

1

ρ((

βAg

r-gMbhbA

2B))

1

ρ(4A

2Bc-2βc)

]

(3.23)

B=

[

01

2μJm+ρ(

2μKdKt

R)

01

ρ(-

2AKdKt+4ABμKdKt

R)]

(3.24)

C= [1 0 0 0

0 0 1 0] (3.25)

D=0 (3.26)

Where

µ=Mb(hb)2+Ib

β= MwL

r2+MwRr2+Mbr2+IwL

+IwR

ρ=μβ-(Mb)2(hb)

2r2

A=Mbhbr

B=Jm

2μJm+ρ

29

3.7 Parameter identification

If equation of the mechanics of the system is complete, the state space representation are

shown inputs, outputs and state variables. The standard formula of state space shown as

below, y(t) shown by output, x(t) shown by state of the system.

Table 3.3 The table of constant parameter for balancing

The constant parameter Value Unit

The mass of the body (𝑀𝑏) 5.2 kg.

The mass of the wheel (𝑀𝑤) 0.5 kg.

The high the body (ℎ𝑏) 0.8 m.

The moment inertia of the wheel (𝐼𝑤) 0.0025 kg.m2

The moment inertia of the body (𝐼𝑏) 1.667 kg.m2

The viscosity friction of wheel (c) 0.002 kg.m2/s

The transmission ratio (𝐾𝑑) 51.8

Torque DC constant (𝐾𝑡) 0.0093687 N.m/A

Back EMF constant (𝐾𝑒) 0.9857 Volt/rad/sec

The friction in the DC motor (𝑏𝑚) 0.002 N.m.s/rad

Resistance (𝑅) 10.585 Ω

The moment inertia of the DC motor (𝐽𝑚) 2.2284x10−6 kg.m2

Gravity (𝑔) 9.8 m/s2

The radius of wheel robot (r) 0.1 m

These parameter were derived from experiments and calculations.

30

3.8 Control algorithms of a Segway-type robot

There are consist of two transfer functions of a Segway-type wheelchair to balance.

Therefore, there are two output or two transfer function of a Segway-type wheelchair

robot system. The first transfer function is the angle of the wheel to changer divided

voltage output and the second transfer function is the leaning angle of the robot to changer

divided voltage output.

In conclusion, the first transfer function is

α

V=

0.0505s2-5.159e-05+1.193

s4+1.155s3-15.59s2-17.96s+2.107

Continuous-time transfer function.

∅

V=

-0.9401s2-1.084s+0.0505

s4+1.155s3-15.59s2-17.96s+2.107

The characteristic equation will be

s4+1.155s3-15.59s2-17.96s+2.107

And the pole of this system is

Figure 3.16 Pole of system

p = 3.9339, -3.9259, -1.2703, 0.1074

31

3.9 Data of experiment

There are control the balancing of robot by PID controller. Thus I would like to keep the

data, Output of PID, set point, value of sensor to read and error of angle of robot. I used

HyperTerminal program to keep data.

Figure 3.17 Data of experiment balancing robot

32

CHAPTER 4

RESULTS AND DISCUSSION

This chapter, as the results divided in two parts, Frist, there are simulation results in

Matlab program. I got two transfer function by calculate from state space A, B, C and D

matrixes with many control algorithms. Second, experiment results.is tested balancing

with real a Segway-type wheelchair robot.

State space matrix is

A = [

0 1 0 0

0 -1.1544 -2.1067 1.033e-04

0 0 0 1

0 0.0169 15.5910 -9.0153e-04

]

B= [

0

0.0505

0

-0.9401

]

C= [1 0 0 0

0 0 1 0]

D=0

4.1 Simulation results in Matlab software

Equation (3.20) and (3.21) is used to balance of a Segway-type wheelchair robot the

parameter gain is by error method

Kp = 1000, Ki = 100, Kp = 60

In the Matlab program, there are Matlab Simulink block which can find the leaning angle

of a Segway-type wheelchair robot and leaning rate of wheels of wheelchair robot.

Moreover, control algorithms used PID controller. Figure 4.1 is PID simulation model.

The PID simulation result for balancing shown on figure 4.2

33

Figure 4.1 The PID simulation model

Figure 4.2 The PID simulation result for balancing

From the simulation result in Figure 4.2 the disturbance noise effect on the angle output.

The system angle of robot cannot be zero which its swing around set point. Average

value of the leaning angle of robot is 0.352 rad. In addition, Average value of the learning

angle of wheel robot is 10.038 rad/s

34

4.2 Experimental result

The software and controller has been designed for a Segway type wheelchair as shown in

Figure 4.3 below. PID controller used for balancing with gain, Kp =160, Ki = 10 and Kd

= 0.09. The result show as figure 4.4

Figure 4.3 Real robot for balancing

Figure 4.4 The PID experiment result of balancing

Average value of the learning angle of robot is 1.012 rad

35

CHAPTER 5

CONCLUSIONS AND FUTURE WORKS

5.1 Conclusions

A Segway-type wheelchair robot is the robot which can balance two wheels. In this thesis,

there are three parts about a Segway-type wheelchair robot. Frist of all, mechanic design

and dynamic model are very importance about the balancing concept. Moreover, all parts,

speed of each motor and the weight of robot are effected on balancing robot also. Second,

electronic design is important also. Moreover, there are using the layout of all electronic

such as Gyroscope & accelerometer sensor, regulator and drive control dc motor. Finally,

PID controller is the control algorithm to balancing the wheelchair robot which A

Segway-type wheelchair robot can be to balance the two wheels.

The result of control consist of two parts; simulation and experiment result. The first one

is simulation result which the dynamic model of a Segway-type wheelchair robot. A

Segway-type wheelchair robot to balance fix by using the Newton Euler and Matlab

program for Simulink the result. The control system selected by PID algorithm. Another,

the experiment result is applied in real system. A Segway-type wheelchair used PID

controller which used to control error of angle of the body robot and used to find position

of right wheel and left wheel for balancing by itself.

In addition, a Segway-type wheelchair robot can be the simulation result that is very good.

The dynamic model provide state space of real robot. Thus, there are two transfer function

to control angle of the body robot and position in rotate of wheels.

5.2 Future works

This thesis, a Segway-type wheelchair robot would like develop to movement, forward,

backward, turn right and turn left by joystick. Some mechanic should have modifies and

implement. For example, motor have to more power and using another algorithm control.

36

REFERENCES

[1] Her-Terng Yau1 , Cheng-Chi Wang2 , Neng-Sheng Pai1 and Ming-Jyi Jang2,

Robust Control Method Applied in Self-Balancing Two-Wheeled Robot,

Taiwan,2009.

[2] M. Baloh, and M. Parent, “Modeling and model verification of an intelligent self-

balancing two-wheeled vehicle for an autonomous urban transportation system,”

Proc. Conf. Comp. Intelligence, Robot. Autonom. Syst., Singapore, 2003.

[3] Vos, D.W. and Von Flotow, A.H.(1999), Dynamics and nonlinear adaptive

control of an autonomous unicycle: theory and experiment, Decision and Control,

1990., Proceedings of the 29th IEEE, pp. 182-187.

[4] Junfeng Wu, Vos, Wanying Zhang and Shengda Wang, A two-wheeled self-

balancing robot with the fuzzy PD control method: theory and experiment.

[5] D. Dubois and H. Prade, “Fuzzy sets in approximate reasoning. I. Inference with

possibility distributions,” Fuzzy Sets and Systems, vol. 40, no. 1, pp. 143–202,

1991.

[6] Segway. Segway - the leader in personal, green transportation. Online, 2013.

http://www.segway.com.

[7] Williams V. & K. Matsuoka, 1991 ‘ Learning to Balance the Inverted Pendulum

Using Neural Networks’, IEEE International Joint Conference on Neural

Networks, vol 1, pp. 214-219.

37

APPENDIX

Appendix A: C code for control a segway-type wheelchair

#include <BNO055.h>

#include <Encoder.h>

#include <DualVNH5019MotorShield.h>

#include <MsTimer2.h>

#include <PID_v1.h>

#include <Wire.h>

#define ENCODER_OPTIMIZE_INTERRUPTS

void loop(void)

imu.readEul();

controlLoop();

//delay(5000);

Serial.print("Setpoint: ");Serial.print(Setpoint);

Serial.print(" ");

Serial.print("PV: ");Serial.print(balanceInput);

Serial.print(" ");

Serial.print("Eror: ");Serial.println(balanceInput);

Serial.print(" ");

Serial.print("Output: ");Serial.print(balanceOutput);