maze solving vehicle

MAZE SOLVING AUTONOMOUS VEHICLE (NATIONAL ENGINEERING ROBOTICS CONTEST 2014)

AUTHORS

M. ISMAIL ZAFAR 10-MCT-08

SAQUIB SAEED 10-MCT-25

OMER SHAHZAD MUGHAL 10-MCT-31

ABDUL HANNAN SHAHID 10-MCT-35

SUPERVISOR

ENGR. SHOAIB ASLAM

JUNE 2014

DEPARTMENT OF MECHATRONICS ENGINEERING UNIVERSITY OF ENGINEERING & TECHNOLOGY TAXILA

SUB CAMPUS CHAKWAL

Maze Solving Autonomous Vehicle

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Table of Contents

List of Figures .................................................................................................................. vii

List of Tables ..................................................................................................................viii

List of Equations ............................................................................................................... ix

List of Software.................................................................................................................. x

List of Symbols ................................................................................................................. xi

List of Abbreviations ....................................................................................................... xii

Certificate ........................................................................................................................xiii

Undertaking ....xiv

Acknowledgment ............................................................................................................. xv

Abstract ........................................................................................................................... xvi

Chapter # 1 ......................................................................................................................... 1

1.1 Introductions ............................................................................................................. 2

1.2 Working Principle..................................................................................................... 2

1.3 Main Features ........................................................................................................... 3

1.4 Applications .............................................................................................................. 3

Chapter # 2 ......................................................................................................................... 4

2.1 Literature review ....................................................................................................... 5

2.2 Research Paper # 1 ................................................................................................... 5

2.2.1 Abstract .............................................................................................................. 5

2.2.2 Working Principle: ............................................................................................. 5

2.2.3 Conclusion:......................................................................................................... 7

2.3 Research Paper # 2 ................................................................................................... 8

2.3.1 Abstract: ............................................................................................................. 8

2.3.2 Working Principle .............................................................................................. 8

2.3.3 Conclusion:....................................................................................................... 10


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2.4 Research Paper # 3 ................................................................................................. 10

2.4.1 Abstract ............................................................................................................ 10

2.4.2Working Principle ............................................................................................. 10

2.4.3 Conclusion:....................................................................................................... 12

2.5 Research Paper # 4 ................................................................................................. 13

2.5.1 Abstract: ........................................................................................................... 13

2.5.2 Methods and Working Principle: ..................................................................... 13

2.5.3 Conclusion ........................................................................................................ 14

2.6 Research Paper # 5 ................................................................................................. 15

2.6.1 Abstract ............................................................................................................ 15

2.6.2 Conclusion ........................................................................................................ 15

Chapter # 3 ....................................................................................................................... 16

3.1 Adopted methodology ............................................................................................ 17

3.1.1 Dead End filling ............................................................................................... 17

3.1.2 Wall Following ................................................................................................. 17

3.1.3 Line Tracking (Pure Pursuit Algorithm) .......................................................... 18

Chapter # 4 ....................................................................................................................... 19

4.1 Mechanical Design ................................................................................................. 20

4.1.1 Selection of Material ........................................................................................ 20

4.1.2 3-Dimensional Modeling and robot dimensions .............................................. 21

4.2 Fabrication .............................................................................................................. 22

4.3 Mechanical Components ........................................................................................ 23

4.4 Feasibility of hardware ........................................................................................... 23

4.4.1 Selection of Motors: ......................................................................................... 23

4.4.2 Acceleration Torque ......................................................................................... 25

4.4.3 Total Torque ..................................................................................................... 26


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4.5 Justification of above design .................................................................................. 26

4.6 Power Calculations ................................................................................................. 26

4.7 Cotter joint design considerations for chains in sprocket chain mechanism .......... 28

4.7.1 Failure of the rods in tension ............................................................................ 30

4.7.2 Failure of spigot in tension ............................................................................... 30

4.7.3 Failure of the rod or cotter in crushing ............................................................. 31

4.7.4 Failure of the socket in tension across the slot ................................................. 32

4.7.5Failure of cotter in shear.................................................................................... 33

4.7.6 Failure of the socket collar in crushing ............................................................ 33

Chapter # 5 ....................................................................................................................... 35

5.1 Electronics Circuitry ............................................................................................... 36

5.2 IR Proximity sensor ................................................................................................ 37

5.2.1 Working ............................................................................................................ 37

5.2.2 Reason for using IR Proximity sensor.............................................................. 38

5.3 Color and Line tracking Sensors ............................................................................ 39

5.3.1 Working ............................................................................................................ 40

5.3.2 Reason for using LDR ...................................................................................... 40

5.4 Motor driving circuit H-Bridge .............................................................................. 40

5.4.1 Using electro - mechanical relays .................................................................... 41

5.4.2 H Bridge using MOSFETs (Switched through Transistors (BJTs)) ............. 42

Chapter # 6 ....................................................................................................................... 44

6.1 Embedded System (ARDUINO Kit) ...................................................................... 45

6.2 Why ARDUINO mega?.......................................................................................... 45

6.2.1 Power ................................................................................................................ 45

6.2.2 Memory ............................................................................................................ 45

6.2.3 USB over current Protection ............................................................................ 46


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6.2.4 ADC ................................................................................................................. 46

6.2.5 ADC Conversion Result ................................................................................... 46

6.2.6 Programming .................................................................................................... 46

6.3 Programming Language used ................................................................................. 46

6.3.1 Examples .......................................................................................................... 47

6.4 Compiling Software ................................................................................................ 48

6.5 Source Code ............................................................................................................ 48

Chapter # 7 ....................................................................................................................... 49

7.1 Mathematical modeling using Control Systems Techniques ................................. 50

7.2 Modeling of electrical circuitry (motor driving circuits)........................................ 50

7.3 Modeling of mechanical and electromechanical part ............................................. 51

7.4 Simulation in MATLAB SIMULINK .................................................................... 54

7.4.1 Simulation Diagram: ........................................................................................ 54

7.4.2 Output Graph of Simulation diagram ............................................................... 55

Chapter # 8 ....................................................................................................................... 56

8.1 Mechatronics system .............................................................................................. 57

8.1.1 Control systems ................................................................................................ 57

8.1.2 Digital control systems (DCS) ......................................................................... 57

8.1.3 Computers ........................................................................................................ 58

8.1.4 Mechanical System .......................................................................................... 58

8.1.5 Electronics systems .......................................................................................... 58

8.2 Phases of Mechatronics system design ................................................................... 58

8.2.1 Modeling and Simulation ................................................................................. 59

8.2.2 Recognition of Need......................................................................................... 59

8.2.3 Conceptual Design ........................................................................................... 59

8.2.4 Mathematical modeling and Control system modeling.................................... 59


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8.2.5 Prototyping and System Development ............................................................. 59

8.3 General Block Diagram of Mechatronics System .................................................. 60

8.4 Block Diagram of our Mechatronics System ......................................................... 61

8.5 Comparison of General and our Mechatronics system design ............................... 62

8.5.1 Recognition of need and evaluation of engineering specs ............................... 62

8.5.2 Mechanical System .......................................................................................... 62

8.5.3 Electrical System .............................................................................................. 62

8.5.4 Electronic System ............................................................................................. 62

8.5.5 Control System ................................................................................................. 62

8.5.6 Operating Hardware ......................................................................................... 62

8.5.7 Process Design ................................................................................................. 63

8.5.8 Electronic Design ............................................................................................. 63

8.5.9 Hardware and Software Integration ................................................................. 63

8.5.10 Fabrication ...................................................................................................... 63

8.5.11 System testing ................................................................................................ 63

Future Work ..................................................................................................................... 65

Conclusion ....................................................................................................................... 68

Appendix .......................................................................................................................... 68

References ........................................................................................................................ 74


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List of Figures

Figure 2.1: Block Diagram RP........................................................................................... 7

Figure 2.2: Pure Pursuit Algorithm .................................................................................... 9

Figure 2.3: Random Mouse Algorithm ............................................................................ 11

Figure 2.4: Tremauxs Algorithm .................................................................................... 12

Figure 4.1(a) : 3D Modeling ............................................................................................ 21

Figure 4.1(b) : Picture of Robot ....................................................................................... 22

Figure 4.2: Free Body Diagram of Robot ........................................................................ 24

Figure 4.3: Free Body Diagram of Mechanical Power Consumption ............................. 27

Figure 4.4: Cotter Joint 2D Drawing ............................................................................... 28

Figure 4.5: Failure of spigot in tension ............................................................................ 31

Figure 4.6:Failure of the rod crushing ............................................................................. 31

Figure 4.7:Failure of socket in tension ............................................................................ 32

Figure 4.8:Failure of cotter in shear ................................................................................. 33

Figure 4.9 Socket collar Failure ....................................................................................... 34

Figure 5.1: Complete circuit of our Project on Proteous ................................................. 37

Figure 5.2: Working of IR Sensor.................................................................................... 38

Figure 5.3: IR sensor principle......................................................................................... 38

Figure 5.4:Color sensor cicuit diagram ............................................................................ 39

Figure 5.5: H-Bridge via Relays ...................................................................................... 41

Figure 5.6: H-Bridge via Mosfets .................................................................................... 42

Figure 6.1: ARDUINO Kit .............................................................................................. 45

Figure 7.1: Electrical Circuit Modeling ........................................................................... 50

Figure 7.2: Modeling of Motors....................................................................................... 51

Figure 7.3: Motor interface .............................................................................................. 53

Figure 7.4: MATLAB SIMULINK diagram ................................................................... 54

Figure 7.5: MATLAB SIMULINK graph ....................................................................... 55

Figure 8.1: Mechatronics system ..................................................................................... 57

Fig 8.2: Phases of Mechatronics system .......................................................................... 58

Fig 8.3: General Block Diagram of Mechatronics system ............................................... 60

Fig 8.3:Block Diagram of our Mechatronics system ....................................................... 61

Figure 8.4: General Block Diagram of our system .......................................................... 63


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List of Tables

Table 4.1: Dimensions of Robot ...................................................................................... 22

Table 4.2: Mechanical Components ................................................................................ 23

Table 5.1: Electrical Components .................................................................................... 36

Table 6.1: General Commands of AURDUINO v1.1.8 ................................................... 47


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List of Equations

Equation 4.1: Weight of Robot ........................................................................................ 24

Equation 4.2: Moment of Inertia ...................................................................................... 24

Equation 4.3: Gravitational Torque ................................................................................. 24

Equation 4.4: Frictional Torque ....................................................................................... 25

Equation 4.5: Load Torque .............................................................................................. 25

Equation 4.6: Uniform velocity equation......................................................................... 25

Equation 4.7: Total Torque .............................................................................................. 26

Equation 4.8: Mechanical Power ..................................................................................... 27

Equation 4.9: Failure of rod ............................................................................................. 30

Equation 4.10: Failure of spigot....................................................................................... 31

Equation 4.11: Failure of the cotter ................................................................................. 31

Equation 4.12: Failure of the socket ................................................................................ 32

Equation 4.13: Failure of cotter ....................................................................................... 33

Equation 4.14: Socket collar failure ................................................................................. 34

Equation 7.1: Loop 1 differential equation. ..................................................................... 50

Equation 7.2: Loop 2 Differential eq. .............................................................................. 51

Equation 7.3: Loop 2 differential eq. ............................................................................... 51

Equation 7.4: Transfer function of motor ........................................................................ 52


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List of Software

1- Solid Edge V16

2- Proteus V7

3- ARDUINO MEGA Training Kit Programming Software

4- MATLAB 2007a

5- Microsoft Office


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List of Symbols

P= load carried by the rods

D= diameter of the rods,

D1= outside diameter of socket,

D2= diameter of spigot or inside diameter of socket

D3= outside diameter of spigot collar

T1= thickness of spigot collar

D4= diameter of socket collar

C = thickness of socket collar

B= mean width of cotter

T = thickness of cotter

L = length of cotter

A= distance from the end of the slot to the end of rod

= Torque

c= Crushing Stress

r = radius of wheel

Tm(s) = in terms of m(s) if we are to separate the input and output variables and obtain

the transfer function, m(s)/Ea(s).

Jm = inertia at the armature and includes both the armature inertia and, the load inertia

Dm = viscous damping at the armature and includes both the armature viscous damping

and, the load viscous damping


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List of Abbreviations

Direct Current (DC)

Rotations per Minute (rpm)

Volts (V)

3-Dimensional (3D)

Infrared (IR)

Input and Output (I/O)

Light Dependent Resistance (LDR)

Artificial Intelligence (AI)

Control System Runs Based maze solving algorithm (LSRB)

Maze Solving Robot (MSR)

Central Processing Unit (CPU)

Analog to Digital Converter (ADC)

Digital to Analog Converter (DAC)

Bipolar Junction Transistor (BJT)

Light Emitting Diode (LED)

Pulse width Modulation (PWM)

Electrically Erasable Program able Read Only Memory (EEPROM)

Alternating Current (AC)

Static Random Access Memory (SRAM)

Universal Storage Bus (USB)

Millie Amperes (mA)

Input Voltage (Vin)

Output Voltage (Vref)

Analog to Digital converter Interrupt Flag (ADIF)

Analog to Digital converter least significant value (ADCL)

Analog to Digital converter highest significant value (ADCH)

Computer Aided Design (CAD)

Metal Oxide Semi-conductor Field Effected Transistor (MOSFET)

Sound Navigated And Ranging (SONAR)

National Engineering Robotics Contest (NERC)

Global Positioning system (GPS)


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Certificate

This is to certify that M. Ismail Zafar, Saquib Saeed, Omer Shahzad Mughal and

Abdul Hannan Shahid have successfully completed their final year project. This

project Maze Solving Autonomous Vehicle had been assigned to them to fulfill

the partial requirements for the bachelor degree of Mechatronics Engineering.

Engr. Shoaib Aslam

Project Supervisor

Engr. Amir Sultan

Chairman


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Undertaking

We certify that project work titled Maze solving autonomous vehicle is our own work.

The work has not, in whole or in part, been presented elsewhere for assessment. Where

material has been used from other sources it has been properly referred.

____________________

M. Ismail Zafar

(10-MCT-08)

____________________

Saquib Saeed

(10-MCT-25)

____________________

Omer Shahzad Mughal

(10-MCT-31)

____________________

Abdul Hannan Shahid

(10-MCT-35)


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Acknowledgment

We have taken efforts in this project. However, it would not have been possible

without the kind and merciful support and help of Allah Almighty and support of many

individuals and organizations. We would like to extend our sincere thanks to all of them.

We are highly indebted to our project advisor Engr. Shoaib Aslam for his

guidance and constant supervision as well as for providing necessary information

regarding the project.

We are thankful to our parents and family members for their support and

motivation throughout the project morally and monetarily.

We are obliged to faculty members of our campus, for the valuable information

provided by them in their respective fields. We are grateful for their cooperation during

the period of our project.


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Abstract

The main objective of the project is to come up with an autonomous robot that

can imitate the behavior of a Self-Guided Vehicle in an industry with manual loading

and automatic unloading at specified location. As we are also have a vision to win the

NERC 2014. So, we are preparing our vehicle on the theme of NERC 2014. Therefore,

we have to design the vehicle in the light of rules of NERC 2014.

We have selected aluminum sheet as material for the base of autonomous vehicle

because of its unique property of providing maximum strength with considerable less

weight than other metals. The DC Gear Motor having torque of 266 Nm and angular

speed 150 rpm was chosen over various other motors because the DC gear motor can

provide much greater torque than simple DC motor at same power rating. Chains of

suitable dimensions were used to provide drive to the wheels through motor. Mechanical

modeling of the project was implemented on Solid Edge (V16) successfully and after

consulting with our project supervisor, 3D model was translated and converted into

hardware.

We have used IR proximity sensors and SONAR sensor to perform path finding

and maze solving operations. IR proximity sensors are preferred over SONAR because

of its precision, high data refreshing rate and it is convenient to interface IR sensor with

AURDUINO kit than SONAR and other proximity sensors. Five IR proximity sensors

are used to solve the maze and for the alignment of vehicle in the arena while just a

single SONAR is interface with AURDUINO for the detection of wall in any case of

reverse motion. LDR based color sensors would be used for color detection and line

tracking operations in the workspace. Color detection is needed at the starting spot

where the vehicle would detect its initial path which it has to follow to reach at

unloading position and it would also be needed at traffic signals (zone detection) where

the vehicle had to stop during the course of its journey.

AURDUINO kit has been preferred over PIC and AVR microcontrollers

because it has more I/O terminals, operating power ratings are more desirable with a

less probability of burning out, data processing and execution speed are higher, higher

analog to digital convertor resolution and also there is no need for separate burner to

burn code into controller of AURDUINO kit.

To check the stability of our system (autonomous vehicle), the complete


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mathematical modeling of the system was done using the techniques of control system

by which an improper fraction of transfer function was obtained. This equation

contains some constant factors related to the specifications of motor and would be

available to us when the pre ordered motors along with their data sheets will arrive.

Using MATLAB, the improper fraction has been converted into a proper one, than we

checked the stability of the equation by undergoing simulation in MATLAB

SIMULINK.


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Chapter # 1

Preliminary Concepts



1.1 Introductions

The main objective of the project is to come up with an autonomous robot that

can imitate the behavior of a Self-Guided Vehicle in an industry with manual loading

and automatic unloading at specified location. A maze is a tour puzzle in the form of a

complex branching passage through which the solver must find a route. In everyday

speech, both maze and labyrinth denote a complex and confusing series of pathways, but

technically the maze is distinguished from the labyrinth, as the labyrinth has a single

through-route with twists and turns but without branches, and is not designed to be as

difficult to navigate. The pathways and walls in a maze or labyrinth are fixed (pre -

determined) puzzles where the walls and paths can change during the game are

categorized as tour puzzles.

The robot consists of Analog sensor array (Five IR Proximity sensors and one

SONAR); the Arduino board must stay centered within the base wood to prevent

compounding errors in distance and damages with the obstacles. Controlling the motors

is responsible for safely moving the robot through the maze. There are two

motors, each, with RPMs of 150 to carry a weight of about 13kg (including board and

battery). In order to ensure that the robot is not slipping and to avoid collision with the

obstacles, the motors are controlled with IR Proximity sensor. And according to our

needs, we can make use of it to control the speed of the motors. The chases need to carry

the board, circuits, sensors and batteries. And the chases are designed to turn 90 and

180. If the and track branching or ending are available in the routing, then it makes the

decision based on the algorithms.

1.2 Working Principle

The vehicle using inputs from the sensors selects the most suitable path of the

given paths to reach a particular point. Then after reaching at that point (where it has

to unload) the vehicle has to manage itself in the middle of walls or obstacles of

maze. For this purpose, a line is present on the floor of maze and by following that

line vehicle will align itself in the center for better unloading. So, these are the main

points in working principle:

1- Wall following and Pledge algorithm

2- Pure pursuit algorithm



1.3 Main Features

The robot is capable of solving the maze provided by using a combination of

algorithms thats why it is able to deal with a large variety of mazes. The robot we have

designed is also equipped with color sensors for detection of traffic signals which is

helpful in zone detection in case of industrial trucks. The robot is also equipped with line

tracking sensor which will guide the robot through an area in which there are no walls

present in maze and also help in attaining a perfect alignment between walls of the path.

We can also use an additional SONAR sensor in case there is noise in the inputs from IR

sensor. The unloading mechanism has two slots which will help in accommodation of

more material to deliver.

1.4 Applications

1- Spy robots

2- Suicidal robots

3- Inspection Robots

4- Automated Industrial Trucks etc.

5- Bomb Sniffing robots



Chapter # 2

Literature review



2.1 Literature review

Many engineers have worked on such type of projects. The main difference

among maze solving robots is the use of technique for solving the maze (finding

path).Here we will discuss those research works which have helped us in compiling

maze solving technique for our robot.

2.2 Research Paper # 1

Title: An Autonomous Robot Framework for Path Finding and Obstacle Evasion

Authors: Imran Sarwar Bajwa,Natasha Nigar and M J Arshad

Year of publication: November 2011

2.2.1 Abstract

When the history of world would be written surely out contemporary age would

be called the age of science and technology. The marvels of science and technology has

not only bewildered human minds but also brought convenience and quality to human

life. Our project is continuation of this tradition of science. We have endeavored to

design an autonomous path tracker vehicle. It has limitless possibilities of usage and it

would certainly become a future workhorse. It can be used to detect the theft vehicles.

Autonomous robot for path finding and obstacle evasion is a vehicle, which follows the

path in two different ways, which are:

2.2.1.1 Line Follower:

It is a vehicle, which is used to follow the reflecting line drawn on the floor. It

captures line position with IR sensors. The sensors will be mounted at front end of the

robot.

2.2.1.2 Obstacle Handling:

When an obstacle is appeared on the following line we will detect through a

sensor.

2.2.2 Working Principle:

There are two things in its working:

2.2.2.1 Line following:

The robot will follow the reflecting line drawn on the floor with the help of LDR

sensor. So, according to our requirement the robot should follow the line perfectly then



the positions of the sensors must be perfect. Now robot is left free on that line. Robot

will follow the line sensing it through the sensors placed on the front bottom of the

robot.

2.2.2.1.1 Pure Pursuit Algorithm

These algorithms utilize the spatial information for the sake of computation of

the guiding commands and assist a robot in following a given path or stripe.

However, both these algorithms do not often consider the actual curves of the target

path/stripe. Due to this short coming of this algorithm, this provides with less

accuracy.

These are the following steps which used to find the unknown path for a robot.

1- Obtain current position of the vehicle.

2- Find the goal point.

3- Calculate the point on the path closest to the vehicle.

4- Compute a certain look-ahead distance D.

5- Obtain goal point by moving distance D up the path from point.

6- Transform goal point to vehicle coordinates.

7- Compute desired curvature of the vehicle.

8- Move vehicle towards goal point with the desired curvature.

9- Obtain new position and go to point 2.

2.2.2.2 Wall Following:

The obstacles in the way of the robot will be detected by the sensors (IR analog)

mounted on the sides, front and back of the robot. When an obstacle will be detected the

robot will stop and turn to that side where the obstacle is not present.

2.2.2.2.1 Dead-end filling Algorithm

Dead-end filling is an algorithm for solving mazes that fills all dead ends,

leaving only the correct way unfilled. It can be used for solving mazes on paper or with

a computer program, but it is not useful to a person inside an unknown maze since this

method looks at the entire maze at once. The method is following:

1- Find all of the dead-ends in the maze, and then

2- "Fill in" the path from each dead-end until the first junction met.

Dead-end filling cannot accidentally "cut off" the start from the finish since each

step of the process preserves the topology of the maze. Furthermore, the process won't



stop "too soon" since the end result cannot contain any dead-ends. Thus if dead-end

filling is done on a perfect maze (maze with no loops) then only the solution will

remain. If it is done on a partially braid maze (maze with some loops), then every

possible solution will remain but nothing more.

Figure 2.1: Block Diagram RP2

2.2.3 Conclusion:

The motion of robot will be controlled by the line tracking and the obstacle

sensors on the path from start to the end point. A vehicle will following an ascender that

will send the path to the follower, follower will follow that path. This is done using

storing the signal values and particular time for which a value is retained is stored in the

memory of controller and when there is no signal interrupt from user then all of the data

from memory contents is sent to the memory of the other controller. Then this data is

executed by the follower which results in following the same path that is followed by the

leader vehicle.




Title: Path Tracking for a Miniature Robot

Authors: Martin Lundgren

Year Of publication: 2003

2.3.1 Abstract:

Path tracking is the process concerned with how to determine speed and steering

settings at each instant of time in order for the robot to follow a certain path. A path

consists of a set of points representing the positional coordinates of a particular route.

Often when implementing a path tracking algorithm, one also have to implement a path

recording unit responsible for saving all the coordinates that constitutes the path. A

human operator then has the possibility to manually steer the robot along some track

while the path recording unit saves the information about the path. The path tracking

algorithm also has to handle unplanned positional or orientation deviations from the

path. Such deviations can be caused by odd-metric errors of some kind, or by new

obstacles occurring on the path that must be avoided.

2.3.2 Working Principle

The robot will find the correct path and required final position by line tracking in

both methods mentioned below. In look a-head distance the robot will find its next

position in the path by comparing the current position with the next specified point

generated by the programmer with his calculation in the program. That program is stored

in the memory of the controller. The next point at some distance in the path is called the

look a-head point. In vector pursuit method there are two different algorithms present all

the time when robot is following a path. One is for straight path and other one is for

circular path. This method is also called the screw theory.

This research paper actually described the following techniques of maze solving:

1- Look a-head distance

2- Vector pursuit algorithm

2.3.2.1 Look a-head distance

This method uses a look a-head point, which is a point on the path a certain

distance L away from the orthogonal projection of the vehicles position on the path. The



distance L between these look a-head points is called a look a-head distance.

In this algorithm the path is divided into small goal positions called look a-

head points as explained above. Once the robot achieves the first position it then

moves towards the second one then towards the third and finally reaches the end

position.

Path tracking techniques that use this look-ahead point are called geometric

algorithms.

There are two problems that need to be considered:

1- Regaining a path

2- Maintaining the path

2.3.2.2 Vector pursuit algorithm

Vector pursuit is a path tracking method that uses the theory of screws first

introduced by Sir Robert S. Ball.

2.3.2.2.1 Screw theory

Screw theory has the following points:

1- Screw control was developed in an attempt to not only have the vehicle arrive at

the goal point, but also to arrive with the correct orientation and curvature.

2- The first screw accounts for the translation from the current vehicle position to

the look-ahead point, while the second screw represents the rotation from the

current vehicle orientation to the orientation at the look-ahead point.

Figure 2.2: Pure Pursuit Algorithm



2.3.3 Conclusion:

1- The look a-head distance method is useful where we just have to follow the path

and no alignment is required means accuracy is not important. Once the robot is

disturbed from the path during motion then it cannot find the path on its own

when its program is based on this method.

2- In vector pursuit method the robot can follow the path but whenever it is

disturbed from the path during motion it has the ability to find the path again on

its own. This is the benefit of this method over the look a-head distance method.


Title: A Maze-Solving Robot

Author: C. Scott Ananian and Greg Humphreys

Year of publication: May 1997

2.4.1 Abstract

In this activity you will use RoboMind, a robot simulation environment, to solve

simply connected mazes. A simply connected maze is a maze has no loops, and no

inaccessible areas. There is programming involved in completing this activity. The

RoboMind programming language is very simple based on the maze solving

algorithms. Algorithms are a description of the steps one takes to solve a problem; a

maze solving algorithm is just the rules that the robot will follow to solve the maze,

once you have translated it into code. However this activity does not include a

programming tutorial. If you don't have any programming experience, you might want

to try the Getting Started activity first, as it includes step-by-step instructions for

programming the RoboMind robot.

2.4.2Working Principle

These algorithms are based on the obstacle detection. In these algorithms when

the robot will find an obstacle in front of it, at sides or at the backside, it will turn and

find the other path where no obstacle is present. By wandering around the maze, using

this method it will find the end of the maze. In solving the maze, robot may or may not

visit a path which it has already visited.

This research paper actually described the following techniques of maze solving:



1- Random mouse algorithm

2- Tremauxs Algorithm

2.4.2.1 Random mouse algorithm

The Random Mouse algorithm is just what it sounds like: it's the way a mouse

would solve a maze. The Random Mouse algorithm is just wandering around the maze,

hoping you find the end. It was quite time wasting technique. The figure mentioned

below gives the best explanation of random mouse algorithm.

Figure 2.3: Random Mouse Algorithm

2.4.2.2 Tremauxs Algorithm

This Maze solving method is designed to be able to be used by a human inside of

the Maze. It's similar to the recursive backtracker and will find a solution for all Mazes:

As you walk down a passage, draw a line behind you to mark your path. When you hit a

dead end turn around and go back the way you came. When you encounter a junction you

haven't visited before, pick a new passage at random. If you're walking down a new

passage and encounter a junction you have visited before, treat it like a dead end and go

back the way you came. (That last step is the key which prevents you from going around



in circles or missing passages in braid Mazes.) If walking down a passage you have

visited before (i.e. marked once) and you encounter a junction, take any new passage if

one is available and otherwise take an old passage (i.e. one you've marked once). All

passages will either be empty, meaning you haven't visited it yet, marked once, meaning

you've gone down it exactly once, or marked twice, meaning you've gone down it and

were forced to backtrack in the opposite direction. When you finally reach the solution,

paths marked exactly once will indicate a direct way back to the start. If the Maze has no

solution, you'll find yourself back at the start with all passages marked twice.

Figure 2.4: Tremauxs Algorithm

2.4.3 Conclusion:

In my view these algorithms are best just for the initial learning and

building concepts about the maze solving techniques. But these algorithms are

not suitable for my project as these are quite time consuming algorithms.

Tremauxs algorithm is the small application of A.I. but it is not the requirement

of my project.




Title: MacroMouse: A Maze Solving Robot Authors: Gagan Awhad, Kris Marose, Xi Qiao, Carl Magnuson

Year of Publication: March 2009

2.5.1 Abstract:

This report is based around the robots involved in a MicroMouse competition,

that is, a robot which is able to search and solve a maze. This project will focus on the

design of such a robot, including the advantages and disadvantages of different robot

designs. It will also touch on methods for solving a maze, specifically focusing on a

real-time search, where the robot searches an unknown maze until it finds a goal. The

project also includes localization and mapping of the maze in real time.

2.5.2 Methods and Working Principle:

The first focus of our work was to familiarize ourselves with the Explorer robot,

set up the build environment and implement and test simple motion and sensing. There

were a number of difficulties however in getting a working build environment such as

changed and undocumented access passwords to online data sources and dead links to

important files. After creating a working build environment the problem was to test

simple motion and sensing. Motion was already written into the Explorer Player driver,

however there was no existing code to read values from the two infrared sensors

mounted on the front of the robot. Reading this data would be essential to localization

and decision planning for mapping the maze. 3 We were able to implement the

necessary sensing functions in the Explorer Player driver and wrote code for the

Roboaudiostix board which handles the sensor I/O to communicate the sensor data to the

Player driver over the i2c bus. However in testing the sensing code we were receiving

nonsense data from the sensors and expect there is some fault in the code running on the

Roboaudiostix. Due to time constraints of the project and continuing difficulties in

reading sensor data we made the decision to stop work on the Explorer sensing and use a

fully functional and well documented robotic platform - the Pioneer robot.

The decision to move to the Pioneer platform changed many of the physical

implementation details. It would not be possible to build a very large physical maze due

to the size needed for each cell to fit the Pioneer plus some padding room to allow for

minor drift and imprecision. The Pioneer does however have the advantage of having a



180 degree laser sensor which is very precise. This became essential in the localization

and motion problem because as we would find out, its odometry is very poor. We also

lost some of the direct hardware control we would have had with the Explorer in moving

to the Pioneer which incorporates its own smoothing and trajectory to commands its

Player driver receives. There was fortunately a much smaller learning curve to working

with the Pioneer as we were already familiar with it from a previous assignment and

because it is a popular commercial product with many resources for help and

information.

2.5.3 Conclusion

The transition from a simulated model to real world testing is not a trivial one,

and exposes many factors which were not or could not be accounted for in the

simulation. The hard constraints of the real world mean that what is theoretically

possible and shown in a simulation may not be necessarily feasible to implement in

practice. The biggest challenge in our transition from simulation to the real world was of

that of accurate movement and localization. Due to the constraints of the Pioneer robot,

we solved the maze at a fairly low speed and did not do more advanced scanning of cells

to look ahead multiple positions as was possible in the simulation. The localization issue

was the biggest factor we had to deal with once we moved to the physical world. If this

problem were solved we could have much easier motion primitives and drift

compensation, have more precise and useful sensing and solved the maze at a higher

speed with essentially no risk of a collision. This project attempted to minimize the

difficulties of localization by leveraging the discrete structure of the maze, something

which did simplify the problem, but did not eliminate the problem of localization.




Title: Maze Solving Robot Using Arduino and LSRB Algorithm

Authors: J.Arun Pandian, R.Karthick, B.Karthikeyan

Year of Publication: June 2010

2.6.1 Abstract

This paper MAZE SOLVING ROBOT USING ARDUINO AND LSRB

ALGORITHM deals with the development maze robot using simple circuits. A MSR (maze

solving robot) is a clever little gadget with a silicon brain that finds its way through an

arbitrary maze. It competes against other members of its species, racing as fast as it can. Here

MSR is an electro-mechanical device, typically consisting of three main subsystems. They are

drive system, an array of sensors, and the control system. The drive system consists of a

mechanical chassis, a set of motors, gears and wheels. The chassis is usually designed

to operate like a wheel-chair, with two large drive wheels on either side of a

lightweight aluminum frame. The chassis is built to house the motors, gear system, batteries,

and circuitry, and must also be small enough to maneuver within the constraints of the maze.

The control system is series of circuit boards functioning as the brain of the critter. The control

system runs a maze solving algorithm (LSRB) based on the information received by the

CPU (ARDUINO BOARD) from the sensors. Typically the first several runs through the

maze will be a search sequence, in which the mouse learns the maze and stores it in memory. It

must then calculate the fastest possible path, which it will repeatedly run trying to achieve

successively faster times. The final sub-system is the sensors. They report to the CPU the

current state of the surroundings where the walls and paths are. These are usually either

infrared sensor which picks up light reflected light of the track. The main objective is to

achieve the fastest maze running time and easily find the goal.

2.6.2 Conclusion

Maze-solving involves Control Engineering and Artificial Intelligence. Using a good

algorithm can achieve the high efficiency of finding the shortest path. The proposed maze-

solving algorithm works better and has short searching time and low space complexity, and it

is significant for robots finding path in some areas like maze-solving.



Chapter # 3

Methodology



3.1 Adopted methodology

After a lot of research we finally select a combination of methodologies for our robot

depending upon our requirements. Let us discuss the methodologies we are using in detail.

3.1.1 Dead End filling

In dead end filling algorithm all the dead paths (paths that a robot will not follow or

those paths that will not lead a robot to its final destination point where it has to arrive for

unloading) are found manually by the programmer and then the alive path that will lead robot

to its final destination point for unloading be programmed in the memory of controller. Robot

will use the saved instructions and running on the correct path, it will reach at that point which

is the requirement of the programmer. As for every new location, the programmer has to do the

whole method and he has to save the multiple programs in the memory of the controller, which

is quite difficult process. So, here we are using this algorithm for just zone detection (by

following the traffic light signal system) so that our robot choose the right path for every new

required position.

3.1.2 Wall Following

After the detection of required path, now the robot has to follow the detected path. So,

for this purpose wall following algorithm is used. The Wall Follower algorithm is very simple

to understand. At the start of the maze, put your left (or right) hand on the wall, and then start

walking. Never take your hand off the wall. For a simply connected maze, you will find the

exit. That's all there is to it. The picture below shows a maze solved using the Wall Follower

algorithm; the red path shows the solution, the gray path shows the other parts of the maze that

were visited while following the wall. Look carefully at the maze, and see if you can figure

out if this was left- or right-hand wall following. In our logic we are using the concept of

priority for handling the conditions of X, T and + with wall following algorithms. The sensors

are just like the hands of the robot.



3.1.3 Line Tracking (Pure Pursuit Algorithm)

The concept of the pure pursuit approach is to calculate the curvature that will take the

vehicle from its current position to a goal position.

Unloading of vehicle is automatic which will save time and reduce the need of manual

labor. The vehicle will have the ability to read and obey traffic signals on its path which will

help in traffic control within an industry.



Chapter # 4

Mechanical Design



4.1 Mechanical Design

4.1.1 Selection of Material

We selected Aluminum for the fabrication of mechanical design. Aluminum is a

lightweight, reasonably cheap metal widely used for packaging and transport.

1- Raw aluminum has low strength and high ductility.

2- Aluminum is quite reactive, but protects itself very effectively with a thin oxide layer.

The surface can be "anodized", to resist corrosion and to give decorative effects.

4.1.1.1 Design Issues

4.1.1.1.1Design strengths

1- High strength-to-weight ratio

2- High stiffness-to-weight ratio

3- High electrical and thermal conductivity

4- Easy to shape

5- Easy to recycle

4.1.1.1.2 Design weaknesses

Arc welding of aluminum is quite difficult.

4.1.1.1.3 Environmental issues

1- Aluminum production uses lots of energy (4% of total US energy consumption!)

2- Aluminum is easily recycled - this only uses 1% of the energy needed to produce

the metal.

3- Aluminum use in cars is growing rapidly - low weight means good fuel

economy and low emissions metal.


University Of Engineering and Technology, Taxila (Sub Campus Chakwal)Page 21

4.1.2 3-Dimensional Modeling and robot dimensions

4.1.2.1 3-Dimensional Modeling

Figure 4.1(a) : 3D Modeling



Now the picture of hardware of the project is following:

Figure 4.1(b) : Picture of Robot

4.1.2.2 Robot Dimensions

Base 30 x 30cm

Aluminum sheet thickness 4 mm

Diameter of tires 3 in

Number of teeth of sprocket 25

Thickness of tires 1 cm

Table 4.1: Dimensions of Robot

4.2 Fabrication

For fabrication of our project we used a private workshop. Workshop provides us

with powered tools and guidance for completing our design of base of our robot. We have

also used the Lathe for the preparing of bushes for barring, Cylindrical Grinder for

smoothing purposes and some hand tools for the opening and fitting the parts of

mechanical in case of any fault during troubleshooting.



4.3 Mechanical Components

Item Specifications Cost(Rs.) Source

Wheels Tensile Strength 3900 psi

Tensile Modulus 8000psi

1000 Lahore, Hall

Road

Acrylic Sheet

Tensile Strength 10,000 psi

Elongation 4.2%

Modulus Of Elasticity

400,000 psi (2800 M Pa)

1000

Lahore, Hall

Road

Sprocket Chain

Mechanism

Tensile Strength 55.76 KPa

Crushing Stress 265.78 Pa

2000 Lahore, Hall

Road

Aluminum Frame Tensile Strength 276MPa 1000 Lahore, Hall

Road

Motors Torque 266.48 Nm 3000 Rawalpindi

Unloading Mechanism

Length 34 cm

Diameter 8.2 cm

Slope 2 Degrees

2000

Chakwal

Table 4.2: Mechanical Components

4.4 Feasibility of hardware

4.4.1 Selection of Motors:

Selection of motor is performed on the following parameters:

1- Torque of the motor

2- RPMs of the motor

3- Gear ratio and the flexibility in the arrangement of gear ratio (as if someone wants to

arrange the gears foe achieving the required speed then the gears should be adjustable)

4- Strength of the shaft of motor

5- Power rating of motor

We have to perform following calculations for the selection of suitable motors for

our vehicle.



Weight of robot = weight of frame + weight of motor +weight of battery +weight of

aluminum sheet +weight of driving mechanism +miscellaneous weight.

............Equation 4.1: Weight of Robot

As the total weight of robot should be less than 90N then we can consider it 107.8N

maximum for calculation the torque and selecting the motors for our robot.

Weight of Robot = 107.8N

Acceleration required =?

Weight of wheels = 4.9N

Moment of inertia of wheel = 1/8*mw*d2

Equation 4.2: Moment of Inertia

Tgravitational = mc*g*sin = mc*g Equation 4.3: Gravitational Torque

As our maze is horizontal, so the reaction of cart and normal are perpendicular to each

other..

W = m*g* sin

W = m*g* sin90

W = m*g*1

W = m*g

Tgravitational = 10.5 kg * 9.8

= 102.9 Nm

Figure 4.2: Free Body Diagram of Robot



Tfrictional = Fr*N*cos Equation 4.4: Frictional Torque

= 90

so

Fr = Cr*N*cos

Fr = 0, as cos90 = 0

Now, we can say that in the case of wheel the frictional force is almost negligible as shown

in the calculations above

Load Torque = Tgravitational + Tfrictional = 102.9 + 0 Equation 4.5: Load Torque

TL = 103Nm

4.4.2 Acceleration Torque

By supposition and observing the mazes in past we got that maximum distance the

robot has to travel from starting point to the traffic signal A is almost 4.5m. Traffic signal

A will be green for 10 seconds, so the minimum speed of our robot should be enough to

reach there before the signal turns red.

Let suppose we have to reach there in 8 seconds, then

S = V*t

V = S/t Equation 4.6: Uniform velocity equation

V = 4.5/8

V = 0.5625 m/sec

r = radius of wheel = 2 inch

= 0.5625/r

= 0.5625/0.0501975 m

= 11.205

= 11.205*60

= 672.344 rpm

As this rpm is very difficult to control during breaking and turns during

maze solving. So the rpm should be in between range of 250rpm to 300rpm.

now suppose we have to reach signal A in 16 seconds

S = V*t

V = S/t

V = 3.5/16

V = 0.21875 m/sec



V = 0.21875 * 60 m/minute

V = 13.125 m/minute

= 13.125/r

= 13.125/0.0501975 m

= 261.46 rpm

The speed is now within our range and we can control it;

=(f- t)/t

=16.3417m/min2

Now,

We will find the acceleration torque as follow

Ta = (mc* ) + 4(1/8 * mw * d2 * )

=10.5 * + 4(1/8(0.125(0.0025) * (16.3417))

= 163.47 + 0.00255339 Ta = 163.48 Nm

4.4.3 Total Torque

Total Torque = 103 + 163.48 Equation 4.7: Total Torque

= 266.48 Nm

4.5 Justification of above design

T = F * r T/r = F = m * g

T/r = m * g=266.48/20 = m=13.324 Kg

r = radius of wheel

The highlighted reverse calculations tell us that we have selected the required

motors to drive the robot.

4.6 Power Calculations

This calculation will result in the demanding quantity of power which my robot

will require to cover the distance of 30 meters in the maze from loading, unloading and

back to loading positions.



Stotal = S1 + S2 + S3

By putting values

Stotal = a*ta(tc-ta)

P = m*a*v

P = (m*s2)/ta(tc-ta)

2 Equation 4.8: Mechanical Power

P = 6.60 Watts

This is the power which our robot requires only for travel. This amount of power

does not include the electrical power losses and power dissipation in stop and pause during

the motion. This is the power which robot consume during the continuous motion.

Figure 4.3: Free Body Diagram of Mechanical Power Consumption



4.7 Cotter joint design considerations for chains in sprocket chain

mechanism

As = 266.4 nm

P = / diameter of sprocket = 55.76 k pa.

t = c = 265.780 pa

The socket and spigot cotter joint is shown in fig.

Let

P= load carried by the rods

D= diameter of the rods,

D1= outside diameter of socket,

D2= diameter of spigot or inside diameter of socket

D3= outside diameter of spigot collar

T1= thickness of spigot collar

D4= diameter of socket collar

C = thickness of socket collar

Figure 4.4: Cotter Joint 2D Drawing



B= mean width of cotter

T = thickness of cotter

L = length of cotter A= distance from the end of the slot to the end of rod

The sprocket chain mechanism is selected on the basis of following parameters:

1- Tensile strength of the Chain

2- Compressive strength of the chain

3- Shear strength of the chain

4- Tensile strength of the sprocket

5- Compressive strength of the sprocket

6- Shear strength of the sprocket

There are two methods of designing. First is, assume or calculate the values of stresses

and find the other parameters mentioned above from them. And the second is, assume or

calculate the other parameters and calculate the values of stresses from them. Now we

have used the first method.



The dimensions for a socket and spigot cotter joint may be obtained by

considering the various modes of failure as discussed below:

4.7.1 Failure of the rods in tension

The rods may fail in tension due to the tensile load p. We know that

D=(4*f/ t ) Equation 4.9: Failure of rod

= 7.8 mm

This will give us the diameter of rod.

4.7.2 Failure of spigot in tension

Since the weakest section of the spigot is that section which has a slot in it for

the cotter, as shown in figure.



D2=[t + {t2 + ( * p)/ t }]/ * 2 Equation 4.10: Failure of spigot

= 12.5 mm

4.7.3 Failure of the rod or cotter in crushing

T = (c * d2)/p Equation 4.11: Failure of the cotter

= 2.4 mm

Figure 9 Failure of spigot in tension 1 Figure 10 Failure of spigot in tension 1 Figure 4.5: Failure of spigot in tension

Figure 4.6:Failure of the rod crushing



4.7.4 Failure of the socket in tension across the slot

We know that the resisting area of the socket across the slot

D1 = 2 * [t + { t2 + (2 * d2

2 )/4 d2 * * t + (p * )/ c }]/

.......Equation 4.12: Failure of the socket

Figure 4.7: Failure of socket in tension



4.7.5Failure of cotter in shear

b = p/( * 2 * t) Equation 4.13: Failure of cotter

= 11.1 mm

4.7.6 Failure of the socket collar in crushing

Figure 4.8: Failure of cotter in shear



D4 = [p/ ( * t)] + d2 Equation 4.14: Socket collar failure

= 23.4 mm 7

Failure of socket end in shearing:

A = p/(d * ) = 6.1 mm

As = 266.4 nm

P = / diameter of sprocket = 55.76 k pa. t = c = 265.780 pa (calculated same as

above)

Figure 4.9 socket collar Failure



Chapter # 5

Electronic Circuitry



5.1 Electronics Circuitry

The electronic circuitry of our project is the consisted of the following small

circuits.

1- IR proximity sensor and SONAR sensor (For Wall Detection)

2- Color sensor

3- LDR module for LINE TRACKING

4- Motor driving circuits (H-Bridges)

5- ARDUINO KIT

Item Serial Number Specifications Cost(Rs.) Source

IR Proximity

Sensor

GP2D120XJ00F 5v & Range=

30 cm

1000 Robocave,

Lahore

MOSFETs IRF 9540 &

75n75

24v & 100 A

75v & 75 A

100 Hall Road,

Lahore

OptoCouplers 813 Sharp 24v & 5 A 100 Chakwal

LDR .. 24v & 10 A 30 Chakwal

Voltage

Comparator

LM324 5v 30 Chakwal

Variable

Resister

.. 20Kohm 50 Hall Road, Lahore

Magnetic Coil .. 24v & 3.13 A 750 Hall Road, Lahore

Table 5.1: Electrical Components

The complete diagram of our circuit on Proteus is following:

This circuit includes ARDUINO kit, IR Proximity sensors, LDR based analog color

sensors and LDR based line tracking sensors. The complete working and theory of the

circuit has been discussed in this chapter.



Figure 5.1: Complete circuit of our Project on Proteus

The detail of all these components is discussed below.

5.2 IR Proximity sensor

Sensors will be outputting an analog voltage that we will be reading with our

Arduino. The typical Arduino has 6 Analog In pins located on them. These analog inputs

act just like a voltage meter, sensing the voltage on that pin, and are actually 10 bit Analog

to digital converters (ADCs). The 10 bit part is the resolution of the ADC. 10 bit, or 2^10 =

1024 values. That means that when we read the voltage on that pin, 0-5v value will be

translated to between 0 (0V) and 1023(5V).

5.2.1 Working

It shines a beam of IR light from an LED, and measures the intensity of light that is

bounced pack using a phototransistor. If you stare at the sensor, you can see one of the

LEDs glowing slightly red as some of the IR falls into the visible-light spectrum.



Circuit Working

5.2.2 Reason for using IR Proximity sensor

1- IR sensor has the more accuracy in detection of edges and corners as this work in

such a way that the IR emitter throws the rays on the IR receiver and the receiver

gives the output.

2- It uses the triangular principle for its working.

3- Refresh rate is high.

4- Easy to construct manually.

5- Low cost.

6- In case of analog IR sensor errors like nose in signals etc are very less due to the

use of light rays as compared to the sound signals in SONAR.

Figure 5.2: Working of IR Sensor

Figure 5.3: IR sensor principle



5.3 Color and Line tracking Sensors

For the color and line tracking sensors we have used the LDR module.

Figure 15 Color sensor cicuit diagram 1 Figure 5.4: Color sensor circuit diagram



5.3.1 Working

As the light dependent resistors gives the different ranges of voltages at output

according to the intensity of light. We know that the different colors of lights have the

different intensity then the LDR will give us the different ranges of voltages across the

green, red and yellow.

5.3.2 Reason for using LDR

The various limitations of the color sensing system are following:

Precise color sensors are expensive. Cheap sensors only detect a few colors.

1- The color sensing system is unable to recognize the brightest and darkest color level

for every of the colors.

2- As, in using the IR sensor we have to face the problems in sun light, because the

sun light has its own IR rays. Therefore the output of IR sensor is distorted in this

case. While on the other hand, LDR is not perfect but quite independent of this

problem in sun light or every other light intensity.

3- Its setting is very easy in case of changing light intensity if the output of LDR has

noise.

LDR is perfect in every case of such problems as compared to the IR sensor for

color sensing. Therefore we have used the LDR module as color sensor.

5.4 Motor driving circuit H-Bridge

An H bridge is an electronic circuit that enables a voltage to be applied across a

load in either direction. These circuits are often used in robotics and other applications

to allow DC motors to run forwards and backwards. H bridges are available as

integrated circuits, or can be built from discrete components.

H- Bridges can be built using following components:

1- Using electro - mechanical Relays

2- Using BJTs

3- Using MOSFETs

We are using the MOSFETs for building our H-Bridge but transistors

(BJTs) are used for switching of MOSFETs.



5.4.1 Using electro - mechanical relays

5.4.1.1 Advantages and disadvantages

1- Relay based circuit are cheaper

2- Easy to control can handle high current and voltage

easily 3- Slow switching not suitable when using

PWM

3- DE bouncing problems

Figure 5.5: H-Bridge via Relays



5.4.2 H Bridge using MOSFETs (Switched through Transistors (BJTs))

The upper portion is P-Channel and the lower portion is N-Channel.

The reason of using such type of combination is the easy switching trough

controller as in this way only two pins of controller will be used instead of four pins (to

switch each MOSFET separately for the alternative combination of switching of

MOSFETs).

Figure 5.6: H-Bridge via MOSFETS



5.4.2.1 Advantages

1- Easy to control can handle high current and voltage easily.

2- Fast switching suitable when using PWM.

3- DE bouncing problems have been solved because there is no mechanical switch is

used.

4- Electrical signal noise is reduced in this case.

5- Refresh rate is high and easily synchronized with the execution rate of the

controller.

6- Highly efficient as compared to the electrical relays.



Chapter # 6

Embedded System



6.1 Embedded System (ARDUINO Kit)

We are using the ARDUINO kit instead of any controller.

Figure 6.1: ARDUINO Kit

6.2 Why ARDUINO mega?

6.2.1 Power

1- The ARDUINO Mega can be powered via the USB connection or with an external

power supply. The power source is selected automatically. External (non-USB)

power can come either from an AC-to-DC adapter or battery.

2- The board can operate on an external supply of 6 to 20 volts. If supplied with less

than 7V, however the 5V pin may supply less than five volts and the board may be

unstable. If using more than 12V, voltage regulator may overheat and damage the

board. The recommended range is 7 to 12 volts.

6.2.2 Memory

The AT mega 1280 has 128 KB of flash memory for storing code of which 4 KB

is used for the bootloader (A Bootloader is the first program which executes before the

main program) whenever a system is initialized), 8 KB of SRAM and 4 KB of EEPROM



(which can be read and written with the EEPROM library).

6.2.3 USB over current Protection

The ARDUINO Mega has a resettable poly fuse that protects your computer's

USB ports from shorts and over current. Although most computers provide their own

internal protection, the fuse provides an extra layer of protection. If more than 500 mA is

applied to the USB port, the fuse will automatically break the connection until the short or

overload is removed.

6.2.4 ADC

1- 10-bit Resolution

2- 13s - 260s Conversion Time

3- 14 Differential input channels

6.2.5 ADC Conversion Result

1- After the conversion is complete (ADIF is high), the conversion result can be found

in the ADC Result Registers (ADCL , ADCH). For single ended conversion, the

result is

2- Where VIN is the voltage on the selected input pin and VREF the selected voltage

differential channels are used, the result is

6.2.6 Programming

1- The ARDUINO Mega can be programmed with the AURDUINO software.

2- The ATmega1280 on the AURDUINO Mega comes pre-burned with a boot loader

that allows you to upload new code to it without the use of an external hardware

programmer.

3- You can also bypass the boot loader and program the microcontroller..

6.3 Programming Language used For programming the ARDUINO microcontroller, we are using C language. Some

general commands and examples are following:



Arduino Programming Basics

Table 6.1: General Commands of AURDUINO v1.1.8

6.3.1 Examples

6.3.1.1 To turn on LED

void setup() {

pinMode(2,OUTPUT);

digitalWrite(2,HIGH);

delay(1000);

digitalWrite(2,LOW);

}

void loop()

{}

6.3.1.2 To Flash LED

void setup() {

pinMode(2,OUTPUT);

}

void loop() {


delay(500);


delay(500);

}

6.3.1.3 To turn on Motor

void setup() {

pinMode(4,OUTPUT);




delay(1000);


}

void loop()

{}

6.4 Compiling Software For programming ARDUINO Microcontroller, we are using software (ARUINO

V1.1.8). As the programming commands and algorithms for programming ARDUINO

Microcontroller are different then other PIC and AVR Microcontroller, therefore the

specially designed compiling software is used for the programming of ARDUINO

Microcontroller.

6.5 Source Code The code burned in the Arduino kit is shown in detail in appendix at the end of the

report. It consist of different portions which shows the use of different commands with

respect to location in the maze.



Chapter # 7

Control Circuitry



7.1 Mathematical modeling using Control Systems Techniques

The mathematical modeling depends on the following parts:

1- Modeling of electrical circuitry (motor driving circuits).

2- Modeling of electromechanical system (motors and mechanical part).

Now the detail is as follow:

7.2 Modeling of electrical circuitry (motor driving circuits)

As shown in the above figure only two MOSFETs will be on and two will

be off. Therefore the circuit can be simplified as shown in fig 1.

Figure 1 contains the two l oops. In loop 1 the transistors R1 and R2 are use d to

switch the MOSFETs in loop 2. Now the calculations are given below:

For loop 1:

By KVL;

V(s) = i1(s)*R1(s) + i2(s)*R2(s) Equation 7.1: Loop 1 differential eq.

V(s)/V1(s) = (R1 + R2)/R0

Figure 7.1: Electrical Circuit Modeling i



V(s)/V1(s) = 1 Equation 7.2: Loop 2 Differential eq.

For loop 2:

By KVL;

V(s) = i1(s)*R1(s) + i2(s)*R2(s) Equation 7.3: Loop 2 differential eq.

V(s)/V1(s) = (R1 + R2)/R0

V(s)/V1(s) = 1

7.3 Modeling of mechanical and electromechanical part

Electromechanical System Transfer Functions:

A magnetic field is developed by stationary permanent magnets or a stationary

electromagnet called the fixed field. A rotating circuit called the armature, through which

current ia (t) flows, passes through this magnetic field at right angles and feels a force,

F=Blia(t) where B is the magnetic field strength and l is the length of the conductor. The

resulting torque turns the rotor, the rotating member of the motor. There is another

phenomenon that occurs in the motor. A conductor moving at right angles to a magnetic

field generates a voltage at the terminal so f the conductor equal to e=Blv, where e is the

voltage and v is the velocity of the conductor normal to the magnetic field. Since the

current-carrying armature is rotating in a magnetic field, its voltage is proportional to

speed. Thus the general transfer function of the motor is following:

Figure 7.2: Modeling of Motors



Tm(s) in terms of m(s) if we are to separate the input and output variables and

obtain the transfer function, m(s)/Ea(s).

Jm = inertia at the armature and includes both the armature i

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