How to Build a LINE FOLLOWER/LINE TRACER ROBOT

The basic connection diagram

LINE FOLLOWER/Line tracer ROBOT

The line follower robot is an autonomous robot i.e. it works automatically!!! . As all ilt for some robots are built for some specific task the purpose of the line follower is to follow a path given to it. The robot can follow a black line drawn in a white background or vice versa. It is also called a line tracer etc… Well that’s all about the basic background of a line follower

Construction

The construction of a line tracer isn’t rocket science… all we require is a basic knowledge of electronic circuitry and its components. If we have interest in it well we can finish the project within a week for newbie’s and if you really know what you are doing well a day or 2 would be more than sufficient. Now lest get started.

Basic Requirements

1> Electronic components (Electronic circuit)

2> Mechanical parts (For the body of robot)

Some of the most common components you will be requiring for building this robot would be

Resistors (1k,2.2k…), Capacitors (5mF..),LED’s , LDR’s or Photodiodes ,Pots (Potentiometers-Variable resistors) connection wires, IC Base, Soldering iron, solder, Copper board (Etching board if you know to design) etc…. Most importantly you will require a motor controller IC (LM342), A microcontroller (ATmeg-8, PIC …) and 2 Geared motors.

For the body of the robot you will have to have some (2-3) L shaped clamps depending upon how you plan to design, a small thick board (wooden, cardboard…)

The total cost would not be more than 1000/- as the only the costliest component is the geared motor which would cost between 200-300 each. Make sure that both the motors RPM (Rotations per minute) are same. Do check this for sure. A small difference of 2 or 3 RPM is all right as it can be adjusted. But a large variation would be unacceptable. Also a smaller RPM would be sufficient. We usually get motors with RPM ranging from 10RPM to 750RPM. Choose a range b/w 50-150 as it below it would be too slow and above it might be hard to control (Not that it cannot be done). Rest of the components can be got easily. Get dozens of LED’s (Min of 2 Required), Resistors of different rating, pots (1k,5k..), connection wires . if required you can build your robot using a bread board also. A list of components to buy is given in a list below. Always keep IC’s, components a little extra in hand as we cannot tell when something might turn faulty or burn out. Extra set of it would be always be helpful .

Theory of the Robot (HOW IT WORKS)

Well before we start actually building the robot lets know what is actually happening on the inside of it. Well we can divide the whole circuit into three parts

1> The sensing part (The sensors sense the line i.e. the path)

2> The controller part (The Microcontroller decides the course of action to be taken )

3> The Navigation part (The motors act accordingly to move through the path)

The sensing part consists of a set of LED’s and LDR/Photodiodes/Phototransistors. Let’s go back to our basics. We all know that the refection and absorption properties of light differ between colours to colour. Black absorbs all the light and doesn’t reflect much while the colour white absorbs maximum amount of light while reflecting back almost none. This principle is used for the sensing of the path. Here a track is painted in black with a white background or a white track is drawn in a black background. When the light from the LED’s hit the Black part of the track reflection of light will be minimum the sensor which is the LDR will be receiving minimum light while if the light from the white part then almost full light of the LED reaches the sensor. Now as the name suggests LDR-Light Dependant Resistor, the resistance of the LDR depends on the amount light reaching it. It ranges from 0 ohm in full light to 15Kohm in dark resistance. With this we can find the variations in the track i.e. where the black line is and where the white background is. Now we can convert this data into digital signals as HIGH or LOW. We can set it as required which becomes our base logic for writing the program for the control of the robot.

Now the data we get from the sensors are gathered and connected to the processing unit i.e. the microcontroller. we can also use Gates to program the same but the disadvantage is that once it is connected we cannot change its logic at any cost and also that it would be hard to troubleshoot it as the size and complexity increases. Now in here we will have to write a program to make the robot work. We can call this unit as the brain centre as this is where the all the control commands are sent and according to the logic written in here the robot works.

The commands/signals sent from the Microcontroller are received in the navigation unit. Here it consists of an IC L293D. It is a motor controller. We can control 2 motors with the same IC. It is basically similar to a H-Bridge. The IC’s inputs are from the Microcontroller and the outputs are connected to the geared motors. This IC helps in changing the direction of rotation of the motor. It is simple logic for the reversal. Usually in a DC motor if we reverse the poles of the battery connected, the direction of rotation would reverse automatically. Here it is done electronically.

To better understand the working a small track through which the robot would navigate is shown. Now we can see that as there are 2 wheels only for this robot and the only 3 actions that can be done are

1> Rotate forward

2> Rotate backward

3> Stop

Now by controlling these actions simultaneously on the motors the following would be the result

1> Both wheel Stop : Robot doesn’t move

2> Both wheel forward : Robot moves forward

3> Both Wheel Reverse : Robot moves Backward

4> Left wheel forward, Right wheel Stop : Robot turns Towards Right

5> Left wheel stop, Right wheel forward : Robot turns Towards left

6> Left wheel forward, Right wheel reverse : Robot turns 90deg towards right (Sharp right)

7> Left wheel reverse, Right wheel forward : Robot turns 90deg towards left (Sharp left)

The other combinations wouldn’t be required much. The above given are some of the most used basic controls that can be done.

THE circuit diagram and connection diagram is as given

Circuit Diagram :

here a s/w is kept for changing the mode

1> Follow a white line in a Black Background

2> Follow a Black line in a White Background

a 7-Segment display is connected. We can also use an LED (2 No's) for indicating in which mode is the Robot working i.e. In white mode or the black mode. There will be couple of more pins left out in the PIC which can be used for additional sensors or some other functions as required.

Basic Electrical

ABBREVATIONS

RESISTANCE

OHM’s LAW

V=I*R where V=Voltage

I=Current

R=Resistance

DC Resistance:

R= ρ*l/A Where ρ = Resistivity of teh material

l =Length of the conductor

A = Area of the conductor

ρ= 1 / Conductivity=Resistivity

Temperature dependance of a resistor

R =R₀[α *(T-T0)+1] where R­­₀=Resistance at Temperature T0

α =% change in resistivity / unit temperature

T =Temperature

AC resistance = 1.6*Dc resistance
note : AC resistance would be always greater than DC resistance because of 'SKIN EFFECT'

Resistance in series

When R1,R2, R3 are connected in series…..

Req=R1+R2+R3

Ø Voltages divides & Current remains same in a series circuit.

Resistance in parallel

When R1,R2,R3 are connected in parallel

1/Req=(1/R1+1/R2+1/R3) =

Req=(R1*R2*R3)/(R1+R2+R3)

Ø Current divides & Voltage remains the same in a parallel circuit.

Ø The equivalent resistance of two or more resistance is always less than the least value of the individual resistor.

VOLTAGE DIVIDER

When two resistance are connected as shown

1) The voltage across Resistor R2 is given as

Vout = R2/(R1+R2)*Vin Where Vout = Output voltage

Vin = Input voltage

The power P dissipated by a resistance R carrying a current I with a voltage drop V is:

P= (I^2)*R = VI = (V^2)/R

The energy W consumed over time t due to power P dissipated in a resistance R carrying a current I with a voltage drop V is:

W=(I^2)*R*t

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CAPACITANCE

C=Q/V Where C= Capacitance

Q= Charge

V= Voltage

C=(Ebsilon0)*(Ebsilonr)*A/D Where C=Capacitance

A=Area

D=Distance b/w the plates

The Energy stored in a capacitor

W(stored)= C(V^2)/2 = (Q^2)/2C= QV/2

Current-voltage relationship…

I(t)=C dV/Dt Where (dV/dT)=Change in Voltage

The power P transferred by a capacitance C holding a changing voltage V with charge Q is:
P = VI = CV(dv/dt) = Q(dv/dt) = Q(dq/dt) / C

Capacitance in series….

When capacitances C1,C2,C3 are connected in series Equivalent capacitance is

1/Ceq=(1/C1+1/C2+1/C3)

Ceq= (C1*C2*C3)+(C1+C2+C3)

Capacitance in parallel….

When capacitances C1,C2 ,C3 are connected in parallel , the Equivalent capacitance is

Ceq=C1+C2+C3

Ø Capacitor blocks DC but passes AC

The power P transferred by a capacitance C holding a changing voltage V with charge Q is:
P = VI = CV(dv/dt) = Q(dv/dt) = Q(dq/dt) / C

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INDUCTANCE

Voltage-Current relationship…

V=L dI/dT where (dI/dT)=Change in current

Inductance in series…

When Inductors L1, L2, L3 are connected in series the equivalent inductance

Leq=L1+L2+L3

When two coupled inductances L₁ and L₂ with mutual inductance M are connected in series, the total inductance L_t is:
L_t = L₁ + L₂ ± 2M
The plus or minus sign indicates that the coupling is either additive or subtractive, depending on the connection polarity.

Inductance in parallel...

When inductance L1,L2,L3 are connected in parallel ,their equivalent inductance

1/Leq = (1/L1+1/L2+1/L3)

Leq = (L1*L2*L3)/L1+L2+L3

The power P transferred by an inductance L carrying a changing current I with magnetic linkage Y is:
P = VI = LI(di/dt) = Y(di/dt) = Y(dy/dt) / L

The energy W stored in an inductance L carrying current I with magnetic linkage Y is:
W = LI² / 2 = YI / 2 = Y² / 2L

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Voltmeter Multiplier

The resistance R_S to be connected in series with a voltmeter of full scale voltage V_V and full scale current drain I_V to increase the full scale voltage to V is:
R_S = (V - V_V) / I_V

The power P dissipated by the resistance R_S with voltage drop (V - V_V) carrying current I_V is:
P = (V - V_V)² / R_S = (V - V_V)I_V = I_V²R_S

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Ammeter Shunt

The resistance R_P to be connected in parallel with an ammeter of full scale current I_A and full scale voltage drop V_A to increase the full scale current to I is:
R_P = V_A / (I - I_A)

The power P dissipated by the resistance R_P with voltage drop V_A carrying current (I - I_A) is:
P = V_A² / R_P = V_A(I - I_A) = (I - I_A)²R_P

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Wheatstone Bridge

The Wheatstone Bridge consists of two resistive potential dividers connected to a common voltage source. If one potential divider has resistances R₁ and R₂ in series and the other potential divider has resistances R₃ and R₄ in series, with R₁ and R₃ connected to one side of the voltage source and R₂ and R₄ connected to the other side of the voltage source, then at the balance point where the two resistively divided voltages are equal:
R₁ / R₂ = R₃ / R₄

If the value of resistance R₄ is unknown and the values of resistances R₃, R₂ and R₁ at the balance point are known, then:
R₄ = R₃R₂ / R₁

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Kennelly's Star-Delta Transformation

A star network of three impedances Z_AN, Z_BN and Z_CN connected together at common node N can be transformed into a delta network of three impedances Z_AB, Z_BC and Z_CA by the following equations:
Z_AB = Z_AN + Z_BN + (Z_ANZ_BN / Z_CN) = (Z_ANZ_BN + Z_BNZ_CN + Z_CNZ_AN) / Z_CN
Z_BC = Z_BN + Z_CN + (Z_BNZ_CN / Z_AN) = (Z_ANZ_BN + Z_BNZ_CN + Z_CNZ_AN) / Z_AN
Z_CA = Z_CN + Z_AN + (Z_CNZ_AN / Z_BN) = (Z_ANZ_BN + Z_BNZ_CN + Z_CNZ_AN) / Z_BN

Similarly, using admittances:
Y_AB = Y_ANY_BN / (Y_AN + Y_BN + Y_CN)
Y_BC = Y_BNY_CN / (Y_AN + Y_BN + Y_CN)
Y_CA = Y_CNY_AN / (Y_AN + Y_BN + Y_CN)

In general terms:
Z_delta = (sum of Z_star pair products) / (opposite Z_star)
Y_delta = (adjacent Y_star pair product) / (sum of Y_star)

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Kennelly's Delta-Star Transformation

A delta network of three impedances Z_AB, Z_BC and Z_CA can be transformed into a star network of three impedances Z_AN, Z_BN and Z_CN connected together at common node N by the following equations:
Z_AN = Z_CAZ_AB / (Z_AB + Z_BC + Z_CA)
Z_BN = Z_ABZ_BC / (Z_AB + Z_BC + Z_CA)
Z_CN = Z_BCZ_CA / (Z_AB + Z_BC + Z_CA)

Similarly, using admittances:
Y_AN = Y_CA + Y_AB + (Y_CAY_AB / Y_BC) = (Y_ABY_BC + Y_BCY_CA + Y_CAY_AB) / Y_BC
Y_BN = Y_AB + Y_BC + (Y_ABY_BC / Y_CA) = (Y_ABY_BC + Y_BCY_CA + Y_CAY_AB) / Y_CA
Y_CN = Y_BC + Y_CA + (Y_BCY_CA / Y_AB) = (Y_ABY_BC + Y_BCY_CA + Y_CAY_AB) / Y_AB

In general terms:
Z_star = (adjacent Z_delta pair product) / (sum of Z_delta)
Y_star = (sum of Y_delta pair products) / (opposite Y_delta)

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KIRCHOFF’S LAW

Kirchhoff's Current Law
At any instant the sum of all the currents flowing into any circuit node is equal to the sum of all the currents flowing out of that node:
SI_in = SI_out

Similarly, at any instant the algebraic sum of all the currents at any circuit node is zero:
SI = 0

Kirchhoff's Voltage Law
At any instant the sum of all the voltage sources in any closed circuit is equal to the sum of all the voltage drops in that circuit:
SE = SIZ

Similarly, at any instant the algebraic sum of all the voltages around any closed circuit is zero:
SE - SIZ = 0

AC CIRCUITS

Impedance

The impedance Z of a resistance R in series with a reactance X is:
Z = R + jX

Rectangular and polar forms of impedance Z:
Z = R + jX = (R² + X²)^½Ðtan^-1(X / R) = |Z|Ðf = |Z|cosf + j|Z|sinf

Addition of impedances Z₁ and Z₂:
Z₁ + Z₂ = (R₁ + jX₁) + (R₂ + jX₂) = (R₁ + R₂) + j(X₁ + X₂)

Subtraction of impedances Z₁ and Z₂:
Z₁ - Z₂ = (R₁ + jX₁) - (R₂ + jX₂) = (R₁ - R₂) + j(X₁ - X₂)

Multiplication of impedances Z₁ and Z₂:
Z₁ * Z₂ = |Z₁|Ðf₁ * |Z₂|Ðf₂ = ( |Z₁| * |Z₂| )Ð(f₁ + f₂)

Division of impedances Z₁ and Z₂:
Z₁ / Z₂ = |Z₁|Ðf₁ / |Z₂|Ðf₂ = ( |Z₁| / |Z₂| )Ð(f₁ - f₂)

In summary:
- use the rectangular form for addition and subtraction,
- use the polar form for multiplication and division.

Admittance

An impedance Z comprising a resistance R in series with a reactance X can be converted to an admittance Y comprising a conductance G in parallel with a susceptance B:
Y = Z ^-1 = 1 / (R + jX) = (R - jX) / (R² + X²) = R / (R² + X²) - jX / (R² + X²) = G - jB
G = R / (R² + X²) = R / |Z|²
B = X / (R² + X²) = X / |Z|²
Using the polar form of impedance Z:
Y = 1 / |Z|Ðf = |Z| ^-1Ð-f = |Y|Ð-f = |Y|cosf - j|Y|sinf

Conversely, an admittance Y comprising a conductance G in parallel with a susceptance B can be converted to an impedance Z comprising a resistance R in series with a reactance X:
Z = Y ^-1 = 1 / (G - jB) = (G + jB) / (G² + B²) = G / (G² + B²) + jB / (G² + B²) = R + jX
R = G / (G² + B²) = G / |Y|²
X = B / (G² + B²) = B / |Y|²
Using the polar form of admittance Y:
Z = 1 / |Y|Ð-f = |Y| ^-1Ðf = |Z|Ðf = |Z|cosf + j|Z|sinf

The total impedance Z_S of impedances Z₁, Z₂, Z₃,... connected in series is:
Z_S = Z₁ + Z₁ + Z₁ +...
The total admittance Y_P of admittances Y₁, Y₂, Y₃,... connected in parallel is:
Y_P = Y₁ + Y₁ + Y₁ +...

In summary:
- use impedances when operating on series circuits,
- use admittances when operating on parallel circuits.

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Reactance

Inductive Reactance
The inductive reactance X_L of an inductance L at angular frequency w and frequency f is:
X_L = wL = 2pfL

For a sinusoidal current i of amplitude I and angular frequency w:
i = I sinwt
If sinusoidal current i is passed through an inductance L, the voltage e across the inductance is:
e = L di/dt = wLI coswt = X_LI coswt

The current through an inductance lags the voltage across it by 90°.

Capacitive Reactance
The capacitive reactance X_C of a capacitance C at angular frequency w and frequency f is:
X_C = 1 / wC = 1 / 2pfC

For a sinusoidal voltage v of amplitude V and angular frequency w:
v = V sinwt
If sinusoidal voltage v is applied across a capacitance C, the current i through the capacitance is:
i = C dv/dt = wCV coswt = V coswt / X_C

The current through a capacitance leads the voltage across it by 90°.

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Resonance

Series Resonance
A series circuit comprising an inductance L, a resistance R and a capacitance C has an impedance Z_S of:
Z_S = R + j(X_L - X_C)
where X_L = wL and X_C = 1 / wC

At resonance, the imaginary part of Z_S is zero:
X_C = X_L
Z_Sr = R
w_r = (1 / LC)^½ = 2pf_r
The quality factor at resonance Q_r is:
Q_r = w_rL / R = (L / CR²)^½ = (1 / R )(L / C)^½ = 1 / w_rCR

Parallel resonance
A parallel circuit comprising an inductance L with a series resistance R, connected in parallel with a capacitance C, has an admittance Y_P of:
Y_P = 1 / (R + jX_L) + 1 / (- jX_C) = (R / (R² + X_L²)) - j(X_L / (R² + X_L²) - 1 / X_C)
where X_L = wL and X_C = 1 / wC

At resonance, the imaginary part of Y_P is zero:
X_C = (R² + X_L²) / X_L = X_L + R² / X_L = X_L(1 + R² / X_L²)
Z_Pr = Y_Pr^-1 = (R² + X_L²) / R = X_LX_C / R = L / CR
w_r = (1 / LC - R² / L²)^½ = 2pf_r
The quality factor at resonance Q_r is:
Q_r = w_rL / R = (L / CR² - 1)^½ = (1 / R )(L / C - R²)^½

Note that for the same values of L, R and C, the parallel resonance frequency is lower than the series resonance frequency, but if the ratio R / L is small then the parallel resonance frequency is close to the series resonance frequency.

Three Phase Power

For a balanced star connected load with line voltage V_line and line current I_line:
V_line = Ö3 V_phase
I_phase = I_line
Z_phase = V_phase / I_phase = V_line / Ö3I_line
S_phase = 3V_phaseI_phase = Ö3V_lineI_line = V_line² / Z_phase = 3I_line²Z_phase

For a balanced delta connected load with line voltage V_line and line current I_line:
V_phase = V_line
I_phase = I_line / Ö3
Z_phase = V_phase / I_phase = Ö3V_line / I_line
S_phase = 3V_phaseI_phase = Ö3V_lineI_line = 3V_line² / Z_phase = I_line²Z_phase

Power Triangle

There are Three kind of power i.e

True power is a function of a circuit's dissipative elements, usually resistances (R).

Reactive power is a function of a circuit's reactance (X).

Apparent power is a function of a circuit's total impedance (Z).

The relation between all the three of them are given as

P=True power , Measured in watts (W)

P = (I^2)*R

Q=Reactive power , Measured in Volt-Ampere-Reactive (VAR)

Q=(I^2)*X

S=Apparent power ,Measured in Volt-Amps (VA)

S=(I^2)*Z

TRANSFORMERS

Two types according to construction

1) Core type

2) Shell type

Induced EMF in the primary winding:

E1 = 4.44 * f * N1 * [Bm] * A

= 4.11 * f * N1 * [fi] Where N1=Number of turns in Primary winding

F=Frequency

[fi]=maximum flux in core

A=Area

[fi]=A*[Bm]

Form Factor = R.M.S Value/Average Value = 1.11

Transformation ratio :K=V2/V1

For an ideal two-winding transformer with primary voltage V₁ applied across N₁ primary turns and secondary voltage V₂ appearing across N₂ secondary turns:
V₁ / V₂ = N₁ / N₂
The primary current I₁ and secondary current I₂ are related by:
I₁ / I₂ = N₂ / N₁ = V₂ / V₁

For an ideal step-down auto-transformer with primary voltage V₁ applied across (N₁ + N₂) primary turns and secondary voltage V₂ appearing across N₂ secondary turns:
V₁ / V₂ = (N₁ + N₂) / N₂
The primary (input) current I₁ and secondary (output) current I₂ are related by:
I₁ / I₂ = N₂ / (N₁ + N₂) = V₂ / V₁
Note that the winding current is I₁ through the N₁ section and (I₂ - I₁) through the N₂ section.

For a single-phase transformer with rated primary voltage V₁, rated primary current I₁, rated secondary voltage V₂ and rated secondary current I₂, the volt-ampere rating S is:
S = V₁I₁ = V₂I₂

For a balanced m-phase transformer with rated primary phase voltage V₁, rated primary current I₁, rated secondary phase voltage V₂ and rated secondary current I₂, the voltampere rating S is:
S = mV₁I₁ = mV₂I₂

The primary circuit impedance Z₁ referred to the secondary circuit for an ideal transformer with N₁ primary turns and N₂ secondary turns is:
Z₁₂ = Z₁(N₂ / N₁)²

The secondary circuit impedance Z₂ referred to the primary circuit for an ideal transformer with N₁ primary turns and N₂ secondary turns is:
Z₂₁ = Z₂(N₁ / N₂)²

The voltage regulation DV₂ of a transformer is the rise in secondary voltage which occurs when rated load is disconnected from the secondary with rated voltage applied to the primary. For a transformer with a secondary voltage E₂ unloaded and V₂ at rated load, the per-unit voltage regulation DV_2pu is:
DV_2pu = (E₂ - V₂) / V₂
Note that the per-unit base voltage is usually V₂ and not E₂.

Tests done in a transformer…

1)Open circuit test (OC): Determines the core loss / High voltage left open

2)Closed circuit test (CC):

Losses in a transformer :

1) Core loss (Iron Loss) : Constant loss

1.1) Hysteresis loss: Wh=Bmax^1.6 * f ^ 2

1.2) Eddy Current loss: We=Bamx^2 * f ^ 2

2) Copper loss: I^2 * R loss. It is a variable loss

Voltage regulation

BASIC Trignometric Formulaes