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ED 3110 : Product Design Lab. 2

I-Glide: Self-balancing Personal Transporter

Rohan Chavan - ED11B010Piyush Jadav - ED11B018

Dhruvesh Patel - ED11B026Shambhuraj Sawant - ED11B034

May 11, 2014

Abstract

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Contents

1 Problem Statement 3

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Existing products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Our Ideation 4

2.1 What is it? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Technical feasibility 5

4 Manufacturing 7

4.1 layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.3 Initial assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5 Electronics 9

5.1 Code and Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.2 Problems faced . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Appendix 14

7 References 17

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1 Problem Statement

To develop a product that addresses the short distance transportation (2-7 km) issues of peopleacross age groups while keeping the product compact, portable and safe.

1.1 Motivation

Around 85% of students in institute either took public transport or cycled to reach their desireddestination. But this model had its deficit. Students complained about parking issues and bikegetting stolen or damaged.

When we interacted with the older age group they complained about safety and parking is-sues issues and an absence of transport option that could directly reach their doorstep. Otherissues also included significant waiting times and overcrowding in public transportation systems.

We wanted a solution that could address all of these issues. This required the final productto be portable, compact and easy to use on daily basis.

1.2 Market

The next step was to study the market that could be targeted. There is a lot of scope for aproduct like this, if tweaked as per the needs as the range would further widened

1. Students and middle-aged group: Our primary target, here the product could elimi-nate issues mentioned above.

2. Mall, airport and hotel staff: The product could be modified to provide safe, stabletransport with an option to carry luggage.

3. Movement of operators in multi-bay plants: This would reduce waiting times andincrease plant efficiency.

1.3 Existing products

Products in the market targetting these problems include Scarpar, Segway and Electric skate-boards among others. But every option here had their disadvantages such as expensive, heavy,availability etc

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2 Our Ideation

Figure 1: Initial layout

2.1 What is it? A self balancing 2 wheeled transporter

Focusing on basic control algorithm for safe propulsion

Compactness and portability to some extent.

Provided with straps to carry around.

Design can be extended further to include variants of the same to meet different marketneeds and safety requirements.

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3 Technical feasibility

The existing literature ofmobile inverted pendulumwas studied thoroughly ([1],[2]). It was con-cluded from this study that though the dynamics of the system is nonlinear, linear approximationworks very well in a sufficiently large range.

The dynamics of the system was modelled using Newtons laws and linearised to arrive atthe following state space model.

States:

x=

y(t)y(t)(t)(t)

Dynamics matrix:

A=

0 1 0 0

0 2KeKm(MbL2+MbRwLJb)

R(2Mb( JwRw2

+Mw)L2+Jb( 2JwRw2

+Mb+2Mw))Rw2gL2Mb

2Mb( JwRw2

+Mw)L2+Jb( 2JwRw2

+Mb+2Mw) 0

0 0 0 1

0 2KeKm((2Jw

Rw2+Mb+2Mw)Rw

LMb)R(2Mb( Jw

Rw2+Mw)L2+Jb( 2Jw

Rw2+Mb+2Mw))Rw2

gLMb(2Jw

Rw2+Mb+2Mw)2Mb( Jw

Rw2+Mw)L2+Jb( 2Jw

Rw2+Mb+2Mw) 0

Input coupling matrix:

B=

02Km(MbL2MbRwL+Jb)

R(2Mb( JwRw2

+Mw)L2+Jb( 2JwRw2

+Mb+2Mw))Rw0

2Km(LMb( 2JwRw2

+Mb+2Mw)Rw)R(2Mb( Jw

Rw2+Mw)L2+Jb( 2Jw

Rw2+Mb+2Mw))Rw

Input:

u= V(t)

State space equation:x(t) = Ax(t) + Bu(t)

Here,

g Acceleration due to gravityJb Moment of inertia of the person about their center of mass

Jw Moment of inertia of wheels

Ke,Km Motor constants

L Height of the pendulum (person)

Mb Mass of the pendulum

Mw Mass of the wheels

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R Motor armature resistance

Rw Radius of wheels

V(t) Control voltage

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4 Manufacturing

4.1 layout

Figure 2: layout of components on the board

4.2 Design Parameters

To maintain a low centre of gravity all the components were placed on the bottom

Components should not hit ground as than balancing and therefore controlling would bedifficult plus damages to product

The centre of gravity could not lowered to an extent that there would be difficulties placingthe components below.

Figure 3: Our final CAD model

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4.3 Initial assembly

The assembly consisted of three major parts - Motor and wheel, axle and platform. The idea wasto check for part availability in the market and than start with actual manufacturing.

1. Wheels used here (fig. 4 ) are electric scooter wheels

2. A safety factor of 1.75 was considered while designing the axles

3. We faced a lot of issues with these mounts and hence we changed them with bushes

Figure 4: Wheel assembly with sprockets

Figure 5: Axle CAD model

Also it was seen that, the weight distribution is uniform

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Figure 6: Wheel-sprocket mounts

Table 1: Dimensions of components

Parts Symbol Dimensions WeightWheels D 25cm 2 kg

Deck L x W x H 80cm x 35cm x 2cm 2.25 kgMotors d1 10cm 4 kgBattery L1XW1 15cm X 6cm 2.2 kg

sprocket diameter D2 12.5cmpitch of the chain p 8mm 0.7 kg

chain length (30)p 24cm NAdistance between tires a 40cm 4.7 kg (axle+sprocket+wheel)

5 Electronics

Electronics part of I-glide consists of basic modules:

1. Sensing module: It consists of following parts: Razor IMU (SEN-10736 RoHS), FTDI BasicBreakout 3.3V (DEV-09873 RoHS)

2. Actuator module: It consists of following parts: 2X 2500 RPM motor, 2X 12V Lead-acidbatteries, 2X DC motor drivers

3. Processing module: It consists of following parts: Arduino UNO.

4. Electrical assembly: It consists of general electrical components like 10, 15, 20A fuse, 10Vand 24V switches, LEDs, Prototype board.

Circuit Schematic:

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Figure 7: Circuit

5.1 Code and Algorithm

For the first implementation PID controller for pitch angle was used. The code is as follows:

# i n c l u d e / To s u pp o rt s e r i a l c om mu ni ca tio n w it h2 d e v i c e s s i mu l t an e o u sl y /

S o f t w a r e S e r i a l m y Se r ia l ( 1 2 , 1 1 ) ;/ RX, TX Se t th e s o f t S e r i a l p or t /

/wor kin g v a r i a b l e s o f t he p id /unsigned long l astTi me=0;double I n p u t =0 , O ut pu t=0 , S e t p o i n t = 0;double ITerm =0 , l a s t I n p u t = 0;double kp , ki , kd ,KP=0.0 05 ,KI=0,KD=0;i nt pwm=0;const double s l o p e = 1 0 . 6 2 5 ; / t o s c a l e t he Output

i n V o l ta g e t o a p p r o p r i a t e PWM s i g n a l/c on st i n t DirPin=4;c on st i n t M1pwmPin=3,M2pwmPin=9;i nt SampleTime=250; // . 2 50 s e c

void S e t T u n i n g s ( double Kp, double Ki , double Kd)// F unc tio n t o f i n d g a in s f o r t he d i s c r e t e syst em{

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double SampleTimeInSec = (( double )SampleTime)/1000;kp = Kp;k i = K iSampleTimeInSec ;kd = Kd/SampleTimeInSec ;

}

/ / Fu nc ti on t o r e ad t h e p i t c h a n g l e v a l ue fr om IMUdouble ReadPitch ( )

{my Seri al . pri n t (#f ) ;while ( m y S e r i a l . a v a i l a b l e ( )


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}

void l oop () / / Main l o o p{

double e r r o r ;Input= ReadPi tch ( ) ;e r r o r = S e t p o i n t Input ;

while ( e r r o r=10) // Loop f o r s o f t s t a r t{ Input= ReadPi tch ( ) ;e r r o r = S e t p o i n t Input ;}

SetTunings(KP,KI,KD);l astTi me=0;pwm=0;

while ( 1 ) / /Main c o n t r o l l o op{Input= ReadPi tch ( ) ;e r r o r = S e t p o i n t Input ;

unsigned long now = m i l l i s ( ) ; / / p r e s e n t t im es ta mpdouble t i meChange = ( double )(now l a s t T i m e ) ; / / t i m ec h a n ge

i f( timeChange>=SampleTime){

/Compute a l l t he w or ki ng e r r o r v a r i a b l e s/

/do o nl y f o r p it ch /ITerm += ( k i e r r o r ) ;double d I n p u t = ( I n p u t l a s t I n p u t ) ;

/Compute PID Output/Output = kp e r r o r + I T e r m kd dInput ;

/Remember s ome v a r i a b l e s f o r n e xt t i me/l a s t I n p u t = I np ut ;l a s t T i m e = n o w ;

}

/ Co nv er t t h e Output i n t o a s i g n a l wh ic hc an b e g i v e n t o pwm /

i f( Output>=0){

pwm= i nt ( s l o p e ( Output ) ) ;an al og Wr it e (M1pwmPin, pwm) ;an al og Wr it e (M2pwmPin, pwm) ;di gi ta l W ri te (D i rPi n , HIGH ) ;

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}e l s e

{pwm= i nt ( s l o p e (Output ) ) ;an al og Wr it e (M1pwmPin, pwm) ;an al og Wr it e (M2pwmPin, pwm) ;di g it al Wr it e ( DirPin ,LOW) ;

}

i f(pwm>100) // s a fe t y c u t o f f {

break ;}

}}

The filter and communication code on the controller on the IMU is quite complicated and hencegiven in Appendix-1 for the sake of completeness.

5.2 Problems faced

1. Serial communication problem: Razor IMU firmware was designed to give continuousstreaming output, while arduino couldnt handle this continuous stream. For this purpose,we needed to change the firmware a bit and write a separate module for communication.Finally everything synced together!

2. Connectors: This is the usual problem of any circuit, connection breaking in between orloose connection. To solve this, we used sealing gun.

3. Motor Driver: This problem was caused because of high initial current requirement of dcmotor. Even after putting fuse, we lost 4 of our working motor drivers. We couldnt fixthis problem. For this purpose, total of 4 types of drivers were tried, but none of themworked successfully. The best way to overcome this problem would be to build our ownmotor driver based on H-bridge circuit.

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6 Appendix

(A) Mathematica code to obtain closed loop system

In[1]:= subs 2 Mw 2 Jw Rw^2 Mb;

subs Jb 2 Mb L^ 2 Mw Jw Rw^2;

In[3]:= A 0, 1, 0, 0, 0, 2 Km KeMb L Rw Jb Mb L^ 2 R Rw^2,

Mb g L^ 2 , 0, 0, 0, 0, 1,

0, 2 Km KeRw Mb L R Rw^2, Mb g L , 0 . subs. subs;

In[4]:= MatrixFormA

Out[4]//MatrixForm=

0 1 0 0

0 2 Ke KmJbL2 MbL Mb Rw

R2 L 2 MbMw JwRw2

JbMb2 Mw 2 JwRw2

Rw2g L 2 Mb

2 L 2 MbMw JwRw2

JbMb2 Mw 2 JwRw2

0

0 0 0 1

02 Ke KmL MbMb2 Mw 2 Jw

Rw2 Rw

R2 L 2 MbMw JwRw2

JbMb2 Mw 2 JwRw2

Rw2g L MbMb2 Mw 2 Jw

Rw2

2 L 2 MbMw JwRw2

JbMb2 Mw 2 JwRw2

0

In[5]:= B 0, 2 KmJb Mb L^ 2 Mb L Rw Rw R ,

0, 2 KmMb L Rw Rw R . subs . subs;

In[6]:=

model StateSpaceModelA, B,

0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, SystemsModelLabels

"Voltage", "vel", "angle", "ang_vel", "pos", "vel", "angle", "ang_vel"

Out[6]=

Voltage

pos 0 1 0 0 0

vel 02 Ke Km

Jb L2 Mb L Mb Rw

R2 L 2 MbMw Jw

Rw2 JbMb 2 Mw 2 Jw

Rw2Rw2

g L 2 Mb

2 L 2 MbMw JwRw2

JbMb 2 Mw 2 JwRw2

0

2 Km

Jb L2 Mb L Mb Rw

R2 L 2 MbMw Jw

Rw2 JbMb 2 Mw 2 Jw

Rw2 Rw

angle 0 0 0 1 0

ang_vel 0

2 Ke KmL Mb Mb 2 Mw 2 JwRw2

Rw

R2 L 2 MbMw JwRw2

JbMb 2 Mw 2 JwRw2

Rw2g L MbMb 2 Mw 2 Jw

Rw2

2 L 2 MbMw JwRw2

JbMb 2 Mw 2 JwRw2

0

2 KmL Mb Mb 2 Mw 2 JwRw2

Rw

R2 L 2 MbMw JwRw2

JbMb 2 Mw 2 JwRw2

Rwvel 0 1 0 0 0

angle 0 0 1 0 0

ang_vel 0 0 0 1 0

Data Rw 0.2, Mw 4, Jw 0.07, L 1.8,

Mb 120, Jb 60, g 9.8, Km 0.069, Ke 0.083, R 0.5 6;

In[8]:= minModel SystemsModelDeletemodel, None, None, 1 . Data

Out[8]=

Voltage

vel 0.11275 0.308242 0 0.271686

angle 0 0 1 0

ang_vel 0.0527333 22.5188 0 0.127068

vel 1 0 0 0angle 0 1 0 0

ang_vel 0 0 1 0

In[9]:=

gains StateFeedbackGainsminModel, 10, 5, 1.5

Out[9]=12.7528, 747.778, 156.231

In[10]:=

rlen L

Figure 8: Code to obtain closed loop system

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Code added for simulation and visualization

In[11]:= animation initial state response

Manipulate

gains StateFeedbackGainsminModel, p1r, p2r, p3r;

fullstateFB SystemsModelStateFeedbackConnectminModel, gains;

soln StateResponsefullstateFB, 0, start, 0, 0, t;

solvt_ soln1;

solt_ soln2;

soldott_ soln3;

solxt_ xt . DSolvex't solvt, x 0 0, x t, t 1;

Voltaget_ gains.solvt, solt, soldott;

Withloc solxrun, run solrun,

topx rlen Sinrun;

topz rlen Cosrun;base Graphics3D

Yellow, Polygon

10, 0.2, 0.2, 10, 10, 0.2, 10, 10, 0.2, 10, .2, 0.2;

rod Graphics3DBlue, Cylinderloc, 0, 0, loc topx, 0, topz, .1;

ball Graphics3DRed, Sphereloc topx, 0, topz, .1;

wheel Graphics3DBlack,

Cylinderloc, .2, 0, loc, .2, 0, .3;

board Graphics3D

Green, Polygonloc 1 Cosrun, .4, Sinrun,

loc 1 Cosrun, .4, Sinrun, loc 1 Cosrun, .4, Sinrun,

loc 1 Cosrun, .4, Sinrun;

Grid

Showbase, rod, ball, board, wheel, PlotRange 8, 8 , 0.5, 2, 1, 2 ,

ImageSize 800, 400, Axes True,

Plotsolxt, t, 0, 10, PlotRange All, PlotLabel "Displacement",

AxesLabel "times", "disp.m", ImageSize 200, 150,

Plotsolvt, t, 0, 10, PlotRange All, PlotLabel "velocity",

AxesLabel "times", "velocity.ms", ImageSize 200, 150,

SpanFromAbove,

Plotsolt, t, 0, 10, PlotRange All, PlotLabel "pitch angle",

AxesLabel "times", "rad", ImageSize 200, 150,

Plotsoldott, t, 0, 10, PlotRange All, PlotLabel "pitch rate",

AxesLabel "times", "'rads", ImageSize 200, 150,

SpanFromAbove,

Plotrlen soldott ^2 9.8,

t, 0, 10, PlotRange All, PlotLabel "Centrpetal acc. ",

AxesLabel "times", "acentg", ImageSize 200, 150,

PlotVoltaget, t, 0, 10, PlotRange All, PlotLabel "sup. Voltage",

AxesLabel "times", "Voltage V", ImageSize 200, 150

,

Alignment Top

,

var name,initial val,"label",

min,max,increment size,Appearance"Labeled",

start, 0.1, "angle ", 8, 8, Appearance "Labeled",

p1r, 3.2, "pole1 real part ", 10, 0, .2, Appearance "Labeled",

p1c,.02,"pole1 complex part",1,0,.02,Appearance"Labeled",

p2r, 2, "pole2 real part", 10, 0, .5, Appearance "Labeled",

p2c,2,"pole2 complex part",10,0,.5,Appearance"Labeled",

p3r, 3, "pole3 real", 10, 0, .2, Appearance "Labeled",

run, 0, "release system", 0,

10, .1, ControlType Trigger, AnimationRate 1,

SynchronousUpdating True, SaveDefinitions True,

AutorunSequencing 1, 3, 5, TrackedSymbols True

Figure 9: Code added for simulation and visualization

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angle q 0.1

pole1 real part -3.2

pole2 real part -2

pole3 real -3

release system

-5

0

50

1

2-1

0

1

2

2 4 6 8 10timeHsL

-2.0

-1.5

-1.0

-0.5

disp.HmL

Displacemen

2 4 6 8 10 timeHsL

-1.5

-1.0

-0.5

elocity.HmsL

velocity

2 4 6 8 10timeHsL

-0.02

0.02

0.04

0.06

0.08

0.10

qHradL

pitch angle

2 4 6 8 10timeHsL

-0.20

-0.15

-0.10

-0.05

q'HradsL

pitch rate

2 4 6 8 10timeHsL

0.002

0.004

0.006

0.008

acentHgL

Centrpetalacc.

2 4 6 8 10timeHsL

10

20

30

VoltageHVL

sup. Voltage

Figure 10: Dynamic simulation

Physical parameters of the system

Mw Mass of the wheels 4Mb Mass of the pendulum 120Ke Motor constant 0.083Km Motor constant 0.069R Motor armature resistance 1Rw Radius of wheels 0.2L Height of the pendulum (person) 1.8Jb Moment of inertia of the person about their center of mass 60

Jw Moment of inertia of wheels 0.07g Acceleration due to gravity 9.8

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7 References

1. Grasser, Felix, et al. JOE: a mobile, inverted pendulum. Industrial Electronics, IEEETransactions on 49.1 (2002): 107-114.

2. Thao, Nguyen Gia Minh, Duong Hoai Nghia, and Nguyen Huu Phuc. A PID backstep-ping controller for two-wheeled self-balancing robot. Strategic Technology (IFOST), 2010International Forum on. IEEE, 2010.

3. https://www.sparkfun.com/products/10736

4. https://www.sparkfun.com/products/9873

5. http://arduino.cc/en/Main/ArduinoBoardUno

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