TR

Depa

ConconsicontrNumeapprocontrtracki Keyw 1. IN to maIn threferrtrajeccontrmatheTheserobotHowerequirwithochallealwayenvirto seenvirAdappropomost propomodeHencstruct

providemaunpre

RACKINUSING

artment of Elec

trol of an indusidered in the doller (GAFPIDerical simulatioach in trajectools are presenting precision c

words: Fuzzy P

NTRODUCTIO

The basic ake the manipuhe robotics litered to as the ctory tracking ol methods dematical mode approaches ts that operatever, operationre robots to pe

out an adequaenging problemys uncertainonments. Thes

ensor imprecisonment chara

ptive control osed for this typ

of the exisosed to control el characteristce, developingture has becom

The adveides us with anding real-woedictable en

  Jou

NG CONTG GENET

ctronics & Com

Email: 1

strial robot incldesign of contD) to trace thion using the dory tracking prted to validate could be achiev

PID, Genetic a

ON

problem in coulator follow a erature, this cmotion controproblem [l]. Cdepend heavil

deling, analysiare suitable f

te in structurns in unstructuerform much mate analytical m in this fieldnties in thse uncertaintiesion and unpreacteristics an

algorithms [pe of control systing adaptivethe specific sy

tics and unkng model-free

me an interestin

ent of fuzzya powerful

rld problems wnvironments

urnal of Theoret

© 2005 - 200

TROL OFTIC ALG

CON1Srinivasan A

1Re

2Ass

mputer Enginee

seenu.phd@gm

A

ludes nonlineatrol laws. Thi

he desired trajdynamic moderoblems. Compthe controller

ved using the p

lgorithm, robo

ontrolling robotdesired trajectontrol problemol problem or Conventional roly upon accuis, and synthefor the controred environmeured environm

more complex tamodel. The m

d is that therehe unstructus are primarily edictability of

nd its dynam[2-4] have bystems. Generae algorithms ystems with knonown paramet

adaptive conng research top

y set techniqtool for solv

with uncertain [5]–[7]. Fu

ical and Applied

07 JATIT. All rights

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15 

F 3-DOF RORITHM

NTROLLE

Alavandar, 2Mesearch Scholarsociate Professoering, Indian In

mail.com,

2mkn

ABSTRACT

rities, uncertains paper presenectory for a tel of three DOparative evaluadesign. The re

proposed contro

ot control, Deg

ts is tory. m is

the obot urate esis. l of ents.

ments asks most are ured due

f the mics. been ally,

are own ters. ntrol ic.

ques ving and

uzzy

controlcompabecausfuzzy-lcombinpave tomanipu

controlmembeexpert'existinmembetrial-anand ausystemon the reprodudesign and cimprov

optimizsets Kamembeand caStonieroptimizalgorith

d Information T

reserved.

ROBOT M TUNEDER M.J.Nigam r or

nstitute of Tech

ndnfec@iitr.ern

nties and externts the Genetithree degree o

OF robot arm ation with respesults presenteoller than conv

gree of Freedom

ller can charing with clase of its non lilogic and convned (hybrid) too appropriate soulators [8-10].

The core ller is the seership function's interpretation

ng iterative aership functiond-error procesutonomy. Ther

matic genetic alsurvival-of-theuction and mutfor searching tomplex memved performanc

GAs have przing the membarr, for exampership functionartpole probler developed azed the memhm [14]. M

echnology

MANIPUD FUZZY

hnology Roork

rnet.in

rnal perturbatioic algorithm tuof freedom (Dshows the effe

pect to PD, PIDed emphasize thventional contro

m (DOF)

haracterize bassical linear inear characterventional-techno design FL colution for con

of designing election of hins that represn of the linguisapproaches foons are basicss and lack learefore, the molgorithm (GA) e-fittest Darwintation, has beethe poorly und

mbership functce.

roven to be a ubership functio

ple, has used ans for a PH conem [13]. Moa fuzzy logic

mbership functMester in [15

ULATORY PID

kee, India-2476

ons that should uned Fuzzy P

DOF) robot arectiveness of tD and Fuzzy Phat a satisfactooller.

better behavPID control

ristics. Recentniques have becontrollers whintrolling the rob

a Fuzzy logigh performansents the humtic variables. T

or choosing tcally a manuarning capabilore efficient a

[11], which anian principle fn applied to FLerstood, irregution space w

useful method fons of the fuz

a GA to generantrol process [1hammadian a

c controller ations by gene5] developed

R

667

be PID rm. the

PID ory

ior ller tly, een ich bot

gic nce

man The the ual lity and cts for LC

ular with

for zzy ate 12] and and etic

a

neuromanipoptimKaynadaptalgorsystemrobot

(FPIDapplieand ssuch trajecCompFuzzycontrfollowfreeddescr4 intr5 deaContrsimulof threspeperfothe stprese

The p

(3) If equbelow

o-fuzzy-geneticpulators; he a

mize the fuzzynak in [16] protation in fuzzithm, they invem having parat manipulators.

In our appD) is designeed to tune andscaling factors a manner that

ctory tracking parative evaluay PID controloller design. Ows. Section 2 om robot arm a

ribes the designroduces the genal with the use roller and Slation results t

he approach anect to PD, PIormed. And Setudied fuzzy c

ented.

potential energy

uation (3) is rw equations can

  Jou

c controllerapplied the geny rule set. Esoposed a procezy logic systemestigate the perameterized T-N

proach, a Fuzzd and then ge

d optimize memof designed f

t a high precisof three DOF

ation with respels are presenteOrganization ointroduces the

and its dynamin of fuzzy PID netic algorithmof GA to Opti

Section 6 proto demonstratend comparativD and Fuzzyction 7 discusscontrol law an

y can be calcul

replaced in ton be obtained

urnal of Theoret

© 2005 - 200

r for ronetic algorithmskil and Efe edure for T-Nms using genrformance of fuNorm in contro

zy PID Controenetic algorithmmbership functfuzzy controllesion controllerrobot is obtain

ect to PD, PID ed to validate of the paper ie three degreec model. Sectiocontroller. Sec

m concepts, Secimize Fuzzy Loovides numere the effectivenve evaluation wy PID controlses the benefit

nd conclusions

lated by

o equation (2),

ical and Applied

07 JATIT. All rights

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16 

obot m to and

Norm netic uzzy ol of

oller m is ions

er in r for ned. and the

s as s of on 3

ction ction ogic rical ness with s is ts of are

2. R

M

manipuapproa

of freedefined

where

is t

generaLagranPotentiL (2)

, the

(4)

d Information T

reserved.

ROBOT ARMODELING

Three Degrulator used forach is shown Fi

Consider a redom (DOF). d by [1],

(1)

T is the torqu

the generalized

alized velocity nge function isial energy (V)

echnology

RM DYNA

ree of freedor numerical simig 1. robot manipula

The torque t

ue, L is the La

d coordinate o

of ith

joint. s described byas follows:

=

AMICS AN

m (DOF) robmulation for th

ator with n degrto be applied

, i = 1, 2, 3…

agrange functio

of ith

joint, is t

y kinetic (K) a

K

ND

bot his

ree is

…n

on,

the

and

K-V

(5) The ederiv

(6) Wheroccurmatri

CorioConsgiven

E, F, angleThe c

equations of moed from (5) an

re G (q) is the irred due to gix,is the ix1

olis Torques. equently, the T

n by,

The coeffic

G, H, K variabe of joints are gcoefficients of

  Jou

otion for the rond are given by

x1 vector that igravity, D(q) vector shown

Torque of three

cients of d matrbles depend on

given below. d matrix are:

urnal of Theoret

© 2005 - 200

obot system can

is formed matris the ixi Ine

n Centrifugal

e DOF robot arm

(7) rix and A, B, Cn mass, length

ical and Applied

07 JATIT. All rights

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17 

n be

rixes ertia and

m is

C, D, and

and c c

,

d Information T

reserved.

coefficients are

(8)

echnology

e found as

)

,

,

,

joint

(9)

(11) whe

is the

are reThe Pin thi

Ta

The dfuzzifproce

(13)

, ,

,

, are theand given Equ

re m is the mas

e half of the len

eplaced into theParameters ands paper are giv

able 1. Parammass of arm

development ofication, defuesses, from equ

  Jou

e potential eneruation (6).

ss, g is the grav

ngth of joints.

e DC motor eqd details of theven in Table 1

meters of 3-DO

0.

f FLC deals wfuzzification uation (12) letti

urnal of Theoret

© 2005 - 200

rgy values of e

(10

vity acceleratio

T1, T

2, T

3 Torq

quation. e robotic arm u

OF robotic arm7 Kg

Figure 2. St

with formulatioand rule b

ing

(14

ical and Applied

07 JATIT. All rights

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18 

ach

0)

on; lc

ques

used

m

3. Fuzz

three-insimulacontrol

(

logic applyinshows controlerror, convermembeframedConverdone b

tructure of Fuzz

n of base

4)

Equati

(16)

d Information T

reserved.

moment of ine

length of arm gravity accele

zy PID ContrThis sectio

nput Fuzzy PIation. The geneller is given by

(12) The above eqform to yieldng to various

the structurller. The threechange in e

rted in to ership ship vald to suit the orting members

by defuzzificati

zy logic contro

on (12) can no

echnology

ertia 5e-10

0.8ration 9.8

oller Design on describes ID controller weral discrete – ty,

quation is convd robust cont

non linear sye of a typice inputs to fuzerror and int

linguistic vlues are assignoutput responsship values toion block.

oller

ow be written a

kg m2

m m

2/s

the design which is used time form of P

verted into fuztroller ready fystems. Figurecal fuzzy logzzification blotegral error a

variables whoned. The rules ae of the syste

o crisp values

(15)

as

of in

PID

zzy for

e 2 gic ock are ose are

em. is

and

differmemb

trianglimit miniminputby ‘nfunct

SimilspecinegatL defare trespe

With compIF e

P

NegaIF e

P

Then IF e

P

Then IF e

P

in

(17)These thre

rent input membership functio

gular membersL. This limi

mum values fos positive deno

n’ are used toions. This is sh

Figure 3. Inlarly, four outfied to represtive large (nl) afines maximumtwo new outp

ectively. This is

Figure 4. Outhe above mem

position rules a

P is Negativ

ative, Then is Negative ,

is .Negativis Positive , e

is .Negativis Positive , e

  Jou

incremental

) ee errors are combership functions used for e

Iship functions it specifies th

or the fuzzificaoted by ‘p’ ando specify the ihown in Figure

nput membershtput memberssent positive and positive lar

m and minimumput terms ces shown in belo

utput membershmbership functare defined as fve , e

I is Ne

is .Negative lae

I is Negative

ve e

I is Negative

ve e

I is Negative

urnal of Theoret

© 2005 - 200

form

onverted into thions. The simp

I, e

P and e

D are

with a threshhe maximum ation process. Td negative denoinput membere 3.

hip functions ship functions (p), negative rge (pl). Param

m outputs, but thenters at +/-ow Figure 4.

hip functions tions, the inferefollows. egative & e

D

arge e & e

D is Posit

& eD is Nega

& eD is Posi

ical and Applied

07 JATIT. All rights

www.jatit.org 

19 

as

hree plest e the

hold and

Two oted ship

are (n),

meter here L/3

ence

D is

tive,

tive,

tive,

Then IF e

P is

Then IF e

P is

Then IF e

P is

Then IF e

P i

Then Treasonusing Zdefuzzoutput

4. GE

techniqselectioeffectivand coGA is commoan inichromoof the pfitness genetic

d Information T

reserved.

is . Positives Negative , e

I

is .Negatives Negative , e

is . Positives Positive , e

I

is . Positiveis Positive , e

I

is .Negative

The fuzzy infeing, based onZadeh’s compo

zification blocu (t) by utilizin

ENETIC ALG

GA is a stochaque based onon. Recently, Gve technique t

ompared with superior in avoon aspect in noitial populatioosomes where problem whichfunction. Figu

c algorithm pro

echnology

e

I is Positive

e e

I is Positive

e

I is Positive &

e

I is Positive

e large

ference engine n the linguistiositional rule ock generates ng the centre of

GORITHMS

astic global sean the mechanGA has been rto solve optimother optimizaoiding local m

onlinear systemon containingeach one repr

h performance ure 5 shows theocess.

& eD is Negativ

& eD is Positiv

& eD is Negativ

& eD is Positiv

performs fuzic control rulof inference. Ta crisp contrf gravity metho

arch optimizatinisms of naturecognized as

mization problemation techniqu

minima which ims. GA starts wg a number resents a solutiis evaluated by

e flow chart of t

ve,

ve,

ve,

ve,

zzy les, The rol od:

ion ural

an ms es; s a

with of

ion y a the

Fi reproRepropopulfitneswith havinare areproschemin Gexchai.e., pselectalteraMutareprothe gGA’s 5. US

C

for cosystemfunct

whereintegr

igure 5. Flow c

GA’s consisoduction, coduction is thelation reproduss of the indiv

higher fitnesng more copiesa number of soduction, such ame,” “ranking s

GA occurs whange partially part of the strted candidatesation of states ation is essentiaoduction and crglobal optimal s can be obtain

SING GA’S TOCONTROLLE

The perforontrolling multms strongly ion parameter

F

e,,,,,,,and are tral controller

  Jou

chart of the gen

st of three crossover, e process wheruced accordinviduals, where s have higher

s in the comingselection schemas “roulette whscheme,” etc. [hen the selecttheir informat

ring is interchs. Mutation is

at a particulaally needed in rossover alone

solution. Furted in [17&18].

O OPTIMIZEERS rmance of Fuzzti input-multi o

depends on rs. GA’s are s

Figure 6.Fitness value =

the proportiongains of Fuzz

urnal of Theoret

© 2005 - 200

netic algorithm

basic operatiand mutatre members ofg to the relathe chromosor probabilities

g generation. Thmes available heel,” “tournam[17-18]. Crossoted chromosotion of the ge

hanged within s the occasionar string positsome cases whare unable to other discussion.

E FUZZY LOG

zy logic controlutput and compthe member

stochastic, rob

Structure of G

nal, derivative zy PID contro

ical and Applied

07 JATIT. All rights

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20 

m

ons: tion. f the ative omes s of here

for ment over

omes enes,

two nally tion. here offer n on

GIC

llers plex ship bust,

and glonear owithouno prioformullearninfuzzy-cgeneticby a lproposGenetialgorithby takmembeoutputsto calc

genetictotally purposthe fitnthe sysfunctioconsidresponintegra

Genetic tuned F

and

oller

which

d Information T

reserved.

obal search algoptimal solutiout derivative inor knowledge late a set of fung, they havcontrol designc fuzzy systemearning proce

sed [19-20]. Fiic tuned Fuzhms can be useking input paership functios desired objeculate optimum

Fitness func algorithms b

depends on se of the optimness of individstem are compon. In roboticered for small

nse time. The fial absolute erro

Fuzzy control s

are to be tune

echnology

gorithms with tons in complenformation. Sinabout the systeunctional contrve been appn for unknows, i.e. fuzzy sysss based on Gigure 6 showszzy control sed to optimize tarameters as

ons or controlctive function

m values of FPID

nctions play abecause the dir

these functionmization problemduals, performapulsory elemenc manipulatorserrors, smoothtness considere

or.

system.

d.

the ability to fiex search spacnce GA’s requem’s behavior rol rules throulied widely

wn plants. Mastems augmentGA’s, have bes the structure system. Genethese parametescaling facto

l rules etc. a[21]. GA is usD controller.

a major role rection of searns. Because tm is to minimiance measures nts of the fitnes fitness can h torques, and fed in this paper

ind ces

uire to

ugh to

any ted een

of etic ers, ors, and sed

in rch the ize of

ess be

fast r is

6.

are shpositiPID, profilthree

SIMULATIDISCUSS Trajectorie

hown in table 2ions followingFuzzy PID a

le of GA tunedjoints.

  Jou

ION RESION

es which are u2. Figures 7-9 bg desired trajeand Figure 10 d Fuzzy PID c

Figure 7 (a)

Figure 7 (b)

urnal of Theoret

© 2005 - 200

SULTS A

used in this wbelow shows joectories with P

shows the ercontrollers for

ical and Applied

07 JATIT. All rights

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21 

AND

work oint PD, rror the

Figure

d Information T

reserved.

Table 2. Set T

1st joint

Fe 7. (a),(b)&(c)

for

F

echnology

Trajectory for s

2nd

join

Figure 7 (c) ) Tracking usinvarious joints

Figure 8 (a)

imulation

nt 3rd

join

ng PD controll

nt

er

Figur

re 9. (a),(b)&(cfo

  Jou

Figure 8 (b)

Figure 9 (a)

Figure 9 (c) c) Tracking usinor various joint

urnal of Theoret

© 2005 - 200

ng FPID contros

ical and Applied

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22 

Figure

oller

Table

d Information T

reserved.

Fe 8. (a),(b)&(c)

for

F

3. Positional e

Controller PD

PID FPID

GAFPID

echnology

Figure 8 (c) ) Tracking usinvarious joints

Figure 9 (b)

errors with diff

IAE I0.4051 0.2

0.3944 0.20.2332 0.10.2113 0.1

ng PID controll

ferent controlle

SE ITAE 2714 0.2766

2642 0.26041596 0.15961436 0.1021

ler

ers

6

4 6

Figu

compprobltuninOptimthree

423.4

3 shodiffer 7. C

and trackiFuzzyand Pthese factorAlgordesigTunintuner algor REFE [1].

[2]. J

aA

ure 10. Error Profi

Fuzzy PIpared to PD lem faced with g of scaling f

mum values fojoints up t

496257, ki = 3.

ows the comparent controllers

CONCLUSION

Due to the parameter vaing control of y PID controllePID controller

controllers is rs with Genrithm are syste

gner but they ng of Fuzzy P

in which seqithms can be fu

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24 

man

oller gs of onal and

kyay ogic

dings on

hms.

arch, ding,

and ems: uzzy tems

World

netic iotic EEE , pp.

ning netic Man,

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echnology