Iccais2013 Eng v5

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2013 International Conference on Control, Automation and Information Sciences (ICCAIS)

Abstract:The paper presents a model refeference adaptive

control algorithm for mobile robot with parameter

uncertainties and unstructured dynamics to guarantee that

robot can track to desired trajectory asymptotically. Thecontroller has been designed in two consecutive parts; one is a

nonlinear kinematic controller and the other is the model

reference adaptive controller using feedback signal from

mobile robots actuator. The simulation results show the

efficiency and the aplication ability of the proposed controller

Index TermsMobile Robot Tracking !onlinear

"ontrol #daptive "ontrol Model Reference #daptive

"ontrol !onholonomic

$ymbolsSymbols Unit Definition

Ik!m2

"oment of inertia of mobile robotm k #ei$t of mobile robot

1t 2tk!m2 "oment of motor (left, ri$t)

, ,x yk k kqAda%ti&e ad'ustment factor of control loo%dynamics

,g b Ada%ti&e ad'ustment factor of sam%lemodel

2 mt #idt$ of mobile robot* mt #$eel radius of mobile robot

I+ SS-." /.*I.#

. mobile robot is an automatic mac$ine t$at isca%able of mo&ement in any i&en en&ironment

because of usin $eels, craler $eels, or les+ Due to t$efleibility in t$e mo&ement of mobile robot, manyresearc$ers are researc$in and de&elo%in its intellienceand ada%tability in different en&ironments+ -$en, t$etrackin control it$ model reference ada%tation for mobilerobot is t$e issue is bein interested, s%ecially $en robot4s

%arameter c$anes and dynamical model is effected byeoenous disturbances+

-

"any studies in non$olonomiccontrol systems $a&e been carried onin %ast decade 51,2,3,67+ 8oream%le, trackin control usindirect ya%uno& met$od

53,10,19,1:7, time &ariant statefeedback 527, and many ot$er

;-ien < =o "an$ orks at Institute of >$ysic, ietnam Academy ofScience and -ec$noloy, =o 1?, oan @uoc iet Street, CauiayDistrict, anoi, ietnam (corres%ondin aut$or emailBnmtienio%+&ast+ac+&n)

"in$ >$an Euan orks at anoi Uni&ersity of Sience and-ec$noloy, =o1, Dai Co iet Street, ai Fa -run District, anoi,ietnam (corres%ondin aut$or emailBmin$%$uoc

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a dI

q

t- = &

"ulti%lyin t$e first %art of .Guation (9) by osc qand t$esecond %art by sin qand addin t$e results t$e folloin isobtainedB

( cos sin ) ,

! !x y xy

a

v d d d m m

dI

q

t tq q

t

= - + = -

= -

&

&

#$ere v and w are t$e linear and anular &elocities ofmobile robot+ -$is is *obot4s dynamic model+ -$e ot$er

%art of normal form is ritten accordin to .Guation (3)Bcos

sin

x v

y v

q

q

q

=

=

=

&

&

&

Usin kinematic model (11) and dynamic model (10)

abo&e,in t$e net section, t$e controller $as been desinedin to consecuti&e %artsK one is a nonlinear kinematiccontroller and t$e ot$er is t$e model reference ada%ti&edynamic controller to %ro&ide trackin of desired linear andanular &elocities

III+ S-*UC-U*./8C/=-*/SS-."

.tractin t$e kinematic model from dynamic eGuations,t$e control system $as been desined in to control loo%+-$e outside< loo% can use t$e nonlinear kinematiccontrollers to stabiliJe t$e confiuration &ariables+ Sincetrackin control of mobile robot is sim%ly reduced to

reulariJation %roblem of error &ariables in kinematicmodel+ /ut%ut of t$e nonlinear kinematic controller

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lobal asym%totic stability of t$e closed loo% system can be%ro&ed by t$e folloin ya%uno& functionB

2 21( ) (1 cos ) !

2 e e e y+ x y k q= + + - 0yk >

A similar controller and a discussion on t$e effect of control%arameters is %resented in 5H,127+

B& T0e reference mode! of ve!ocity errors:/ut%ut of t$e nonlinear controller of last section is t$e

desired linear and anular &elocities for NinematicstabiliJation (%osition and orientation of robot)+ -$ese&alues are as t$e reference in%uts for t$e dynamic controller+In t$is section, t$e folloin control las are used to

%re%are trackin of dv and d' it$ assumin t$at uncertain%arameters (m and I) and eoenous disturbance constant (

xyd , d ) ere i&enB

( )

( )

! d ! d xy

a d a d

mv k v v md

I' k ' ' Idq

t

t

= + - +

= + - +

&

&

#$ere !k and ak are to %ositi&e control %arameters+Substitutin .Guation (21) in .Guation (10)B

( )

( )

d ! d xy

xy

!d d

mv k v v md v d

m

kv v v

m

+ - +

= - =

+ -

&&

&

( )

( )

d a d

ad d

I' k ' ' Idd

I

k

I

q

q

+ - += - =

+ -

&&

&

.rror of desired &elocity and actual &elocity is defined asB

e d

e d

v v v

' '

= -

= -

Substitutin .Guation (23) in .Guation (22)B

0

0

!e e

ae e

kv v

m

k' '

I

+ =

+ =

&

&

ConseGuently e%onential con&erence of v and w to t$edesired &alues is uaranteed+

Fecause ,! ak k is o%tional, let1! ak k T

m I

= =

t$en t$e reference model for &elocity error is1 1

1

0 0

0

e e

e e

v T v T

' T '

- -

-

+ = >

+ =

&

&

$ere 1T is in&erse of t$e time constant of error dam%in-, $ic$ s$ould be manually tuned de%endin on se&eral

%arametersK suc$ as Actuator limitations, con&erence rateof nonlinear kinematic controller 510,127 and in a discrete

system, at least four times larer t$an t$e sam%le time ( sT

)+Substitutin 1T in eGuation (26) to eGuation (21),t$e

eGuation (21) as reritenB1

1

1

( )

( ) ( cos sin )

( )

! d d xy

d d x y

a d d

mv mT v v md

mv mT v v m d d

I' IT ' ' Idq

t

q q

t

-

-

-

= + - +

= + - + +

= + - +

&

&

&

C& Mode! reference ada*tive contro!) Inner !oo* dynamic

contro!!er

In t$e control structure of last section t$e &alues of

uncertain elements ( , , , , , )x y xym I d d d d are assumed to

be knon+ In fact, not only t$e measurements of t$eseelements $a&e uncertainties, but also t$ey c$ane in a larearea in most a%%lications+ 8urt$ermore, eoenous

disturbance d is noticeable $en t$e robot orks in

different terains+ So t$e control las s$ould be ritten in

t$is formB1

1

OO O O( )

OO O O( )

! d d xy

a d d

mv mT v v md

I' IT ' ' Idq

t

t

-

-

= + - +

= + - +

&

&

1

1O O

1

O OO O O( ) ( cos sin )

O OO O ( ) cos sin

OO O O( )

! d d x y

d d mx my

a d d

mv mT v v m d d

mv mT v v d d

I' IT ' ' Idq

t q q

q q

t

-

-

-

= + - + +

= + - + +

= + - +

&

&

&

-$e errors beteen m and Om , I and OI , Oandxy xyd d ,

Oandd d affect t$e rate of con&erence, and may cause

undesired oscillations es%ecially in a diital im%lementationof controller+ In order to attenuate t$is effect, a%%ro%riateada%tation rules are %ro&ided in t$is section+ 8ormulation isdescribed for linear &elocity+ Similar ork can be done foranular &elocity+

Similar to t$e control las (2:), t$e model referenceada%ti&e control la (model reference is defined by eGuation(26) ) s$ould beB

1( ) cos sin! m d m d mx myv T v vt q q q q q q -

= + - + +&

"ulti%lyin bot$ t$e left and t$e ri$t $and side of t$e firsteGuation of eGuation (10) it$ mB

( cos sin )( cos sin )

! x y

! mx my

mv m d d

d d

t q q

t q q

= - +

= - +

&

Substitutin .Guation (2?) in .Guation (2)B1

1

( ) cos sin

( cos sin )

( ) ( )cos

( )sin

m d m d mx my

mx my

m d m d mx mx

my my

mv v T v v

d d

v T v v d

d

q q q q q q

q q

q q q q

q q

-

-

= + - + +

- +

= + - + -

+ -

& &

&

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-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

(a)

0 2 4 6 8 10-15

-10

-5

0

5

10

15

20

25

30

35

(b)Figure .a/ ,esired and tracking tra7ectory8 ./T0e !inearve!ocity and t0e angu!ar ve!ocity in a sim*!e contro! system 'it0

t0e different va!ues of uncertain *arameters&

-6 -4 -2 0 2 4 6-5

-4

-3

-2

-1

0

1

2

3

4

5

(a)

0 2 4 6 8 10-10

0

10

20

30

40

50

60

70

(b)

Figure ; .a/ ,esired and tracking tra7ectory8 ./T0e !inearve!ocity and t0e angu!ar ve!ocity in a ada*tive contro! system 'it0

t0e different va!ues of uncertain *arameters&

I+ C/=CUSI/=

-$e article suests alorit$m of trackin control t$at notonly uarantees t$e trackin of robot to desired tra'ectoryGuickly,eactly but also robot4s mo&ement smoot$ly on

bad terrain+ -$e main c$aracteristic of t$e %ro%osedcontroller is its robustness of %erformance aainst t$ec$anes in uncertain %arameters of robot and ot$ereoenous disturbances + -$e analysis and simulationresults s$o t$at t$e trackin errors con&ere to Jero andkinematic4s c$aracteristics are im%ro&ed

Simulations $a&e s$on eactness of t$eory4sanalysis and efficiency of met$od+

*.8.*.=C.S

517+ /+T+ Sordalen, /+ .eland+ .%onential stabiliJation ofnon$olonomic c$ained systemsV, I... -ran+ /n Automatic Control,

H0, 1, %%+ 36

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5167+ asan "e$r'erdi, "aarouf Saad, Dynamic trackin control of mobilerobot usin e%onential slidin mode, I.C/= 2010 < 39t$, 2010+

5197+ "+ + AmooJar, + "+ X$an, -ra'ectory -rackin of #$eeled"obile *obotsB A Ninematical A%%roac$, "ec$atronics and.mbedded Systems and A%%lications (".SA), 2012 I...!AS".International Conference, 2012+

51:7+-airen Sun, Cai$on X$an, ailon >eiK ya%uno&+=+"in$B ZSome of ne researc$results in t$e De&erlo%ment of "obile *obot mounted Cameraautomatically Seac$in and -rackin "o&in -aretVK -$e 9nd iet=amConference on "ec$atronics C" 2012, 12!2012
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Iccais2013 Eng v5