TRACKING CONTROL OF A MOBILE ROBOT USING
NEURAL DYNAMICS BASED APPROACHES

A Thesis

Presented ta

The Faculty of Graduate Studies
of

The Cnivrrsity of Guelph

In partial fulfilrnent of requirements
For the degree of

.Master of Science
Apnl. 2001

@ Guangfeng Yuan. 100 1


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ABSTRACT
TRACKING CONTROL OF A MOBILE ROBOT USING

NEURAL DYNAMICS BASED APPROACHES

Giionpkng YUAN
University of Guelph. 7001

Advisors: Dr. Simon X. YANG

Dr. Gauri S. MI'ITAL


Due to disturbances and noise. mobile robots are unavoidabl y away from a desired path.
Thus how to control a mobile robot to track the path is a fundarnentally important issue in

rohoiics. In rhis thesis. a novel tracking control approach is developed for a car-likç
robot. n,hich i s hased on the biickstepping techniques and a neural dynamics model. Thc
proposcd control aleonthm can generate smooth and reasonable velocity commünds. It
rcsol\.c.s thc problem of the speed thnist jump caused by most previous tracking

conirollcrs. irfhich is not truc in the real world. In addition. unlike some existing path
irackcrs. the proposed tracking controller c m deal with arbitrai1y large tracking m o n . A
novcl iracking control algorithm for a discrete trajectory is proposed as well. The stability
of thc control systems are analysed and proved using a Lyapunov stability theory.
Simulation results dernonstrate the efficiency of the proposed tracking control algonthrns.

Somc ccrnpririsons are conducted to illustrate that the proposed controi aiporithms excel
ihc prewous bac kstepping-based approaches. A path information based path-traclins

model for point robots is also proposed. The integrated system of the path planner and the
pcith tracker is also simulated in this thesis.


Acknowledgements
1 am indebted to my advisor Dr. Yang for his suidance and advice during the course of
this resea-ch. The valuable suggestions and opinions of my CO-advisorDr. Yittal for my
thesis arc also very much appreciated. 1 would also like to thank my classrnates for their

hclp and suppon.

Final1y. 1 would like to xknowledgernrnt the patience. loving çare and effective support


provided to me by my wife Ellia Miüo Zhang. my fither-in-law Jixian Zhang and my
motht'r-in-law Xia Mi. My thanks also go to my parents for their love and suppon.


Contents

.

1 introduction .................................................................
1.1

Models of Wheeled LMobiIe Robots .............................................

1 .2

Robot Control System .............................................................

1 -3 Problem Identification.............................................................
1 .4

Contributions of this Thesis .......................................................

1.5 Ovcrview of this Thesis ............................................................

2. Background of Path Tracking

...........................................

2.1


Relationship of a 'Mobile Robot Model and Other Models ..................

2.7

Kinematical Constraint and Dynamics of Mobile Robots .....................

2.3

Pîth Tracking Problem.............................................................

2.4

Nonholonomic S ystrm ............................................................

.7 .

Conclusions ..........................................................................

3 . Literature Review for Path Tracking

..................................

3.1

Sliding Mode based Approaches to Path Trackine ...........................

3.2

Linearizlition based Approaches ..................................................


3.3

Fuzzy blised Approaches .........................................................

Scural Network based Approaches .............................................
.
' - 3 Bîck-stepping based Approaches ................................................

3.4
1

3.6

Paih Tracking with Dynamics ....................................................

3.7

.............................................
Conclusions .........................
.

.

4 The Proposed Mode1 and Results
4.1

.........................................

The Tracking Controller and the Systern Architecture........................
4.1.1 The Modrl for Piith-tracking Control ...................................


4.2

4.12

ReferenceVelocity ........................................................

4.1.3

System Architecture ......................................................

Simulation Results ................................................................
4.2.1

TrackingaStraightLine ..................................................

4.2.2

Tracking ri Circular Path ..................................................


4.2.3 Trackins ri U-shaped Path .................................................
Cornparisons.........................................................................
Discussion ...........................................................................
4.1.1 Parameter Sensitivity ........................................................
4 - 4 2 Rrindorn Errors ................................................................

1.4.3 Charrictenstics of Shunting Model .........................................
Conclusions ..........................................................................


5 . Error Dynarnics and Stability Analyses

................................

3.1

Error Dynarnics .............................................................................

7.2

Stability and Convergence Analysis ..........
.....

............................

5.3 Rémarks ..............................................................................

.

.....

6 Integrated System of Path Planner and Tracking Controller

Introduction..........................................................................
Thc Modél ...........................................................................
Discrete Path .............................................

6.2.1

Definition of


6.2.:

Tracking Control Algonthms for a Discrere Pÿth .....................

6.2.3

The S ystem Architecture .................................................

ri

6.3.4 Definition of Reference Velocities ......................................
.A niil ysis of Stability and Convergence ...........................................

Simulation Results ..................................................................
6.4.1 Tracking a Discrets Path .................................................
6 . 4 . Tracking Control in a House-like Environment .......................

6.1.3 Tracking Control for a Moving Target ..................................
Compati sons ........................................................................
6.5.1

Comprinson of tnr tracking mode1 and the irnproved mode1 ........

6 - 5 2 Cornparison of the typiclil mode1 and ihe improved mode1..........

Conclusions ..........................................................................

.


7 Conclusions and Future Work
7.1

...........................................

Conclusions ..........................................................................

120

120


7.2

Future Work .........................................................................

122

7.3

lmplementittion of Control System for a Real Robot ..........................

123

References

........................................................................

126



List of Figures
Fisure 1.1:

Scheme of mobile platform. ........... ......... ...... .... ...... . . . .........

3

Figurc 1.7:

Sçheme of a rem-steering mobile robot.. .... ....... ... . ....... ...........

4

Figure 1.3:

Sçheme of a front-steering mobile robot.. ... .... ................ . .......

5

Fisure 2.1:

Schemeofarnobilerobotmodel ..........................................

12

Figure 2.2:

Scheme of the posture error for a wheeled mobile robot .......... .....


15

Figurc 3.1:

Angular velocity (radls) versus time (s) (from Rois C r al.. 1996).... ..

23

Figure 3.7:

Fonvard and angular velocities versus time while tracking a straight.
line i l l and i r 2 are the fonvard speed and angular speed. respectivel y.. 24

Figurc 3.3:

Scheme of f u u y rulcs based modrl. <:the lateroi displacement.
(Il:

the orientation. y: the cuwriture. ils: the distance betwen the

robot and the nearest point of the desire püth.. . ...... . . .... .. . . . ..... ...

27

Figurc 3.1:

Structure of tracking control system architecture using fuzzy rule ...

27


Figxc 3.5:

Tracking a circular path using backstepping based model. The sol id
line denotes the desired path: The dashed dot line is the tracked plith ... 29

Figurc 3.6:

Fonviird and üngullir velocity variations versus time while tracking

ti

çircular path by using bacbstepping-based mo.. .... ......... .............

Figure 3.7:

30

Trrtckin? a circular path using the improved typical backsteppinp
hüsed model. The solid line drnotes the desired path. The dashed
line is the tracked pnth .... .......... .... ... .... .. .................. ...... ...
Fonvard and anguiar velocities Vary versus time while tracking

32

ÿ.

çircular path using the improved backsteppins-based model. ........... 33
Figurc 3.9:

Kinrmatics (vclocity control) pan and dynnmics (forcdtorqur)pans

o f ;i mobile robot control system ........... .. .... ..... ... ..... .. ..... . ........... ... 36

Figurc 1 . 1 :

Diagram of the control system architecture for a mobile robot.. ........ 4 1

Figurc 1.2:

Tracking performance while tracking a strai~htline. Solid line denotes the
reference path. and dashed line represents the actual path.. ......... 42
Fonvard and angular velocities variations versus time while tracking
ri straioht
C

line .............. .............. ..-........... ............. ....... ..... 43

The tracking errors of the longitude. lateral. anentation versus


time while the mobile robot follows a straight line ..... ...... ........ ..
Figure 4.5:

Changes in the orientation of the mobile robot with time
while tracking a straight line.. ............. ..- ............. . ........... .....

Figure 4.6:

Trac king performance w hi le the robot trcicks a circulür path.. ........

Figure 4.7:


Fonvard and angular velocities vs. time while tracking a circular
Path.. ......... .......... ........ ................ ........ .... . ... ...... ... ...

Figure 4.8:

The tracking errors of the longitude. lateral. orientation over
tracking a circular path ... ........... . ......... ............. ....... ... .....

Figure 4.9:

Changes in the orientation of the mobile robot with time
while tracking time while a circle ......... ... . . .... ....... . ... ............

Fiyrc 4.10:

Tracking performance while a robot follows a U-shaped path ........

Figure 4.1 1 :

Fonvard and angular velocities versus time whiie tracking ri
LI-shaped path.. ................. . ...... . .............. ........... ..... ... ....
Tracking mors of the longitude. later~l.orientation over time
L\

Figure 4.13:

hile traçkin~_
ii U-shapcd paih ... .. . .. .. .... . .. . ... . . ..... .. . .... .........


Changes in the orientation of the mobile robot with time
whilc tracking ri U-shaped path.. ........ ..... .... ......... ........ ..... ..
The reference angulrir speed over time w hi le trac king
ci

Figurc 4.145:

The desired forward speed ovcr time while trackinz
ci

Figure -1.16:

U-shaped path.. . ............. ............. ............ .. . .............. ....
U-shaped path ....................................... ...... . .. ..... .........

Tracking performance while a robot follows a circular path using
backstepping based model ............ . ............ . ............ ........ ...

Figurc 4.17:

Fonvard and an_oularvelocities venus time while tracking a circle
using backstepping-based rnodel.. ........ ............. . .... .......... -....

Figurc -1.1 S:

Tr~ckinzerron of the longitude. lateral. orientation versus time
w hi le

Figurc 4.19:


trac king a circle using bac kstepping-based model ......... .......

The orientation of the mobile robot over time while trxking a
circle using backstepping-based model.. ....................... ..........

Figure 4.10:

Tracking performance while tracking a circular path using the
typical improved backstepping based model (Zhang et (11.. 1999).


Solid line denotes the reference path and dashed line represents
the tracked path.. .............................................................
Figure 4.2 1:

Fonvard and angular velocities versus time using the improved
Backstepping (Zhang er rd.. 1999) based model ...........................

Figure 1.22:

Tracking errors of the longitude. latenl. orientation versus time
using the improved backstepping based model.. ........................

Figure 1.23:

Changes in the orientation of the mobile robot with time using the
improved backstepping biised model.. ....................................

Fisure 4.24:


The effecects of parameter A on the tracking performances while
tracking a straight line using the proposed model under the
conditions of Fig. 4.2.. ......................................................

Figure 1.25: The effects of parameter A on the changes in velocities venus time
under the conditions of Fig. 4.3 ............................................
Figurc 4 26:

Thc cffects parameten B and D on the tracking performances whilr
tracking a straight line using the proposed rnodel under the samc
conditions as Fig. 4.2 .......................................................
The effects of parameters B and D on the c h a n p

in

velocitics

versus tinie under the conditions of Fig. 4.3 ..............................

The effects of random errors on the trackin_operformances while
tracking a straight line using the proposed model under conditions
of Fis. 4.2......................................................................
Fiourc 1.29:

The effrcts of randorn errors on the changes in velocities versus time
under the conditions of Fig. 4.3.. ..........................................
The chanses in tncking CITOB venus time under the conditions of
Fig. 4.2. A: The rindom errors rire added in the rniddle frorn 1 s to 2 S .

B: The rrindorn errors are added at the stan frorn O s to 1 S............. 67

Dynamic response to different value of the parmeter A for
the rnodel ( B = 1.D = 1) ....................................................

65

Dynamic response to di fferent value of
the parameter B (A = 10. D = 1). ...........................................
Figurc 4.33:

Dynamic response to different value of the panmeter D

69


( A = 10. B = 1)................................................................

.

Figure 4.34:

Dynamic response vs . excitatory input ( A = 10 B = 1, D = 1)..........

Figure 4.35:

Dynamic response vs . minus excitatory input (A = 10. B = 1 D = 1 )..

Figure 1.36:

Dynamic response vs . inhibitory input (A = 10. B = 1. D = 1 )..........


Figure 4.37:

Dynamic response vs . minus inhibitory input (A = 10. B = 1. D = 1 )..

Figure 5.1:

Fonvard speed projection to Canesian coordinate system for a

.

nonholonomic mobile robot ................................................
Figure 5.2:

X,. and Y,. time denvative projection to X R mis ...........................

Figure 6.1:

Scheme of the discrete path ................................................

Fisure 6.7:

Diagram of the s ystem architecture for the integrated system .........

Fiyre 6.3:

Trücking performance while triicking a discrete path using the

l
proposed m ~ d e...............................................................
Foward and angulrir velocities versus tirne while tracking

a disçrete path ................................................................

.

Trricking mors of the longitude laterril . orientation over time whilc:
tracking ri discrete path ......................................................
Figure 6.6:

Rrference linear vrlocity versus time while tracking a
disçrete path ..................................................................
Changes in orientation over time while tnickinz a discrete path ......
Trac king performance w hi le trac king the püth generated b y the
path planner in a house-like environment.................................

Figure 6.9:

.

Tracking errors of the longitude lateral . orientation aver time
while triicking the path generrited by the path planner in a
house-li ke environment .....................................................
Changes in fonvard and anguiar velocities versus time in a
house-Iike environment ......................................................

Figue 6.1 1 :

Amplification of velocities (O - 6 s) in a house-like environment ....

Figure 6.12:


.A rnplification of velocities (10-13 s) in a house-li ke environment ...

Fisure 6.13:

Changes in the orientation with time in a house-like environment....

Figure 6.14:

Reference Iinear velocit y over time in a house-li ke environment......

Figure 6.15:

Reference linear velocit y for start period of the motion in a



List of Tables
Tablc 3.1:

Advantages and disûdvantages of the five classification
rnethodsiine .....................................................................

37


List of Symbols
the parameters of the shunting model

the rear axis centre point (referred to as guidance point) of ii mobile robot
the mass centre point of a mobile robot

the distance between C and C,\,
the distance between the centre points of two rear wheels
ti

5-by- 1 error vector

ri

3-by- 1 error vector

the longitudinal error that is trmsformed from the difference of X
direction in the world coordinate system
the lateral error that is transfomed from the difference of Y
direction in the world coordinate system
rhc error of iiçtual and desired driving velocities
the error of actuiii and desired cingular velocities
the orientation rrror of the desired orientation ana the present orientation
ihs excitatory input function of the shunting model
the inhibitop input function of the shunting modrl

3 x 2. lacobian matrix (also called transformation mritrix Te)
the gain parameters of the proposed model
the Lyripunov tùnction candidate
the present 3-by- I posture vector
the desired 3-by- 1 posture vector

n dimensional generalized coordinates vector
the radius of the wheels
The 2-by- 1 velocity vector
the present foward velocity of mobile robots (also called

veloci ty)
the drsired forwnrd velocity of mobile robots (also called
velocity)


output of the shunting mode1
the present angular velocity of mobile robots (also called rotational
velocity)
the desired angular velocity of mobile robots (also called rotational
velocity)
the present state S-by-l vector
the desired state 5-by- 1 vector
the coordinates of the guidance point of mobile robots
the coordinates of the desired state of mobile robot
the world coordinate system
the local coordinate system attached to the mobile platform
the heading orientation of a mobile robot taken counter-clockwise form
the ,Y-ais
the tangent angular degree of desired state takrn counter-clockw ise fom
the ,Y-mis
the orientation y i n
the steenng ansle

XII


Chapter 1

Introduction
Robots have hem widrly ussd in recent yrars. .A production line consisting of robots may shonen

thc tirne nèeded to make products and reduce the need for h u m n labours in industry. Robots can
rilso libcratcr humrins from hrizrirdous or dangerous works such ris miIitary duty. fire fighting. seacuplorrition. and spacr-exploration. Robots begin to affect Our daily lifr like o f k e automation
rind surgcr).. -4s tvrll. robots may help the handicapped y o p l e in their daily life rictivities.
.(iutonomous robots have ri major influence on human life in the future.

Thc robots studird in history can be ctassified into two catt'goriss: robot manipulators (e.2..

Jiigannathan. 1907) and uheeled mobile robots (C.E.. Yang and Kim. 1 9 9 9 ~1999b: 1999~).
.(ilthou$ hoth of thcm possess similar wsys in control fields. there are many differences. For
instrinct.. k i r kincmritics and dynamics are different. Robot manipulators arc: often refsrred to as

"rnulti-joint" robots. The wheeled mobile robots rire usurtlly referrcd to ris mobile robots. In this
thesis. the rrscarch intcrest is focused on the mobile robots. Mobile robots rire nomally squipped
N

i t h rw o

M

h w l s (e.g.. Koh and Cho. 1999) or three wheels ( c g . . Zhang rr

li!.

1999) or four

ithet.1~icr.g.. C~irricciolio, 1999). The tracking control algorithms proposed in this thesis are
sui:ribls t'or riil mobile robots if the robots can be considered as a referencr point whose velocitirs
3rc the control input commands of robots (iv,.
\r., ). Thus the whsel rational speeds can be obtained
from the sperds of the refirence point. accordin9 to the geometric relationship betiveen the

rckrcncc point and the wheels (sec chapter 1).


The rest of this chapter is organized as follows. Section 1.1 introduces the models of wheeled
mobile robots that were used in the literature. The general system structure of the robots' system
is proc'ided in section 1.3. The objective and contributions of this thssis rire summarized in
scctions 1 .-3 and I.4. respsctivrly. An outline of this thesis ic p:esen:cd

iii

section 1.5. Sumrnary is

g i ~ c nin section 1.6.

1.1 XIodels of WheeIed 3lobile Robots

In tcr111s of the c!;tssification criterion of the siinplifird kinematica1 robot model. the wheclrd
mohilc robot modèl clin be divided into four catcgories. The f i r ~ one
t ( t g . . Mario Aguilar et

(11..

199-3)is crilled the "point robot" model. This model has two inputs (the point position .ri. and y, )
in ~Iic
Tlic second ciilcpor) is shoivn in Fig. 1.1. The sirnplified kinematical mode1 is defineci as. Jiang ;inci Yijineijer. 1997)

\\

hcre .im d i.,
are the vslocitirs in X and Y direction in the global frame. resprctively. The

rckrencc point is drfined ris the middle point in the rear axle of the wheeled mobile robot. The
t-ariahlc il, Jenoies the headicg direction that is t ~ k e ncountercIockwise from the X-axis.
il.,

arc

t k

Y,

and

lincar velocity and the angulrir velociry. respectively. Linerir vrlocity is also crillsd

"lonyitudinnl speed" or "forward sprrd". and angular velociry is also called "rotational sprcd".
The corltrol ;iI~orithmsfor this modrl have three inputs
comrnands ( i.,. N., 1.

(.K.

y , . O,.) and two output sterring


,Y

-VC.

Figure 1.1: Scheme of ri mobile platform.

III tliis sirnplified iiiodel. the front wheel s h o w in Fig. 1.1 is a passive wheel. This rnodcl can
~ I s ohr: 3pplir.d io a two-whrrl robot with a diffrrential diive (details rire in chaptrr 1). As sho~vn

in Fig. 1.1. the Cartesirin coordinrite system is denoted ivith {,Y,

Y},and the

local coordinrite

ï>,stcrnattachc'd to the robot piatform is denoted with {.YR. Y R } .The scaiars C and CI! rire the

ccntrc of the reiir axis and mriss centre of a robot. respectively. The scrilar tl is rhe disiance
bctu c m C and Ci,.

As il1usicitr:d ir. Fig. 1.2. the third cstegory of the sirnplificütion mode1 (Kang et cil.. 1998;

Kamga

CI

commands

(11.. 1996: Tan rt (11.. 1999) has four inputs
i 1..

. i t . , 1.

(.K..

F,..O.. CD)and two output steering

As shown in Fig. 1.2. the Canrsian coordinatr system is denoted ivith ( X . O.

Y ) . and local coordinaie systrm attiiched to the robot platform is denoted with

scrilrir C is the centre of the rem rixis.

{&. Y R J The
.


x

-rc'

Figure 1.1:Scheme of a rerir-stèering mobile robot.

This riiudcl can bt. Jcscribed as.

nhcrc .i-,and

\., are

the vcilocities in ,Y and Y direction in global frame. respectivrly. The

~iiriableO, denotes the orientation angle that is taken countertlockwise from the ,Y-lixis. The
Icngth heiut.cn the front axie and the reûr anlc is denotrd with o. Variable Yiiriahle

1..

is the linex velocity and

rt:.

represrnts the angular steering vrlocity of the stecring

u h t t 1s. The conrrol algorithrns for this mode1 have three inputs (x,. y,.

commaniis ( i.,. ir.,

i.

O,) and two output steering


Figure 1.3: Scheme of

ri

front-steiiring mobile robot.

tn ccirnprtrison tu thc third simplitïed model. the fourth mode1 is brised on the front wheel driven

rnobile robot. It is dstinsd as.

As shown in Fis. 1.3. the reference point of the mobile robot is locriied in the middlc point of the

front axlt.. whtre i,.
and j,.
are the velocities of X and Y direction in global frime. resprictively.

The others art. the srime ris in Eq. ( 1.2). The fourth mode1 crin be refsrred in Hemami et (II. ( 1994)
and Srotsky and Hu ( 1997).


The sirnplified mobile robot mode1 used in this thesis is the second category introduced above.
Because the second category was mostly common used. The control algorithms proposed in this
thcsis are bascd on this simplified model. As far as the third modei and the fourth model are
cnncerned. the- crin rtlso suit three-wheel robots with one steering wheel although Figs. 1.2 and
1 .-3 shoii the robots' models with four wheels.

1.1 Robot Control Systern

For ii sornpltitcly automated robot. the control system is the b r i n of the robot. The control systern
i s compostxi of the following four subsystems: scnsor subsystcm. path planner. path tricking

controlltir. ~indtorque controller. The srnsor subsystsm is to acquirc the information from the
sliünging en\ ironmrint. The path planner (also callrd motion planner) ïims nt planning ;in optimal

~ollision-ri~oidancc
rcal-timt. path according to the information from the senor subsystem. The
ot7jccti\t of thc path tracking controller is to control the robot's vslocitirs so thlit the robot czin
follotr ihe planncd path at certain velocities: the torque controller is to control robots* torque or
force or \«lwgc (DeSantis. 1995bl to trick the velocitirs that is output from the path tracking
controllrr. The path plïnner communicates with the path trxkcr by sharing memory. The velocity
ul'a niohilc robot is fcrd bock to the torque controller and the position stnte of robots is fced

hack to the pnth trxkcr via intcgrator. In this thesis. the resclirch focus is placed on the path
tracking control algorithms.

1.3 Problem f dentification

Hou io resol\,r the path-trricking problem is a key question in robotics. The objective of path
tracking is ro control a robot to t r x k a planned path or a known paih by controlling sperds of the


robot. that is. the m o r between the desired path and the actual path converges to zero. The e r o r
betwen the refrrence path and the curent position of the robots crin't be avoided. that is. the
robot deviates the desired path. which is caused by the slippage. disturbances. noise. vehicletcrrriin interaction and measure m o r s of sènsors including externiil and intemal sensors.
Thcrefort.. how to control a robot to precisely aacking a given path or tnijectory is a crucial
problem.

T h c traditional npproochcs were employed to solvr the problem ( t g . . Aguilar r t tif.. 1997; Yang
iirid Kirn. 1 9 9 9 ~1999b; Karnga er

tri..

1996; Walsh r r cd.. 1994; DeSantis. 1995b; Fisrro and

Lc~vis.1997; Kanayama C r crl.. 1990: Zhang r r cri.. 1999). Unfonunately. most approaches caused
s p e t d jiirtip ~ h e nm o r s change suddenly. The spsed jump doss not hold in the real world

htxause the tirne derivative of the velocity approachcs to indefinitr. To rcsolve the problem. a
nci~cl-trackingiontroller will be propossd in rhis thcsis by using neural dynrimics and
hrichrippin~h a s d approaches. In addition. the path ro be trricked may bc. continuous or discrete.
T h t continuous path is the first derivative of the path is continuous. The discrrte picth mrans that
ilic püih consists o f line segments. In this thesis. both of thcm are studied. One model is proposed

lor continuous path and another model for discrete path. Furthemore. the combined systcm of
path plrinncr and path trricker is also invrstigated.

1.4 Contributions of this Thesis

In this tliesis. cornpletr reviçw of path-tracking dgorithms is conductrd. .A common problem of
the c s i s t i n ~path-trac kins cilgorithm. the speed lump. has been discovcred. which will k detailed

in chaptrir 3. Novrl tracking controllers are proposrd to solve this problem by using a
hackstepping technique and a neural mode1 kcause shunting model is usrd to process signal for
thc first time. The stability and convergence of the proposrd tracking controllers are ngorously


provrd using

ri

Lyripunov stability theory. A lot of simulation studies are conducted to

dernonstrate t ht: effectiveness of the prop~sedtrac king controllers. Two full papers from rny
thesis have rilready ricceptsd by the best conference on robotics and automation. ICRA'2001
i Jan. 13".

200 1 ). Thcy iverr fully perr reviewed by at least two independent reviewers. These

provcd the contri butions of the thesis. Contributions of this thesis are summarized as:
The novel neural dynrimics basrd tncking controllsr is proposed to solve the prithtracking problem. According to the litrrature. it is the first time that the shunting mode1 is
uscd for trricking control design (Steering commands).

The propossd models rtlsotve the abrupt jump of vrlocity

rit

initial moment or ~vhsnsver

thtxe art. suddenIy c h a n p in tracking mors.
Thc proposed tracking control algorithms crin deril with very large trricking mors.
The mode1 for a continuous path and models t'or a discrets path rire proposed

Thc proposcd modsls converge frister than many previous controllers such ris in Jiang and
Sijmcijcr ( 1997). Kanriyrima rr nt. ( 1990) and Ahmadi cr (11. ( 2 0 ) undsr the sams
conditions.
Thc proposeci tracking coriirol algorithms can be combined with the prith planner
proposed by Yang and Meng (1995; 2000a: 2IXX)b: 2 0 c ) .

1.5 Overview of this Thesis

This thesis consists of eight chripters. Chapter 1 provides mobile robots' sirnplifisd models and
c;ptt.ms that ha\.e k e n studied in the literature. Problem identification and contributions of this

h s i s ;1re alsu described in chripter 1.


Chapter Z introducss background of path tracking. The relationship of sirnplified robot model
uscd in this thesis and the other robot models are given in section 2.1. from the control point of
vie~v. Section 1.3 presents the kinemritical constraint and error dynamics of the sirnplified robot
mucicl. The definition of nonholonomic systems is given in section 2.4. Section 2.5 draws
conclusions.

C'haptcr 3 rttL ie~vsthe literature of the cracking control aigorithms for mobile robots. The previous

;ipproxhcs the prsvious methods in the path trxking control crin l
x classified into the following
( 1s) Stide mode technique brised approaches: ( 2 ) Input-output lineanzation brised
f?vc c a t q ~ r i ~

approrichcs: ( 3 ) Fuzzy rules based approaches: (4) Neural network brtsed ripproaches: and ( 5 )
Backstcpping technique basrd approachrs. Drriwbacks of thest: five cliissificritions are analyzed
2s

nc.11.

In chripttx 4. the biological neural dynamics based trrtcking controller and the systern structure are
prcscntcd. Thc simulation results are crirried out to prove thrit the proposed trricking control
a l p i t h i n is valid. Finally. the comparisons of the proposed trricking control model and the
prcvious models and conclusions rire shown.

Ch~iptcr5 analyzes the stribility and convergence of the propossd tracking controller using

ri.

L'apunov function crindidrite. Derivation ~f the error dynrimic equation is provided in detail. This
chaptcr is closcd Lvith conclusions.

Chripter 6 addresses the irnproved trricking controller for discrete pliths using neurril mode1 brised
approriches. The integrated system architecture of path planning and path trlicker is d s o given.
Siniulation results demonstrrite the validity and effectiveness of the proposed models.
Funhcrmorc. the stribility and convergence of the propased mode1 rire rinalyzed and the proposed


tracking control mode1 and the previous rnodels are compared. In this chapter. the integrated

system of prith planner and path trricker is also studied.

FinriIll;. the conclusions and future work are presented in chapter 7. The Investigation of
implenientlition of real robots is also presented. Some limitations of this thesis rire given in this
chlipter ris ~vcll.