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hl. Stankovski, SS Cyril and Methodius Univ., R. of Macedonia, Inilestkl‘i!etCaliiiit.cdll.isli
’I. Kolcmishevska-C;uRiilor.aka, SS Cyril and Methodius Univ.,RM, tdniak~rir?clf.u%im.cdu.nrli
D. Stankovski, SS Cyril and Methodius Univ., R. of Macedonia,
P. Roshkovski, SS Cyril and Methodius Univ., R. of Macedonia,,nl.lnli
H, Mileva SS Cyril and Methodius Univ., R. of Macedonia, mI~ile~ir)m~il.corii.~~~k

    Path tracking i s one o f thc most signilicani liinctions 01’ mtnnoinous vehicles and mobile
robots. In generat, tracking involves both sensing and control components. I n the Instittile of
Automation Systems Engineering in Skopje, Repiihlic of Macedonia, last year start project for
autonomous vehicles and mobile robots control. This paper presents our results in this direction,
hierarchical architecture in aiitonomnus vehicle control. The higli-level layer huilds a model of
the environment and generates a plan for action. The low level blindly exccuies this plan. From
the control point of view. tracking involves the gcneralion o f steering command and a vclociiy
command to be Sent to low level m o h n controllers. 111 this paper we discuss steering command
using fuzzy togic and present simulation model and rcsiilts.

KEYH’OHDS: mobile robot, autonoinous veliiclc, fuzzy logic, path tracking, hierarchical control

                                      1. IN‘I’H0UUCTIC)N
     The development o f robotic systems in a scientific as well as in the engineering field, in the
last decade note a big growth, (Yen et al, 1995; Tunstcl, 2000). I [trwevcr, speaking in words of
applied robotics, ttie manipulators and mobile robois stilt remain main domain of interest
(Saffintti. 2000; Stankovski et $1, 2002 a, h), in particular when non-holonainicily constmiills
have to he satisfied (Dimirovski et al, 2001; Ollero et al. 2000). Navigation of autunomous
mobile robots in unknown and unprcdictablr environments i s a challenging domain i o test and/or
demonstrate knowledge representation and reasoning techniques because i t involves a ruimbcr of
unique chariicierisiics and features. Jus! to name a few, thesc are as follows: the jiipiit to control
system i s inaccurate, sparse, rtncertaiti, and/or unreliahle; no complete mathematical
representation exists ot’thc process iermcd “navigntion”, althtrugh. as demonstrated by Iiiimilns, a
set of skills for accomplishing this proccss exists that c m typically be representcd io a liiigui?,tic
mniiner ab IF - THEN rules; (Takeuclii et ill. 1488) (he approximations involved in the numerical
reprcsentation o f the system and its environment are significant: a navigation environment i s in
general dynamic and unpredictable, typically leading to large iiiicertaitities in i t s representation
(Gndjevac, 1995; Gdjevac and Steele, 2000).
                                                                        been implemented as fuzzy
It i our study, the sensor-based reasoning iiccded for navigation l i a ~
IF-THEN roles that compute decisions with respect to navigation for various combitinlions of
input data, i.e., fuzzy rules describe behaviour suiiahle for path tracking. Path tracking is lint o f
ttie most significant Functions of ilumtomous vehicles and inohile robots. I n general, tracking
involves both scnsing and control components. In our study the path has becn previously
computed by mapping cnvironmen! (Kralievski et i l l , 2003).

     In the cases of traditional planning of robot motion the approach is IO solve the configuration
of the environmcnl with constrains of the types of equality and inequality. These restriction^ are
determined from kinematics o f the system, as a front wheels can not slide lateral, hut they can

move front, back and rotate only. On the oiher liand in the robot motion control there exist many
other difficulties (Ollero et ai, 2000). as:
 I . Keprctsenlation of inaccuracies in ~neasurements.
2. Ikprcsentation of incomplete environment inkiiination and the need to dcal with imprecisc
     or incomplete perception ofthe enviroiimcnt;
3. Flexibility to apply convenient nonlinear control laws derived f o and experienced human
     driver and expressed in kirm of IF-THEN rules;
4. Learning from input output data collected when human driver is operating the vehicle for thc
     purpose of path tracking;
The problem of representing inaccuracies can be solvcd by means of statistical approaches
(Kalman filtering tcckniques). Furzy logic can hc applied to the same effect without thc need for
precise information, which can be very difticuli and/or expensive to obtain, Fuzzy logic offers the
possibility to integrate the two sources of ittt'onnation that are typically used in mobile robotic
applications: driving knowledge acquired the form of IF-THEN rules from an experienced driver,
and driving control laws directly extracted from the sensor data recorded while the vehicle is
bring operated by a human driver.
Vehicle motion is organised in two levels: tracking control on the upper level and direct control
ofthe steering angle and velocity on the tower level. Upper level involves ruzzy logic controller
for gcncratioii o f steering command and a veloci~ycommand to be send to low level motibn

                                    3. TRACKlNG FUNCTION
     Problcm of tracking a path usually previously is recorded in a tile. This path can be obtained
in sevcml ways (Dimirovski c I al, 2001: Ollerro er al. 21100):
     Uomputcd by a path plannerembcdded In il classical planner-based architecture for
     autonomous vehicle conirol.
     Recorded by the vchicle itsclf while a human-operator is driving the vehicle. In this case
     dead reckoning, including navigation seiisors (gyroscopes, compass, and accelerometers) is
     iisually applied. Furthennorc, Global Positioning Systems (GPS) and, in particular,
     Iliffercntial Global Positioning Systein (DGPS) are very uscful 10record the path in the case
     o r outdoor navigation.
1    Provided by a telcoperator from a remote control station. Here we have picture from camera
     for the envi-mnment where mobile vehicle need to move.
 Our case is as the last one; we use camera for environment picture generation. With appropriate
picture processing we find path.
The recorded path typically consists of a scquencr of poses ( i , v coordinates and orientation,
 angle cp) along with the curvature of each pose. If there is only one (x,y) sequence available, the
orieritation and curvature can be reconstructed by geometrical methods. After the path is
 recordcd, the path tracking consist of the generation of steering commands. The generation of
 these commands takes inlo account the actual positian/orieiitation of the vehicle and the
 constraints imposed by it and its low-level motion controllers.
The seii5ors can be used for path recording. While many sensors exist than can be uscd for
position estimation, thcre is no single sensor that provides a good solution in every situation.
Therefore, a combination of sensors is usually applied, and the readings of all these sensors are
combined in some way to obtain an estimation ofihc actual position ot'thc robot. Dead reckoning
sensors include odoinetry sensors (incremental and absolute optical cncoders) and attitude and
heading S ~ I I S O ~ S
                    (magnetic compass, inclinometers and gyroscopes).
DGPS can provide centimeter accuracy and acceptable update frequency to he used in real time
tracking, The main problem with GPS is the need for the receivcrs to he i n direct sight with the
saicllites, and thus periodic signal blockage occurs due to buildings, foliage and hilly tcrrain.
Furthennore, differential GPS has insufficient reliability for primaty position estimation.

                                               25 8
Ultrasonic sensors and laser range finders are well known proximity sensors widely used in
autonomous navigation for applications such as wall following and corridor following. The
sensor can be set up in such a way that i t scans ihe environment, usually in a plane, or in a fixcd
orieritarion pointing io a fixed dircction.
As far as the environment perception i5 conceined we will rocus on the visual tracking of the
targets. Thus, the problem considered in this paper is thc tracking of the path by a vehicle when
ihe path is previously recorded hy a camera. The problem is so complicated when thc camera is
on the vehicle and moving together with vehicle.
Fuzzy logic control can hclp to solve the problem of path tracking. The inlerpalation capabilities
of furzy controllers allow to achieve a good performance in vehicle control, based [in a limited
set of training input-output data pairs and without the need o f building 3 model of the system.
Most visual tracking methods are based on techniques that define correspondences in a sequence
of images. The image processing time is usually a very important constraint for the application or
these techniques in real-time. Once the relative positioii of the iarget to be tracked, with respect to
the robot, has been ubiained, the c w " algoriihm can he applied to generatc the steering and
velocity commands.
The fuzzy logic approach is usefiil for this kind of problems hecause it can dcal with unccriainiy
problems, such as the tomporary loss of the obiect position, due to sudden changes of itlu-
minatinn o r the limited field of view 01' the vision system. It can also help to clnulate the
nonlinear behaviour of a human-driver.

                               4. FUZZY LOGIC CClNTKOLLER
     Paih tracking is a nonlinear control problem. There are tnany algorithms that have heen used
for path tracking, hut there is no geneal solution that caii giiarantee robustness when the
curvature ofthc path varies, and the velocity of the vehicle also changes. Fuzzy logic is a suitable
technique to apply to path tracking strategies delined hy means ot'rules. The rcsulting controllers
are known as direct fuzzy utintrollers (Macda et. a l . , l W I : Ollcrro et al.. 2000). The conimllcr
inputs are the variables defining the state of ]he vehicle with respect to the path. The output ofthe
fuzzy controller is the stesring command to be executed by the low-level motion controllers.
Consider a goal point in the path at a look-ahead distance away as in Fig. I(a). The goal point has
il negativc .x cvordinate (ncgative x) and thr path tangent in i h i s point is the same as thc vehicle's
heading (zero heading in the vchicte's coordinate kame, or 4 = 0). Then, the vehicle must be
turned to the Icn by a cetlain amount as it1 Fig. I(a).

 Fig. I FUZZVlogic p t h Iimking s/inlcgv with rwinbie      CY,.r. 11 nnd &./or. /i(zxi>logic cotirrollcr.
Consider now the situation illustrated by Figure l(b). In 111iscase .r is zero, hut #is positive and
the vehicle must be turned again to the left by a certain amount. I t seems clear that fiizzy logic
could he uscd lo interpret this heuristic knowledge to generate the steering command fi. from thc
values o f x and 4. I t is also advisable to select addiiional inputs to thc controller: the distance s

betweeii the vehicle and the nearest point in the path, the curvature error ybctweeii the path to be
tracked and the vehicle, and the vehicle's velocity 1'. Thus, when s is shorter the curvature can
change more abruptly. The curvature command has to he increased when the curvature error yis
positive, arid decrcascd when this error is negative. When the velocity is high, thc desired
ctirvatiire should change in a smooth way, but if the velocity is low tlie curvature can change
The above heuristics can be used to define the rules o f a conventional Mamdani controller. When
contlicts appear in applying the above Iieurisiic rules, tlie error in position x will he the in051
significant one, while the enor in curvature will be the least. The rulcsare ofthe form

K,: 1f.r is NEGATIVE-LARGE and is POSITIVE and y is NEAR-ZERO and                                                            I'   is

wlicie     is !he requested curvature (stccring command], SMALL, POSITIVE, NECATIVE-
LARGE, MEDIUM and NEAK-ZEKO am labels associated with the corrcsponding litiguisric
variables, and R, is tlie i-th rule of the set o f fuzzy rules of the controllcr. These labels are
represented by fuzzy subsets. The membership functions defining these fuzzy subscts are shown
i n Figure 2. Tlie set ol' fuzzy rules represents a l'uzzy relation bctwccn the antecedents and thc
consequents o f the rules.
                 NL       N    NS     NZ PS            P            Pt                 N                NL       P

                  1                  ;r                         1              -0 3                 b            0.3
                         NC    N     .NZ P                 PL                  NZ,             PS       P        PL

                  .xi6               *I                         "IS                                 I '      075

                          NL    PS        P       PL                          NL           N        ,NZ      P         PI.

From the control law point ofview, thc fuzzy direct controller is denoted by a nonlinear function:

                                              yr = *.r,         4 y. s. v )
                                                                    I                                                                  (2)
Notice that .c, #, and y are delincd with respect io a goal point in the path to be tracked. Since the
vehicle catinot correct the errors w.r.t. the nearest point on the path to track, the goal point cannot
be selected as the [iearest point on the path. but at some distancc, D. ahead from this nearest point
(Ollero et al. 2000). This distance is usually measurcd over the desired path in order to make the
searcli easier. The look-ahead distance allows the vehicle to anticipate actions.
The appropriate selection oftlie look-ahead distance plays an important role. A larger look-ahead
distance implies smoother control, hut i t also means worse tracking. A smaller look-ahead can
reduce the tracking errors, but [he magnitude of the control actions increases and can even make
tlie motion unstable. So, it would hr: hcncficial to consider the look-ahead a5 a parameter that has
to be adjusted depcnding on vehicle's situation with respect to the desired path. Changes in the
look-ahead distance must be accomplished smooihly i n order to changc ihe desired curvature i n
the same way from one control period to the iiext.
The selection of the goal point i s typically done iii a hcuristic way. There are no precise rules io
select the distance to this point. A fuzzy goal point selector can bc considercd. The fuzzy rules
hased sclcctor has been defined using the fallowing guidelines:
  Larger error5 in position, orientation. or curvature imply [hat the look-ahead D should be
  increased while smaller errors shoutd lead to a dccrease i n D.
    As the vehicle move5 faster, LJ should be increased. The opposite occurs when the vehiclc
    decreases its velocity.
   The look-ahead D has to be increased when s is larger, and decreased when s is smaller.
Then the rules represciiting the goal point sclector can be defincd as

Ri: I f K is NEGATWII-LARGE and 4 is POSITIVE and y is ZERO and                      LJ   is MEDIUM       (3)
and s is SMALL, Thcn D is MEDIUM.
The distance 0 ahead to the goal point we can see in Fig. 1 . [t should he noted that the above
two-level structure is a particular case of the supervisory path cracker prcserzted in (Olterro et al,
19951. There fuzzy logic is used to update in rcal time the paramcters of ihc pure-pursuit and
generalized prcdictive path tracking mcthods. More details of die two-level path tracking
structure are given in (Sanches et al, 199Y), Ollerro et al, 2000). These two references include
experiments with mobile robots.

                         5. SIMULATION MODEL AND RESUI,'lS
   We build simulatioti scheme for this two level controller for mohilc vehicle i n MATLAB
SlMULlNK environment. Our fuzzy logic controller is constructed on the grounds of rules (I),
and the goal point se[ector is built using thc rules (3). Simulation is wiih constant velocity,
because our first ilext step will he hardware and software realization ofmobile vehicle and parh

        Fig.3 Sinlrhtion rmilts,for. /racking,/or explicit j   ~ d iisii7g.jiizz.v
                                                                     i               logic coi7tr-ullrv
tracking with constant velocity. Resutting tracking we can see on frg.3. Path generation curve we
have from our algorithm presented in Kraljevski ct al, 2003. We can see that our fuzzy logic
controllt.r has good tracking possibilities.

                                         6. CONCI.USION
    We studied the application of fuzzy logic controllers for navigation of mobile vehicks and
robots. We propose that f u m y logic controller can be reali7e incorporating heuristic driving nilcs
represented by the IF-THAN rules.
Two lcvel fuzzy systems can be used to redocc the complexiiy to select tlic optimal values of
control signals of steering angle and vehicle's vclocity. Fuzzy logic controller work in two pm-ts:
goal point select and steering angle generation. In this papcr we work only with steering angle

                                                26 1
guneration, with constant vclocity. Path tracking is accomplished on the grounds of the paih
generated from an environment image scanned by camera.
We have developed a simulation sctup in MATLAB SIMULINK environmuiii, and presented our
results. Next stcp is practical realimrion o f prupoiud fuzzy logic controller.

The authors would like to acknowledge the important cantributions made by Professor G. M.
Dimirovski in this research.

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