amr in dynamic environment

8/3/2019 AMR in Dynamic Environment

1/17

Autonomous mobile robot navigation system designed in dynamic

environment based on transferable belief model

Wang Yaonan a, Yang Yimin a,, Yuan Xiaofang a, Zuo Yi a,b, Zhou Yuanli a, Yin Feng a, Tan Lei a

a College of Electrical and Information Engineering, Hunan University, Changsha, Hunan 410082, PR Chinab Key Laboratory of Regenerative Energy, Electric-Technology of Hunan Province, Changsha University of Science and Technology, Changsha, Hunan 410004,

PR China

a r t i c l e i n f o

Article history:

Received 2 February 2010

Received in revised form 19 March 2011

Accepted 12 May 2011

Available online 20 May 2011

Keywords:

Navigation

Path planning

Mobile robot

Robust tracking control

Transferable belief model

Dynamic environment

a b s t r a c t

This paper investigates the possibility of using transferable belief model (TBM) as a prom-

ising alternative for the problem of path planning of nonholonomic mobile robot equipped

with ultrasonic sensors in an unknown dynamic environment, where the workspace is

cluttered with static obstacles and moving obstacles. The concept of the transferable belief

model is introduced and used to design a fusion of ultrasonic sensor data. A new strategy

for path planning of mobile robot is proposed based on transferable belief model. The

robots path is controlled using proposed navigation strategy that depends on navigation

parameters which is modified by TBM pignistic belief value. These parameters are tuned

in real time to adjust the path of the robot. A major advantage of the proposed method

is that, with detection of the robots trapped state by ultrasonic sensor, the navigation

law can determine which obstacle is dynamic or static without any previous knowledge,

and then select the relevant obstacles for corresponding robot avoidance motion. Simula-

tion is used to illustrate collision detection and path planning.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

During the past few years, autonomous navigation of

nonholonomic systems such as nonholonomic mobile

robot has received wide attention and is a topic of great

research interest. The navigation systems including map

building and path planning implies that the robot is

capable of reacting to static obstacles and unpredictable

dynamic object that may impede the successful exactionof a task. To achieve this level of robustness, many litera-

tures that deals with path planning is rapidly growing.

The work of Rueb and Wong [1], Habib and Yuta [2],

Mataric [3], Rimon and Koditschek [4] and Borenstein

and Koren [5] are among the earliest attempts to solve

the problem of path planning. Various classical approaches

designed originally are extended in order to be applicable

in real applications. Probabilistic roadmap methods are

used in [69]. Potential field method is suggested in

[1012]. These methods perform well in static environ-

ments. However, this does not automatically imply good

performance in dynamic environment. Additionally, these

methods have limited performance when obstacles are al-

lowed to move in the workspace.

Recently, other kinds of research were proposed [13

21], which extended the various approaches to dynamicenvironment. For example, dynamic potential field method

[1315], kinematics methods to solve the problem of colli-

sion detection [16], sensor-based path-planning methods

[1720]. Sensor-based path-planning methods are widely

used to navigation in dynamic environments. The robot

calculates and estimates the motion of the moving obsta-

cles based on its sensory system. There also exist methods

with other algorithms such as genetic algorithms [21], fuz-

zy system [22], intelligent algorithms [23,24] to solve this

problem. These methods have the ability of wheeled mo-

bile robots to navigate safely and avoid moving obstacle

0263-2241/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.measurement.2011.05.010

Corresponding author.

E-mail address: [email protected] (Y. Yimin).

Measurement 44 (2011) 13891405

Contents lists available at ScienceDirect

Measurement

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / m e a s u r e m e n t
http://dx.doi.org/10.1016/j.measurement.2011.05.010mailto:%3Cxml_chg_old%[email protected]%3C/xml_chg_old%3E%3Cxml_chg_new%[email protected]%3C/xml_chg_new%3Ehttp://dx.doi.org/10.1016/j.measurement.2011.05.010http://www.sciencedirect.com/science/journal/02632241http://www.elsevier.com/locate/measurementhttp://www.elsevier.com/locate/measurementhttp://www.sciencedirect.com/science/journal/02632241http://dx.doi.org/10.1016/j.measurement.2011.05.010mailto:%3Cxml_chg_old%[email protected]%3C/xml_chg_old%3E%3Cxml_chg_new%[email protected]%3C/xml_chg_new%3Ehttp://dx.doi.org/10.1016/j.measurement.2011.05.010


2/17

in dynamic environment. However, most of the proposed

approaches for mobile robots in the literature did not con-

sider autonomous navigation in an environment which in-

cludes both static obstacles and dynamic obstacles.

Furthermore, in the nature of the real world, any prior

knowledge about the environment is, in general, incom-

plete, uncertain, or completely unknown. These methods

assume that, each moving objects velocity and direction

is exactly known, but this prior knowledge is not easy to

gain.

The transferable belief model (TBM) is a model for the

quantified representation of epistemic uncertainty and

which can be an agent, an intelligent sensor, etc., and pro-

vides a highly flexible model to manage the uncertainty

encountered in the multi-sensor data fusion problems.

Application of the transferable belief model (TBM) to many

areas has been presented in [2529] including classifica-

tion and target identification during recent times. And we

feel it appealing when using navigation of mobile robots.

This work investigates the possibility of using transfer-

able belief model (TBM) as a promising alternative for nav-

igation system of nonholomonic mobile robot. First, a

neural robust tracking controller, comprising adaptive

wavelet neural network controller (AWNN), is used to

achieve the tracking control of the mobile manipulator un-

der some uncertainties without any knowledge of those ro-

bot parameters. Then, based on transferable belief model

(TBM) to design a fusion of ultrasonic sensor data, a new

approach for path planning is proposed. The local map,

represented as an occupancy grid, with the time update

is proven to be suitable for real-time applications. Attrac-

tive and repulsion potential function is modified by TBM

pignistic belief value. Taking the velocity of the obstacles

and static object into account, the suggested method can

determine which obstacle is dynamic or static without

any previous knowledge of moving obstacles, then select-

ing the relevant obstacles for corresponding robot avoid-

ance motion.

The rest of the paper is organized as follows: Section 2

shows the mathematical representation of mobile robot

with two actuated wheels. Section 3 discusses the nonlin-

ear kinematics-WNN back stepping controller as applied to

the tracking problem. Section 4 proposed a new method

for map building based on sonic rangefinder. A path-plan-

ning approach is discussed in Section 5. Simulation and

experiment are shown in Section 6.

2. Model of a mobile robot with two actuated wheels

The kinematic model of an ideal mobile robot is widely

used in the mobile robot (MR) control [3037]. The MR

with two driven wheels shown in Fig. 1 is a typical exam-

ple of nonholonomic mechanical systems. OXYis the refer-

ence coordinate system; OrXrYr is the coordinate system

fixed to the mobile robot; Or the middle between the right

and left driving wheels, is the origin of the mobile robot; d

is the distance from Or to P; 2b is the distance between the

two driving wheels and r is the radius of the wheel. In the

2-D Cartesian space, the pose of the robot is represented by

q x;y; hT 1

where (x,y)T is the coordinate ofOr in the reference coordi-

nate system, and the heading direction h is taken counter-

clockwise from the OX-axis.The motion model including kinematics and dynamics

of the nonholonomic mobile robot system can be described

by Hou et al. [34]. It is assumed that the wheels of the ro-

bot do not slide. This is expressed by the nonholonomic

constraint.

_x sin h _y cos h 0 2

All kinematic equality constraints are assumed to be

independent of time and to be expressed as follows:

Aq _q 0 3

By appropriate procedures and definitions, the robot

dynamics can be transformed as [30,34]

M _vw Vvw F sed s 4

where

M

r2

4b2mb

2 I0 Iw

r2

4b2mb

2 I0

r2

4b2mb

2 I0

r2

4b2mb

2 I0 Iw

@ 1A

V

0 r2

2b2mcd _h

r2

4b2mcd _h 0

BB@

1CCA

F JTF

sed JTsed

B 1 0

0 1

where m = mc + 2mw, I0 = mcd

2 + 2mwb2 + Ic + 2Im; mc and

mw are the masses of the robot body and wheel with actu-

ator, respectively; Ic, Iw and Im are the moments of inertia of

the robot body about the vertical axis throughp, the wheel

with a motor about the wheel axis, and the wheel with a

motor about the wheel diameter, respectively.

y

x

rX

rY

rO

P

d

2r

2b

left wheel

right wheel

O

Fig. 1. Nonholonomic mobile robot.

1390 W. Yaonan et al. / Measurement 44 (2011) 13891405
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


3/17

Since the wheels of the robot are driven by actuators, it

is necessary to take the dynamics of the wheel actuators

into account. The motor models attained by neglecting

the voltage on the inductances are:

sr kavr kbxr=Ra; sl kavl kbxl=Ra 5

where vr and vl are the input voltages applied to the right

and left motors; kb is equal to the voltage constant multi-plied by the gear ratio; Ra is the electric resistance con-

stant; sr and sl are the right and left motor torquesmultiplied by the gear ratio; and ka is the torque constant

multiplied by the gear ratio. The dynamic equations of the

motor-wheels are:

sr kavr

Ra

kakbxrRa

; sl kavl

R

kakbxlRa

6

By using (4)(6), the mobile robot model including the

robot kinematics, robot dynamics, and wheel actuator

dynamics can be written as:

M _v

w Vv

w F sed

kavr

Ra

kakbxrRa

7

wH XV 8

where V, X is selected as

X 1

rRr

1

r R

r

" #9

V v

w

!10

3. Nonlinear kinematic-WNN backstepping controller

In area of research of trajectory tracking in mobile robot,

based on whether the system is described by a kinematic

model or a dynamic model, the tracking-control problem

is classified as either a kinematic or a dynamic tracking-con-

trol problem. Using kinematic or dynamic models of non-

holonomic mobile robots, various approaches [21,3237]

consider that wheel torques are control inputs though in

reality wheels are driven by actuators and therefore using

actuator input voltages as control inputs is more realistic.

To this effect, actuator dynamics is combined with the mo-

bile robot dynamics. In this section, a neural robusttracking

controller is discussed briefly to achieve thetrackingcontrol

under some uncertainties without any knowledge of those

robot parameters from our recent work [36]. More detail,

proof and simulation can be also found in [36].

Recall the robot dynamics (10)

M _vw Vvw F sed kavr

Ra

kakbxrRa

11

The controller for s is chosen as

s ^f K4ec c 12

where K4 is a positive definite diagonal gain matrix, andf is

an estimation of f(x) that is defined by

fx Mq _vc Vmq; _qvc Fv 13

where x vTvTc _vTc, so error can be defined as

ec vc v 14

Using (11)(14), the error dynamics stable the input term

is chosen as

M_ec Vmec K4ec ~f sd

kakbRa

BXvc kaRa

Bu

c 15

The function in braces in (15) can be approximated by

an AWNN, such that

M _vc Vmvc F cWwxi; c; m 16where the term cWwxi; c; m represents an adaptiveapproximation WNN. The structure for the tracking control

system is presented in Fig. 2. In this figure, no knowledge

Fig. 2. Structure of the wavelet neural network-based robust control system.

W. Yaonan et al. / Measurement 44 (2011) 13891405 1391


4/17

of the dynamics of the cart is assumed. The function of

WANN is to reconstruct the dynamic (16) by learning it

on-line.

Assumption 3.1. The approximation errors and distur-

bances are bounded, i.e., the specified constants De and Drsatisfy kefk6 De and ksdk 6 Dr, respectively.

For case of notation, the approximation error

~

f can berewritten as

~f WT eW fWT bW ef 17where ~W W cW and ~w w w. The controller isdesigned to achieve good tracking and stability results

with the connecting weights, dilation, and translation

parameters of the WNN tuned on line. To achieve this,

the linearization technique is used to transform the

nonlinear output of WNN into partially linear from so

that the Lyapunov theorem extension can be applied.

The expansion of ~w in Taylor series is obtained as

follows:

~w

~w11

~w12

..

.

~wpq

26666664

37777775 @w11@m

@w11@m

..

.

@w11@m

266666664

377777775

Tmm

m m

@w11@m

@w11@m

..

.

@w11@m

266666664

377777775

Tcc

c c H

18

H is a vector of higher-order terms and assume to be

bounded by a positive constant. Substituting (18) into

(17), it is revealed that

~f sd cWT~w ~WT~w ~WTw ef sd

cWTw ATm BTc cWTAT ~m BT~c r 19where r WTA

Tm BTc H cWTATm BTc ef

sdBy substituting (19) into (15), the closed-loop system

dynamics can be rewritten as

M_ec K4 Vm

ec kakb

RaBXvc

kaRa

Bu

~WT w ATm BTc

cWT AT ~m BT~c r c

20

Moreover, assume the following inequality:

krk @X2m

4 WT A

Tm BTc H

cWT ATm BTc

ef sd @X2m

46

@X2m4

WT AT

m BTc H

ef sd cW ATm BTc 6 kpp

where @ is a positive constant; pT 1kcWk; kp kp1kp2; kp1 P kW

TATm BTc; H ef sdk; kp2 PkATm BTck, i.e., kp is an uncertainty bound.

The robust term c is designed as

c kpp sgnec 21

Definition 1. considering (21) for nonholonomic mobile

robot, if using controller (12), the closed loop error

dynamics given by (20) is locally asymptotically stable

with the approximation network parameter tuning laws

given by.

_

cW g1w AT

m BTcec g1@keckcW 22_m g

2cW Aec g2@keckm 23

_c g3cW Bec g3@k@kc 24

_bK g4keckp 25where g1, g2, g3, g4 are positive constants; kp is an on lineestimated value of the uncertain bound kp.

4. Map building

An occupancy grid is essentially a data structure that

indicates the certainty that a specific part of space is occu-

pied by an obstacle, which is widely used in map building

in mobile robot [1721]. It represents an environment as a

two-dimensional array. Each element of the array corre-

sponds to a specific square on the surface of the actual

world, and its value shows the certainty that there is some

obstacle there. When new information about the world is

received, the array is adjusted on the basis of the nature

of the information.

Here, the proposed map-building process utilizes Trans-

ferable Belief Model (TBM). The sonar sensor readings are

interpreted by this theory and used to modify the map

using transferable belief model rule. Whenever the robot

moves, it catches new information about the environment

and updates the old map. Because of using this uncertain

theory to build an occupancy map of the whole environ-

ment, it represent important point of view what we must

to consider: any position in the updated map of the whole

environment do not exist absolute exactness for the reason

that any obstacle can not be measured absolutely right-

ness. So every discrete region of the path position may be

in two states: belief degree E, O and uncertain degree H.

For this purpose, the map building system to process the

readings in order to assess, as accurately as possible, which

cells are occupied by obstacles (partially certain) and

which cells are (partially) empty and thus suitable for ro-

bot navigation.

4.1. Review theory of transferable belief model

In this section, we briefly regroup some basic of the be-

lief function theory as explained in the transferable belief

model ( TBM). More details can be found in [2529].

A.1 (Frame of discernment). The frame of discernment is

a finite set of mutually exclusive elements, denoted

X hereafter. Beware that the frame of discernment

is not necessarily exhaustive.



5/17

A.2 (Basic belief assignment). A basic belief assignment

(bba) is a mapping mX from 2X to [0,1] that satisfiesPA#Xm

XA 1. The basic belief mass (bbm) m(A),

A # X, is the value taken by the bba at A.

A.3 (Categorical belief function). A categorical belief

function onX focused onA # X, is a belief function

which related bba mX satisfies:

mX 1 if A A

0 otherwise

&26

When all bbas are categorical, the TBM becomes equivalent

to classical propositional logic. Two limiting cases of cate-

gorical bbas have received special names.

A.4 (Normalizing or nonnormalizing) The basic belief

mass m(A) represents the part of belief exactly com-

mitted to the subset A ofX given a piece of evidence,

or equivalently to the fact that all we know is that A

holds. Normalizing a bba means requiring that

E(H

) = 0 and that the sum of all bbms givens tothe non-empty subsets is 1. This means closing the

world. When a bba means requiring that m(H) > 0

and we call this open world. In TBM, we do not

require m(H) = 0 as in Shafers work.

A.5 ( Related function) the degree of belief bel(A) is

defined as: bel(A): 2X? [0,1] with, for all A # X

belA X

hB#A

mB 27

The degree of plausibility pl(A) is defined as: pl: 2X? [0,1]

with, for all A # X

plA XB#H;B\Ah

mB belH belA 28

The commonality function q is defined as: q: 2X? [0,1]

with, for all A # X

qA X

A# B;B#X

mB 29

The function q,bel,pl are always in one to one correspon-

dence. More details and proofs of the relationship among

functions above can be found in [26,27].

A.6 (The conjunctive rule). Given two bbas mX1

; mX2

from

different sensor respectively, the bba that results

from their conjunctive combination defined by

mE1 \ mE2A X

B;C#H;B\CA

mE1B mE2C;

8A#H 30

A.7 (The pignistic transformation for decision). The

pignistic transformation maps bbas to so called pig-

nistic probability functions. The pignistic transfor-

mation of mX is given by

BetPXA XB#X jA \ BjmXB

jBj1 mXh; 8A 2 X 31

where jAj is the number of elements ofX inA. This solution

is a classical probability measure from which expected

utilities can be computed in order to take optimal deci-

sions. Some of its detail and justifications can be found in

[25,29]

4.2. sensor modeling and measurements interpretation

The Polaroid Ultrasonic Rangefinder is used for map

building. This is a very common device that can detect dis-

tances in the range of 0.475 m with 1% accuracy. In [21],

the sensor model converts the range information into

probability values. The model in Figs. 3 and 4 is given by

Eqs. (32)(37).

In region I, where R e < r< R + e

x

b@b

2 ejRrje

22

32

EOjx

0 1 < x < 0

12

2x21x2 1 0 6x 6 1( 33

EEjx 0:8 EOjx 34

In region II, where Rmin < r< R e

x

b@b

2 Rer

Re

22

35

EOjx 0 1 < x < 01

2 2x

2

1x2

1

0 6x 6 1

(36

EEjx 0:8 EOjx 37R is the range response form the ultrasonic sensor, and

(r, @) is the coordinate of a point inside the sonar cone. e isthe range error, and it distributes the evidence in Region I.

b is the half open beam angle of the sonar cone.

4.3. The fusion of data from sonar

The sonar data interpreted by Transferable Belief Model

of evidence are collected and updated into a map using the

same theory of evidence. In our approach, the basic

30o

270

300

330

0

30

60

90

Fig. 3. Typical beam pattern of Polaroid ultrasonic sensor.



6/17

probability assignment corresponding to a range reading r

is obtained directly using Eqs. (32)(37). The next example

illustrates the usage of transferable belief model for map-

building process.

Example 1. Let the robot be located in cell (15,10) in the

beginning of the navigation process. The condition is

shown in Table 1 and Figs. 5 and 6. The new basic

probability assignments for cells in the map become (the

first lies in region I and the second lies in region II):

(Static obstacles)

xS00

153

15 2

1027102

2

2 0:1878 xS1

0

15315

2 1027

102 2

2 0:1878

ES00

x 12

2x2

1x2

1 0:5341 ES0

0x 1

2 2x

2

1x2

1

0:5341

ES00

O 0:8 ExS00

0:2659 ES00

O 0:8 ExS00

0:2659

EH 0:2 EH 0:2

and

xS01

156

15 2

2j109j

2 2

2 0:3050 x

S11

150

15 2

2j109j

2 2

2 0:6250

ES01 x

1

2 2x2

1x2 1 0:5851 ES11 x 12 2x21x2 1 0:7809ES0

1O 0:8 Ex

S11

0:2149 ES11

O 0:8 ExS11

0:0191

EH 0:2 EH 0:2

(Dynamic obstacles)

xS24

153

15 2

1025102

2

2 0:3903 x

S25

153

15 2

2j1011j

2 2

2 0:4450

ES24

x 12

2x2

1x2

1

0:6322 E

S24

x 12

2x2

1x2

1

0:6625

ES01

O 0:8 ExS11

0:1678 ES01

O 0:8 ExS11

0:1375

EH 0:2 EH 0:2

In the next moment, the robot is moving in a direction de-

picted by the broken line and sonars scan the environment

again. This situation is given in Fig. 6. S0, S1 and S2 detect

some possible obstacles on @S10 6; r

S00 4; r

S10 5;

rS01 6; rS11 6; r

S21 7; r

S12 9; r

S22 9; @

S00 3; @

S01

6; @S11 0; @

S21 3; @

S12 3; @

S22 6; r

S26 3; @

S26 6:

xS00

153

15 2

1024102

2

2 0:3100 x

S10

156

15 2

1025102

2

2 0:2503

ExS00

12

2x2

1x2

1

0:5877 Ex

S10

12

2x2

1x2

1

0:5590

EOS00

0:8 ExS00

0:2123 EOS10

0:8 ExS00

0:2410

EH 0:2 EH 0:2

xS01

156

15 2

1026102

2

2 0:2112 x

S11

150

15 2

1026102

2

2 0:6250

ExS01

12

2x2

1x2

1

0:5427 Ex

S11

12

2x2

1x2

1

0:7809

EOS01

0:8 ExS00

0:2573 EOS11

0:8 ExS00

0:0191

EH 0:2 EH 0:2

y

r

x

R

anglePr ofile for the

l

15

15

Pr ofile for the range

l

R R R +minR

Fig. 4. The profile of the ultrasonic sensor model.

Table 1

Condition of this example.

Robot position xr = 15, yr = 10

Dynamic

obstacles

position

and its

moving

direction

X4x = 14, X4y = 10 moving direction

in a positive X-axis direction.

X5x = 15, X5y = 7 moving direction

in a positive X-axis direction.

Static

obstacles

position X0x 8; X0y 8

X1x 10; X1y 5

Distances r

and angles

@ detected

by different

sonar

X0 : rS00

7; @S00

3; rS10

7; @S10

3

X1 : rS01

9; @S01

6; rS11

9; @S11

0

X4 : rS24

5; @S24

3

X5 : rS25

11; @S25

3



7/17

xS21

153

15 2

1027102

2

2 0:3278 x

S12

153

15 2

2 109j j

102 2

2 0:3278

ExS21

12

2x2

1x2

1

0:5970 Ex

S21

12

2x2

1x2

1

0:5970

EOS21

0:8 ExS00

0:2030 EOS21

0:8 ExS00

0:2030

EH 0:2 EH 0:2

(Dynamic obstacle)

xS22

156

15 2

2j109j

102 2

2 0:1878 x

S26

156

15 2

1023102

2

2 0:3753

ExS22

12

2x2

1x2

1

0:5341 Ex

S26

12

2x2

1x2

1

0:6235

EOS22

0:8 ExS00

0:2659 EOS26

0:8 ExS26

0:1765

EH 0:2 EH 0:2

Fig. 5. Initial position.

Fig. 6. Occupancy determination based on sonar measurements in t= 2 s .



8/17

Evidence about occupancies of cells including dynamic ob-

ject are combination using transferable belief model,

which is shown in Table 2.

From the new results it can be concluded that the evi-

dence about the occupancy of cells is increased. This pro-

cess continues until the target is reached.

5. Path planning

In this section, we adopt a new path planning strategy,

in which the robot replans the path as new observations

are acquired. Whats more, the navigation recognition

law that can determine which obstacle is dynamic or staticwithout any previous knowledge is discussed in this

section.

5.1. dynamic object recognition law

Condition 1. Consider the pignistic value and basic prob-

ability assignments given by transferable belief model

based on update information. At ttime, suppose the

number of the sensor is i; interval time is 1, Event A is

moving obstacle if satisfying that:

(1) mS1Si12t AE m

S1Si12t AH ! 1

(2) mS1Si12t AHP 0:5

Proof. Let H= {h1, h2, . . . , hn} denote a set of n hypothesis.

Given the likelihoods l(hijx) for every hi 2 H Let X denote

the set of possible values this observation can take.

mxA Yhi 2A

lhijxYhi 2

A

1 lhijx 38

plxA 1 Yhi2A1 lhijx 39BetPA

XA#X

mXA

A1 mXH; 8A 2 X 40

Supposethesensor measurement isA 2 Xandits likelihoods

are mS1S2Si12t AO a; m

S1S2Si12t AE b, with (38)

mS1S2Si12t AH 1 a1 b 41

From (40),

BetS1S2 Si12t Ah1

a1 b Pn1

i1 Cini1 b

ni1=i 1

1 1 a1 b

aPn1i0 Cinibi1 bni1=i 11 1 a1 b 42

The sum can be simplified to from Delmotte [28]:Xn1i0

Cinibi1 b

ni1=i 1

1 1 bn

nb43

Thus:

BetS1S2 Si12t Ah1

a

nb

1 1 bn

1 1 a1 bn1

44

Let n = 2 for the reason these are two hypothesis including

occupancy (O) and empty (E):

BetS1S2Si12t AO

a2b

1 1 b2

1 1 a1 b

a

2b

1 1 2b b2

1 1 b a ab

a

2b

2b b2

b a ab

a

2b

2b b2

b a ab

a2 b

21 mH

45

IfBetS1S2Si12t AO ( Bet

S1S2Si12t AH, it means event A of

occupancy is unbelievable, thus if"e and e is a small con-

stant, andBet

S1 S2 Si12t

AO

BetS1 S2Si12t

Ah< e we can belief that event A is

occupancy is unlikelihood.

BetS1S2 Si12t AO

BetS1 S2 Si12t AH

a2 b

21 mXx1; . .. ;xiH0mS1

S2 Si12t AH

1 mS1S2 Si12t AH

a2 b

2mS1 S2 Si12t AH

46

IfBet

S1 S2 Si12t

AO

BetS1 S2 Si12t

AH< e, we get:

mS1S2Si12t AO ! 0 and m

S1 S2 Si12t AE

! 1 and mS1S2Si12t AHP 0:5

Table 2

Probabilitic result from transferable belief model.

H H

(unknown)

Occupancy Empty

mS01

T0 0.3362 0.3921 0.1293

mS11

T0 0.3362 0.3921 0.1293

mS0 S11

T0 0.6642 0.2561 0.0505

mS01 T1 0.3248 0.4629 0.0875

mS02

T1 0.3347 0.4243 0.1063

mS0 S11

T1 0.5409 0.4550 0.0022

mS21

T4 0.3007 0.5261 0.0671

mS21

T5 0.2911 0.5714 0.0464

mS02

T0 0.3248 0.4629 0.0875

mS12

T0 0.3320 0.4243 0.1063

mS0 S12

T0 0.5371 0.3117 0.0344

mS0 S112 T0

0.5281 0.3874 0.0476

mS02 T10.3396 0.4031 0.1177

mS12

T1 0.2149 0.7660 0.0042

mS22

T1 0.3212 0.4758 0.0818

mS0 S1 S22

T1 0.5478 0.2516 0.0004

mS0 S1 S212 T1 0.5273 0.3582 0.0682

mS12

T2 0.4212 0.4758 0.0818

mS22 T20.3420 0.3921 0.1239

mS1 S22 T2

0.6444 0.3016 0.0368

mS22

T6 0.3086 0.5149 0.0661

mS212T6 m EHS26

1

(dyanmic obstacle)

0.8444 0.1203 0.0309

mTS24

1 m EHS24

2

(dynamic obstacle)

0.8442 0.1222 0.0292

mTS25

1 m EHS25

2

(dyanmic obstacle)

0.8436 0.1289 0.0239



9/17

Because mS1S2Si12t AH m

S1S2Si12t AE m

S1S212t

SiAO 1, we get the condition:

(1) mS1Si12t AE m

S1Si12t AH ! 1

(2) mS1Si12t AHP 0:5If satisfying the condition, we

believe this obstacle is dynamic. And the velocity

of this dynamic obstacle is defined:

vobst

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix

BetPS

1S

2Si

tO

xBetP

S1

S2

SitT

O2 y

BetPS

1S

2Si

tO

yBetP

S1

S2

SitT

O2

r 0T

47

where T is interval.

5.2. potential field method based on TBM

The potential field method has been studied extensively

for autonomous mobile robot path planning in the past

decade. An attractive potential which drives the mobile ro-

bot to its destination can be described by Ge and Cui

[10,13]. In this paper, we proposed a new method to

modify this potential field method based on TBM in com-

plex dynamic environment under static and dynamic

obstacle.

Let x;yBetPX TtOand [xr,yr] is the position both from

dynamic obstacle and robot. vobst ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix

BetPS1 S2 Sit

O x

BetPS1 S2 SitT

O

2 y

BetPS1S2 Sit

O y

BetPS1 S2 SitT

O

2

r 0T,

vRO(t) = [v(t) vobs(t)]TnRO, at t time,

Fattq; v

BetPS1 S2 Si12t Om@qkqtart qtk

2nRT if not satisfy condition:1

BetPS1 S2 Sit Om@qkqtart qtk2

nRT

BetPS1 S2 Sit On@vkvtart vtk2

nVRT if satisfy condition:1

8>>>:48

where q(t) and qtar(t) denote the positions of the robot andthe target at time t, respectively; q = [xyz]T in a 3-dimen-sional space or q = [xy]T in a 2-dimensional space; v(t)and vtar(t) denote the velocities of the robot and the target

at time t, respectively; kqtar(t) q(t)k is the Euclidean dis-tance between the robot and the target at time t;

kvtar(t) v(t)k is the magnitude of the relative velocity be-

tween the target and the robot at time t; @q and @v are sca-

lar positive parameters; nand mare positive constants;

BetPX(O) is pignsitic decision value that sensor detect the

occupancy belief value both for static and dynamic respec-

tively; nRT being the unit vector pointing from the robot to

the target and nVRTbeing the unit vector denoting the rela-

tive velocity direction of the target with respect to therobot.

Also a repulsive potential can be written as:

Frep q;v

0; ifqs q;qobs qmvROPq0orvRO 6 0

or satisfy condition:1

Frep1 Frep2; if 0 < qsq;qobs qmvRO 0

or satisfy condition:1

not defined; if vRO > 0 and qsq;qobs >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>: 49

where

Frepv1 gBetPXOv

qsq;qobs qmvRO2

1 vRO

amax

nRO

Frepv2 BetPXOvgvROvRO?

qsq;qobsamaxqsq;qobs qmvRO2

nRO?

qmv

RO

v2ROt

2amax

BetPXOv XO#X

mXOv

jOvj1 mXH; 8A#X

With q0 is a positive constant describing the influencerange of the obstacle; qs(q(t),qobs(t)) is denoted the short-est distance between the robot and the body of the obsta-

cle; vRO(t) is the relative velocity between the robot and the

obstacle in the direction from the robot to the obstacle; nROis a unit vector pointing from the robot to the obstacle; a

and g is a positive constant; BetPX(O) and BetPX(Ov) arepignsitic decision value that sensor detect the occupancy

belief value both for static and dynamic respectively;

mX(H) is unknown value from pignistic transformation.From Eqs. (48) and (49), we obtain the potential total

virtual force which drives the reference point of the mobile

robot to the destination, described by:

Ftotal Fatt Frep 50

Assuming that the target moves outward or synchronously

with the obstacle, the robot is obstructed by the obstacle

and cannot reach the target. Refs. [1317] indicate in highly

dynamic environment, waiting method is often adopted

where both the target and the obstacle are moving.

5.3. Local minimum problems

Like other local path planning approaches, the proposed

navigation algorithm has a local minimum problem. To de-

tect the outbreak of local minimum, we adopt the method

in [5] (see Fig. 7), which compares the robot-to-target

direction, ht, with the actual instantaneous direction of tra-

vel, h0. If the robots direction of travel is more than a cer-

tain angle (90 in most cases) off the target point, that is,

when

jht h0j > hs 51

where hs is a trap warning angle, and typically 90. We re-

gard it is very likely about to get trapped.

Fig. 7. Incorporating a virtual target on local-minimum alert.



10/17

Consider a common situation as shown in Fig. 8, in

which the robot needs to detour around a long wall to

reach the goal. At position A, the robot is heading to the

goal position and hence hs = 0.

But at position B, the robot changes its direction by

repulsive force from detected wall and hsP 90. In such

a situation, the original target point is replaced with the

virtual target point. The virtual target point is placed by

following equations:

xv xi m coshi bvt

yv

yi m sinhi bvt 52

hv h0 bvt

where m is the distance that the robot needs to travel toreach the virtual goal. Also

v L BetPXO R 53

where L is the distance between the robot and the obstacle

near the virtual target detected by the longest-range sen-

sor in the corresponding direction. BetPX(O) is a pignsitic

decision value that sensor detect the occupancy belief va-

lue in hv that direction. R is an offset which depends on

the size of the robot. bvt is a certain angler, and typically

45.

Based on (51)(53), the robot escapes from this trap-

ping point and moves to point C. When the robot escapes

from the condition above or when no obstacle is detected,

the original target point is restores, and the robot contin-

ues to proceed to the target point.

6. Simulation and experiment results

To show the usefulness of the proposed approach, a ser-

ies of simulations have been conducted using an arbitrarily

constructed environment including obstacles.

6.1. Simulation results

In these simulations, the positions of all the obstacles

including moving obstacles in the workspace are unknownto the robot. The robot is aware of its start and finish posi-

tions only. Simulation results obtained in three working

scenarios are presented in Figs. 913. The robot has been

modeled as a small circle, and imaginary sensors (sixteen

in number) are placed in the form of the arc along the cir-

cumference of the robot. The minimum distance obtained

within the cone of each sensor is considered as the dis-

tance of the obstacle from the sensor which detects any

obstacle. And any distance information detected from so-

nar is adding Gaussian White Noise. The first to fourth

experiments are conducted to verify the proposed method

in the MATLAB environment, and the fifth experiment is

carried out from Mobilesim environment.Experiment 1: Fig. 9 represents the obstacle avoidance

path of the mobile robot in static case. Table 3 shows the

condition settings of this experiment. As seen from the vir-

tual plane shown in Fig. 9a, with the decrease of distance

between Obs6 and robot, BetPX(O) became much large

which lead the repulsive force much large. Ultimately, ro-

bot changes its path by deviating to the right. The complete

process is shown in Fig. 9.

Experiment 2: This example illustrates the collision

avoidance process in dynamic environment. The scenarioFig. 8. Anti-deadlock mechanism.

Fig. 9. Collision avoidance (static case).



11/17

shown in Fig. 10 has some similarity with the scenarios of

example 1 but adding two moving obstacles. Fig. 10 thor-

oughly plots the obstacle avoidance path of the mobile ro-

bot in discrete time while it is maneuvered in a complex

environment (including dynamic and static obstacle)

where two rectangular shapes of obstacles are moving in

Fig. 10. Collision avoidance (dynamic case).



12/17

different directions and different velocity, meanwhile, five

static obstacles also set in this environment. Table 4 shows

the condition settings of this experiment.

Fig. 10 represents the scenario and the virtual plane in

different time intervals: (a and b) 06 t6 5s; (c and d)

06 t6 10s; (e and f) 0 6 t6 15s; (g and h) 0 6 t6 37s. As

seen from Fig. 10(c and d), the robot is in a collision course

with both ObsD1, Obs1 and Obs2. However, it is more ur-

gent to avoid collision with ObsD1, and the robot slows

down to accomplish this. The robot avoids collision with

Obs2 as shown in Fig. 10e and f. Fig. 10e and f show the ro-

bot neglect this moving obstacle and can not change its

path for the reason there is no collision risk with ObsD2.

The complete process is shown in Fig. 10g and h.

Experiment 3: For local minimum problem avoidance, a

rigorous testing is carried out in cluttered maze consisting

of concave obstacles and dynamic obstacles (Fig. 11). Inthe

following Figs. 11 and 12, h represents the static obstacle

and represents the dynamic obstacle. Point a, b, c, . . . rep-

resent several trapping points. represents the real goal

Fig. 11. Collision avoidance (local minimum case).



13/17

Fig. 11 (continued)

Fig. 12. Collision avoidance (mazes case).



14/17

and represents the current virtual goal.? represents the

potential total virtual force which drives the reference

point of the mobile robot to the current position. Table 5

shows the dynamic obstacles sets of this experiment.

Fig. 11 represents the scenario and the virtual plane in

different time intervals: (b and c) 0 6 t6 10s; (d and e)

06t6 30

s; (f and g) 0 6

t6 40

s. As seen from Fig. 11b

and c, the robot does not detect the obsD1 until it reaches

point A at which time it turns to the right-the side with the

lowest collision possibility. Since the obsD1 is now to

change its moving direction and move away from the ro-

bot, the robot continues to track the virtual goal in a coun-

terclockwise direction until it reaches the virtual goal at

point B. Since the goal is now to the left of the robot, it con-

tinues to track the current virtual goal (point C) at which

time the robot detects obsD2. But in Fig. 11b, it shows

the robot neglects this moving obstacle and can not change

its path for the reason that there is no collision risk with

ObsD2. In Fig. 11d and e, there are several local minimum

points including point D, E, F. At these points where the ro-

bots direction of travel is more than a certain angle

(jht h0j > 90) off the target point, the robot turns its

direction and tracks current virtual goal. Then the robot

continues to see the wall on its left until it arrives at point

H and I after which it goes towards a real target point. The

complete process is shown in Fig. 11f and g and the robot

moves counterclockwise around obstacles through point J

and K to the final goal.

Fig. 13. Collision avoidance based on Mobilesim environment (dynamic case).

Table 3

Experimental conditions of obstacle avoidance (static case).

Initial robot position xr = 0[m], yr = 0[m]

Goal position Goalx = 30[m], Goaly = 20.5[m],

Obstacle position Obs1x = 8[m], Obs1y = 10[m]

Obs2x = 13[m], Obs2y = 10[m]

Obs3x = 18[m], Obs3y = 20[m]

Obs4x = 20[m], Obs4y = 15[m]

Obs5x = 24[m], Obs5y = 20[m]

Obs6x = 9[m]? 12[m], Obs6y = 10[m]

Processing time 30 s



15/17

Experiment 4: In this experiment, the more complex

test is performed to present the effectiveness of the pro-

posed approach in cluttered environment with obstacle

loops and mazes. Similar as experiment 3, h represents

the static obstacle and represents the dynamic obstacle.

Fig. 12a, c and e thoroughly plot the obstacle avoidance

path of the mobile robot in discrete time while it is maneu-

vered in a dynamic environment where many dynamic

obstacles are moving in different direction. Whereas,

Fig. 12b, d and f give some detail information about how

the robot navigation system behaves at each discrete time.

The proposed algorithm performs well in a cluttered dy-

namic environment, as shown in Fig. 12a and b. The pro-

cesses for wall following, passing through a narrow door

and escaping from local minimum point using our algo-

rithm are shown in Fig. 12cf.

Experiment 5: This example is shown in Fig. 13. This

illustrates the collision avoidance process by change both

seed and orientation when facing with multi-moving

obstacle. Fig. 13a represents the scenario, while Fig. 13b

e indicate the virtual plane in different time intervals: (b)

06 t6 1.2; (c) 06 t6 5.1; (d) 06 t6 6.3; (e) 06 t6 8.1.

As seen from the virtual plane shown in Fig. 13b, there is

a collision risk with D1 in the time 06 t6 1.2. The robot

changes its path by deviating to the right, as shown in

Fig. 13b. In Fig. 13c and d, robot changes its orientation

by avoiding collision with D1 and D2 using proposed

method.

6.2. Experiment with a pioneer robot

The method presented in this paper has been tested on

a Pioneer robot. The robot and the experiment setup are

shown in Fig. 14. The laptop on top on the robot is in

charge of all computation: motion control, planning, SLAM

and so on. The navigation is carried out in real-time and we

only use sonar to detect obstacle.

In order to simulate dynamic obstacle, two football mo-

bile robots (MT-Robot) are used based on remote control.The orientation of the two MT-Robot is shown in Fig. 15.

The track line of Pioneer robot is indicated approximately

with blue color in this figure. The room is a clean environ-

ment with long wall obstacles and measures approxi-

mately 8.6 m by 6.5 m. The objects were placed in the

room and their positions are point out as shown in

Fig. 15. The position of the robot is recorded at regular time

intervals. During the test executions, all programs were

run under the Windows NT operating system, directly on

the main processor of the robot, a Pentium 2.3G. A test case

is presented in Fig. 15.

In this experiment, the goal position is aligned to the

front of the mobile robot which is obstructed by obstacleswall and two MT-Robots. The mobile robot starts to move

towards according to the real goal. As it moves, it detects

obstacles in front and in the left from its ultrasonic sensors.

The navigation law makes a correct decision by indicating

the right direction to the mobile robot until it reaches the

virtual goal. Then the mobile robot keeps moving and de-

tects dynamic obstacles in right direction. The robot makes

the correct decision and turns to the left avoiding the de-

tected obstacles successfully and then reaches the goal.

Although feature detectors using sonar is not very

accurate especially in complex environment and real

Table 4

Experimental conditions of obstacle avoidance (dynamic case).


Goal position Goalx = 29[m], Goaly = 25[m],

Initial dynamic obstacle

position and its moving

direction and velocity

ObsD1x = 10[m], ObsD1y = 0[m]

moving direction and velocity

moving in a positive Y-axis

direction at 0.88(m/s)

ObsD2x = 12[m], ObsD1y = 15[m]

moving direction and velocity

moving in a positive X-axis

direction at 0.19(m/s).

Static obstacle position

Obs1x 8m; Obs1y 10m

Obs2x 12m; Obs2y 10m





Fig. 14. Pioneer robot.

Table 5

Experimental conditions of dynamic obstacles.


Goal position Goalx = 29[m], Goaly = 25[m],

Dynamic obstacle position and

its moving direction and

velocity

ObsD 1x = 0[m]M 6[m],

ObsD1y = 5[m], moving back and

forth along X-axis and its velocity

at 1.20(m/s)

ObsD2x = 10[m],

ObsD1y = 5[m]M 10[m], moving

back and forth along Y-axis and its

velocity at 1.00(m/s)

ObsD3x

= 15[m]M 22[m],

ObsD3y = 10[m], moving back and

forth along X-axis and its velocity

at 0.70(m/s)

ObsD4 = (0,20)M (5,25), moving

back and forth and its velocity at

0.71(m/s)




16/17

performance, in this experiment, it is not very robust as

compared with simulation experiment in Matlab or

Mobilesim (Process time became long, waiting motion

happened frequently), it also can achieve the goal based

on this navigation method. Furthermore, the performance

of the simulation and the real robot is different. The simu-

lation has a faster cycle time for the iterations of the pro-

posed method. This allows the robot to follow the

smoother path. The reactions of the robot in the simulation

are also different from the real robot. For instance, once a

speed command is given to the real robot, the set point is

obtained over a period of time. In the simulation, the speed

set point is almost immediately achieved.

From these results, it shows that based on our collision

avoidance algorithm, the mobile robot can find a safe and

smooth path for attaining the target position autono-

mously whether in a static or dynamic environment when

adding highly noise to the sensor.

7. Conclusion

In this paper, a new mobile robot navigation strategy

for nonholomonic mobile robot in dynamic environment

was designed and fully tested in this work based on trans-

ferable belief model. The aim was to let the robot find a

collision-free trajectory between the starting configuration

and the goal configuration in a dynamic environment con-

taining some obstacle (including static and moving object).

For this purpose, a navigation strategy which consists of

sonar data interpretation and fusion, map building, and

path planning is designed. The sonar data fusion and dy-

namic object distinguish law were discussed using trans-

ferable belief model. Based on proposed judging law, a

path planning algorithm is modified based on potential

field method. Simulation and experiment results validate

the effectiveness of the proposed method. Though mobile

robot is discussed, the method is generally applicable to

other type of problem, as well as to pattern recognition,

objective classification.

Acknowledgements

The authors thank the anonymous editor and reviewer

for their invaluable suggestions, which has been incorpo-

rated to improve the quality of this paper dramatically.

This work was supported by National Natural Science

Foundation of China (60775047, 60673084), National High

Technology Research and Development Program of China

(863 Program: 2008AA04Z214), National Technology Sup-

port Project (2008BAF36B01) and Research Foundation of

Hunan Provincial Education Department (10C0356).

References

[1] K.D. Rueb, A.K.C. Wong, Structuring free space as a hypergrarph for

roving robot path planning and navigation, IEEE Transactions on

Pattern Analysis and Machine Intelligence 9 (2) (1987) 263273.

[2] M.K. Habib, S. Yuta, Efficient online path planning algorithm and

navigation for a mobile robot, International Journal of Electronics 69

(2) (1990) 187210.

[3] M.J. Mataric, Integration of representation into goal-riven behavior-

based robots, IEEE Transactions on Robotics and Automation 8 (3)

(1992) 304312.

[4] E. Rimon, D.E. Koditschek, Exact robot navigation using artificial

potential function, IEEE Transactions on Robotics and Automation 8

(5) (1992) 501518.

[5] J. Borensein, Y. Koren, Real-time obstacle avoidance for fast mobile

robots, IEEE Transactions on Systems Man and Cybernetics 19 (5)

(1989) 11791187.[6] S. Thrun, W. Burgard, D. Fox, A probabilistic approach to concurrent

mapping and localization for mobile robots, Machine Learning 31

(13) (1998) 2953.

[7] P. Svestka, M.H. Overmars, Motion planning for carlike robotsusing a

probabilistic learning approach, International Journal of Robotics

Research 16 (2) (1997) 119143.

[8] S. Thrun, Probabilistic algorithms in robotics, Ai Magazine 21 (4)

(2000) 93109.

[9] C.M. Clark, Probabilistic road map sampling strategies for multi-

robot motion planning, Robotics and Autonomous Systems 53 (34)

(2005) 244264.

[10] S.S. Ge, Y.J. Cui, New potential functions for mobile robot path

planning, IEEE Transactions on Robotics and Automation 16 (5)

(2000) 615620.

[11] K.P. Valavanis, T. Hebert, R. Kolluru, et al., Mobile robot navigation in

2-D dynamic environments using an electrostatic potential field,

IEEE Transactions on Systems Man and Cybernetics Part A Systemsand Humans 30 (2) (2000) 187196.

Fig. 15. Mobile robot and experiment.



17/17

[12] N.C. Tsourveloudis, K.P. Valavanis, T. Hebert, Autonomous vehicle

navigation utilizing electrostatic potential fields and fuzzy logic, IEEE

Transactions on Robotics and Automation 17 (4) (2001) 490497.

[13] S.S. Ge, Y.J. Cui, Dynamic motion planning for mobile robots using

potential field method, Autonomous Robots 13 (3) (2002) 207222.

[14] J. Ren, K.A. McIsaac, R.V. Patel, Modified Newtons method applied to

potential field based navigation for nonholonomic robots in dynamic

environments, Robotica 26 (2008) 285294.

[15] L. Yin, Y.X. Yin, C.J. Lin, A new potential field method for mobile robot

path planning in the dynamicenvironments, Asian Journal of Control

11 (2) (2009) 214225.[16] F. Belkhouche, B. Belkhouche, Kinematics-based characterization of

the collision course, International Journal of Robotics & Automation

23 (2) (2008) 127136.

[17] Y.C. Chang, Y. Yamamoto, On-line path planning strategy integrated

with collision and dead-lock avoidance schemes for wheeled mobile

robot in indoor environments, Industrial Robot An International

Journal 35 (5) (2008) 421434.

[18] A.O. Djekoune, K. Achour, R. Toumi, A sensor based navigation

algorithm for a mobile robot using the DVFF approach, International

Journal of Advanced Robotic Systems 6 (2) (2009) 97108.

[19] J. Minguez, L. Montano, Sensor-based robot motion generation in

unknown, dynamic and troublesome scenarios, Robotics and

Autonomous Systems 52 (4) (2005) 290311.

[20] L. Moreno, E. Dapena, Path quality measures for sensor-based

motion planning, Robotics and Autonomous Systems 44 (2) (2003)

131150.

[21] J. Velagic, B. Lacevic, B. Perunicic, A 3-level autonomous mobilerobot navigation system designed by using reasoning/search

approaches, Robotics and Autonomous Systems 54 (12) (2006)

9891004.

[22] X.Y. Yang, M. Moallem, R.V. Patel, A layered goal-oriented fuzzy

motion planning strategy for mobile robot navigation, IEEE

Transactions on Systems Man and Cybernetics Part B Cybernetics

35 (6) (2005) 12141224.

[23] T. Kondo, Evolutionary design and behavior analysis of

neuromodulatory neural networks for mobile robots control,

Applied Soft Computing 7 (1) (2007) 189202.

[24] J.A. Fernandez-Leon, G.G. Acosta, M.A. Mayosky, Behavioral control

through evolutionary neurocontrollers for autonomous mobile robot

navigation, Roboticsand AutonomousSystems 57(4) (2009)411419.

[25] P. Smets, Analyzing the combination of conflicting belief functions,

Information Fusion 8 (4) (2007) 387412.

[26] F. Delmotte, P. Smets, Target identification based on the transferable

belief model interpretation of DempsterShafer model, IEEETransactions on Systems Man and Cybernetics Part A Systems

and Humans 34 (4) (2004) 457471.

[27] T. Denoeux, P. Smets, Classification using belief functions:

Relationship between case-based and model-based approaches,

IEEE Transactions on Systems Man and Cybernetics Part A

Systems and Humans 36 (6) (2006) 13951406.

[28] F. Delmotte, Comparison of the performances of decision aimed

algorithms with Bayesian and beliefs basis, International Journal of

Intelligent Systems 16 (8) (2001) 963981.

[29] P. Smets, Application of the transferable belief model to diagnostic

problems, International Journal of Intelligent Systems 13 (3) (1998)

127157.

[30] R. Fierro, F.L. Lewis, Control of a nonholonomic mobile robot:

Backstepping kinematics into dynamics, Journal of Robotic Systems

14 (3) (1997) 149163.

[31] Q.J. Zhang, J. Shippen, B. Jones, Robust backstepping and neural

network control of a low-quality nonholonomic mobile robot,International Journal of Machine Tools & Manufacture 39 (7)

(1999) 11171134.

[32] S.X. Yang, M. Meng, Real-time fine motion control of robot

manipulators with unknown dynamics, Dynamics of Continuous

Discrete and Impulsive Systems-Series B Applications &

Algorithms 8 (3) (2001) 339358.

[33] G. Antonelli, S. Chiaverini, G. Fusco, A fuzzy-logic-based approach for

mobile robot path tracking, IEEE Transactions on Fuzzy Systems 15

(2) (2007) 211221.

[34] Z.G. Hou, A.M. Zou, L. Cheng, et al., Adaptive control of an electrically

driven nonholonomic mobile robot via backstepping and Fuzzy

approach, IEEE Transactions on Control Systems Technology 17 (4)

(2009) 803815.

[35] W. Sun, Y.N. Wang, A robust robotic tracking controller based on

neural network, International Journal of Robotics & Automation 20

(3) (2005) 199204.

[36] Y. Zuo, Y.N. Wang, X.Z. Liu, et al., Neural network robust control for a

nonholonomic mobile robot including actuator dynamics,

International Journal of innovative Computing, Information and

Control 6 (8) (2010) 34373449.

[37] Y.N. Wang, W. Sun, Y.Q. Xiang, et al., Neural network-based robust

tracking control for robots, Intelligent Automation and Soft

Computing 15 (2) (2009) 211222.

Wang Yaonan received the B.S. degree in

computer engineering from East China Sci-ence and Technology University (ECSTU),

Shanghai, China, in 1982 and the M.S., and

Ph.D. degrees in electrical engineering from

Hunan University, Changsha, China, in 1990

and 1994, respectively.

From 1994 to 1995, he was a Postdoctoral

Research Fellow with the Normal University

of Defence Technology. From 1981 to 1994, he

worked with ECSTU. From 1998 to 2000, he

was a senior Humboldt Fellow in Germany,

and from 2001 to 2004, he was a visiting professor with the University of

Bremen, Bremen, Germany. He has been a Professor at Hunan University

since 1995. His research interests are intelligent control and information

processing, robot control and navigation, image processing, and industrial

process control.

Yang Yimin received the B.E.E., and M.S.E.E.

degrees in 2005 and 2009, respectively, from

Xiangtan University and Hunan University,

Hunan, China. Now, He is currently working

toward the Ph.D. degree in Hunan University.

His research interests include robot control

and navigation, intelligent information pro-

cessing, and artificial neural networks.

Yuan Xiaofang received the B.S., M.S., and

Ph.D. degrees in electrical engineering from

Hunan University, Changsha, China, in 2001,

2006 and 2008, respectively.

He is currently a lecturer with the College of

Electrical and Information engineering, Hunan

University. His research interests include

intelligent control theory and applications,

kernel methods, andartificial neural networks.

Zuo Yi received the Ph.D. degree in ControlScience and Engineering from Hunan Univer-

sity, Changsha, China, in 2009. He is a visiting

scholar in University of Waterloo from 2008

to 2009. His scientific interests include neural

networks and robotic robust control.


amr in dynamic environment

Documents