OBSTACLE AVOIDANCE FOR AUTONOMOUS MOBILE

ROBOTS BASED ON POSITION PREDICTION

USING FUZZY INFERENCE

Takafumi Suzuki

Graduate School of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

Masaki Takahashi

Department of System Design Engineering, Faculuty of Science and Technolog

Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

Keywords: Autonomous Mobile Robot, Obstacle Avoidance, Fuzzy Potential Method, Omni-directional Mobile Robot.

Abstract: This study presents an obstacle avoidance method for Autonomous Mobile Robot by Fuzzy Potential

Method (FPM) considering velocities of obstacles relative to the robot. The FPM, which is presented by

Tsuzaki, is action control method for autonomous mobile robot. In the proposed method, to decide a

velocity vector command of the robot to avoid moving obstacles safely, Potential Membership Function

(PMF) considering time until colliding and relative velocity is designed. By means of considering predicted

positions of the robot and the obstacle calculated from the time and the relative velocity, the robot can start

avoiding behaviour at an appropriate time according to the velocity of the obstacle and the robot. To verify

the effectiveness of the proposed method, numerical simulations and simplified experiment intended for an

omni-directional autonomous mobile robot are carried out.

1 INTRODUCTION

In the future, it’s not difficult to image that we will

often come across many autonomous mobile robots

traversing densely populated place we live in. In

such situation, because the autonomous mobile

robots need to carry out their tasks in a place with

unknown obstacles, the obstacle avoidance is one of

the important functions of the robots. With a view to

implementation of autonomous mobile robot

working in doors, we employ an omni-directional

platform as shown in Figure 1(a). For experimental

verification, an omni-directional mobile robot shown

in Figure 1(b) is developed. The robot has an omni-

directional camera for environmental recognition,

and can move to all directions by four omni wheels.

While there are many studies about obstacle

avoidance method focusing attention on possibility

of avoidance, this paper presents the method

focusing on not only possibility but also safer

trajectory of avoidance. Even if there are the same

situations that the robot needs to avoid a static

obstacle, timing of beginning avoidance behaviour

should vary according to the robot speed. If the

obstacles are moving also, the timing should vary

according to the velocities of the obstacles. To cite a

case, in a situation that a robot and an obstacle go by

each other as shown in Figure 2, the robot should

avoid along the curved line like (iii) according to the

speeds of the obstacle and own speed. To get to the

goal with efficient and safe avoidance behaviour in

the unknown environment for the robots, predicting

the future obstacles’ position by their current

(a) (b)

Figure 1: An omni-directional platform of a prototype

robot (a) and an example of a situation that the robot needs

to avoid the other robot (b).

299

Suzuki T. and Takahashi M. (2009).

OBSTACLE AVOIDANCE FOR AUTONOMOUS MOBILE ROBOTS BASED ON POSITION PREDICTION USING FUZZY INFERENCE.

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 299-304

DOI: 10.5220/0002217102990304

Copyright

c

SciTePress

y

x

Robot

Robot

Obstacle

Obstacle

Goal point

Goal point

(i)

(i)

(ii)

(ii)

(iii)

(iii)

y

x

y

x

Robot

Robot

Obstacle

Obstacle

Goal point

Goal point

(i)

(i)

(ii)

(ii)

(iii)

(iii)

Figure 2: Example of a situation of obstacle avoidance.

0

180−

180

direction

direction

[deg]

[deg]

1

0

μ

μ

0

180−

180

direction

direction

[deg]

[deg]

1

0

μ

μ

0

180−

180

direction

direction

[deg]

[deg]

1

0

μ

μ

0

180−

180

direction

direction

[deg]

[deg]

1

0

μ

μ

0

180−

180

direction

direction

[deg]

[deg]

1

0

μ

μ

0

180−

180

direction

direction

[deg]

[deg]

1

0

μ

μ

Figure 3: Example of PMF.

movements is needed. This paper introduces a real-

time obstacle avoidance method introducing the

velocity of obstacle relative to the robot. By means

of considering predicted positions of the robot and

the obstacle calculated from the time and the relative

velocity, the robot can start avoiding behaviour at an

appropriate time according to the velocity of the

obstacle and the robot. Some researches focus

attention on the velocity of obstacle (Ko et al., 1996)

to avoid moving obstacles efficiently. In this

research, virtual distance function is defined based

on distance from the obstacle and speed of obstacle,

however, only projection of the obstacle velocity on

the unit vector from the obstacle to the robot is

considered. In other words, the velocity of the robot

is not considered. On the other hand, in (Ge et al.,

2002), the velocity of the obstacle relative to the

robot is considered. Our approach also employs the

relative velocity. In addition to this approach, a

position vector of the obstacle relative to the robot in

the future is calculated by the relative position and

the velocity. To solve the real-time motion planning

problem, fuzzy potential method (FPM) is proposed

by Tsuzaki (Tsuzaki et al., 2003). In this research,

the method is applied to autonomous mobile robot

which plays soccer. By adequate designing of

potential membership function (PMF), it is realized

that wheeled robots can get to the goal with

conveying a soccer ball and avoiding obstacles. This

method is easy to understand at a glance. However,

in dynamic environment, to avoid moving obstacles

efficiently, more specific guideline of designing is

desired. In this paper, we introduce design method

of PMF considering the predicted positions and

discuss the availability by comparing the design of

PMF considering the relative velocity and that not

considering.

δ

out

v

2

w

v

1

w

v

4

w

v

3

w

v

x

r

v

y

r

v

φ

out

θ

L

δ

out

v

2

w

v

1

w

v

4

w

v

3

w

v

x

r

v

y

r

v

φ

out

θ

LL

Figure 4: An omni-directional platform.

2 FUZZY POTENTIAL METHOD

(FPM) FOR

OMNI-DIRECTIONAL

PLATFORM

In the Fuzzy Potential Method (FPM), a recent

command velocity vector considering element

actions is decided. Element actions are represented

as Potential Membership Functions (PMFs), and

then they are integrated by means of fuzzy inference.

Furthermore, by using a state evaluator, the PMFs

are modified adaptively according to the situation.

The directions on the horizontal axis in Figure 3

correspond to the directions which are from -180 to

180 degrees and measured clockwise from the front

direction of the robot. The priority for the direction

is represented on the vertical axis. By use of the

priority, direction and configured maximum and

minimum speed, the current command velocity

vector

out

v is calculated. The command velocity

vector is realized by four DC motors and omni

wheels using following equations:

cos

x

r out out

v

θ

= v

(1)

sin

y

r out out

v

θ

= v

(2)

1

2

3

4

cos sin

cos sin

cos sin

cos sin

w

x

r

w

y

r

w

w

L

v

v

L

v

v

L

v

L

v

δδ

δδ

δδ

φ

δδ

⎛⎞

⎛⎞

⎛⎞

⎜⎟

⎜⎟

−−

⎜⎟

⎜⎟

⎜⎟

=

⎜⎟

⎜⎟

⎜⎟

−−

⎜⎟

⎜⎟

⎜⎟

⎜⎟

⎝⎠

⎜⎟

−−

⎝⎠

⎝⎠

(3)

where

out

v and

φ

are respectively current command

velocity vector and rotational speed.

δ

is an angle

of gradient for each wheel.

L is a half of a distance

between two catawampus wheels.

w

i

v is a command

movement speed of each

-thi wheel.

PMF idea allows us to represent our knowledge

and experiences easily, and furthermore it gives us

easy understanding. The priority can be seen as a

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

300

desire for each direction of the robot. In this paper,

to discuss an obstacle avoidance problem, methods

for generating of PMF to head to the goal and to

avoid moving obstacles are introduced. This method

has two steps. First step is generating PMFs. Second

step is deciding the command velocity vector by use

of fuzzy inference to integrate the PMFs.

Hereinafter, design method of PMF considering the

obstacle velocity relative to the robot and way to

decide the command velocity vector by fuzzy

inference are described.

y

x

Robot

Obstacle

Predicted coordinate

Goal point

,_ro p

θ

φ

,_ro p

r

α

y

x

y

x

Robot

Obstacle

Predicted coordinate

Goal point

,_ro p

θ

φ

,_ro p

r

α

Figure 5: Predicted coordinate.

3 FPM CONSIDERING THE

RELATIVE VELOCITY

To realize the obstacle avoidance in dynamic

environment, the proposed method employs two

different PMFs, one is considering the velocity of

obstacle relative to the robot, the other is to head to

the goal. PMF is denoted by

μ

which is function of

θ

. Note

θ

is the direction from -180 to 180 degrees

measured clockwise from front direction of the

robot. To simplify the analysis, it is assumed that the

autonomous mobile robots detect obstacles by

equipped external sensors and are capable of

calculating the positions and velocities of obstacles

relative to the robot. The shapes of the robot and the

obstacles are treated as circles on 2D surface.

3.1 Design of PMFs

3.1.1 PMF for an Obstacle

To avoid moving obstacles safely and efficiently, an

inverted triangular PMF by specifying a vertex,

height and base width is generated. Because this

PMF considers future positions of the robot and the

obstacle, the robot can start avoiding the obstacle

early and be prompted not to go on to the future

collision position. For the purpose of safe avoidance,

the PMF

o

μ

is generated.

First, to predict the future state of both the obstacle

and the robot with the aim of efficient avoidance, a

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1

θ

[deg]

p[-]

a

[deg]

θ

μ

o

1.0

,_ro p

θ

b

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1

θ

[deg]

p[-]

a

[deg]

θ

μ

o

1.0

,_ro p

θ

b

Figure 6: PMF for obstacle considering relative velocity.

predicted relative position vector, in

T

γ

seconds,

,_ _ _

(r ,r )

ro p x p y p

=

r

is calculated as following

equation:

,_ , ,ro p ro ro

T

γ

=

+rrv

(4)

where

,

(r ,r )

ro x y

=

r is current position vector of the

obstacle relative to the robot, and

,

(v ,v )

ro x y

=v is

the current velocity vector of obstacle relative to the

robot.

γ

is an arbitrary parameter from 0 to 1.

T

,which is the time until the distance between the

obstacle and the robot is minimum, is defined as

following equation:

,

,

ro

ro

T

−

=

r

p

v

(5)

where

(p ,p )

x

y

=

p is a position vector of the

obstacle relative to the robot when a distance in the

future between the obstacles and the robot is

minimum.

p is calculated by means of relative

position and velocity vector as following equation:

{

}

(v v )r r (v v v v )

p

p

(v v )p

yxy x yx xy

x

y

yxx

⎛⎞

−+

⎛⎞

⎜⎟

=

⎜⎟

⎜⎟

−

⎝⎠

⎝⎠

(6)

As described above, the predicted relative position

vector, at the time

T

γ

seconds from now,

,_ro p

r is

calculated as Figure 3 shows. By use of this position

vector, a predicted obstacle direction relative to the

robot

,_ro p

θ

is calculated as following:

_

,_

_

r

arctan

r

yp

ro p

xp

θ

⎛⎞

=

⎜⎟

⎜⎟

⎝⎠

(7)

where,

,_ro p

θ

is decided to be the vertex of the

inverted triangle.

Next, as a measure to decide how far the robot

should depart from the obstacle,

a is defined as the

height of the inverted triangular PMF.

a is

described as following equation:

,_

,_

,

ro p

ro p

ro

aif

R

α

α

α

−

=

<

−

r

r

(8)

,ro r o

RRR

=

+

(9)

OBSTACLE AVOIDANCE FOR AUTONOMOUS MOBILE ROBOTS BASED ON POSITION PREDICTION USING

FUZZY INFERENCE

301

where

r

R and

o

R denote respectively the radius of

the robot and that of the obstacle treated as circles. If

the calculated obstacle position at

T

γ

seconds later

is inside of a circle with radius

α

from the robot

position at

T

γ

seconds later, the PMF for obstacle

avoidance considering the relative velocity is

generated. In other words, if a predicted relative

distance

,_ro p

r is below

α

, a is defined and the

inverted triangular PMF corresponding to the

obstacle is generated. Smaller the predicted relative

distance is, larger the value of

a is.

In addition, a base width of inverted triangular

PMF is decided by following equation:

,ro

b

η

φ

=+v

(10)

where

φ

is decided based on the sum of radiuses of

the robot and the obstacle, and predicted relative

position vector as Figure 3 shows.

φ

is calculated

by following equation:

,

,_

arcsin

ro

ro p

R

φ

⎛⎞

⎜⎟

=

⎜⎟

⎝⎠

r

(11)

b increases up to

π

[rad] in proportion to an

absolute value of the relative velocity and predicted

relative distance. If the obstacle comes at rapidly, for

instance, the value of

b

increases. Hence, the base

width grows shown in Figure 4, and the value of

priority for the direction of the obstacle relative to

the robot comes about to be reduced.

η

is a gain.

As mentioned above, by deciding the vertex, the

height and the base width of inverted triangle

considering the predicted relative position, PMF

o

μ

,

which aims to early starting of avoidance behavior

and prompt the direction of the velocity vector to be

far from obstacle direction in response to the fast-

moving obstacle, is generated.

3.1.2 PMF for a Goal

To head to the goal, a PMF

d

μ

shaped like triangle

as shown in Figure 5. As a measure to decide how

much the robot want to head to the goal,

c

is

defined as the height of the triangular PMF.

c

gets

the maximum value at an angle of the goal direction

relative to the front direction of the robot,

d

θ

, and is

described as following equation:

,

,

,

1.0

rd

rd

rd

if

c

if

ε

ε

ε

⎧

≤

⎪

=

⎨

⎪

>

⎩

r

r

r

(12)

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1

θ

[deg]

p[-]

[deg]

θ

c

1.0

μ

d

d

θ

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1

θ

[deg]

p[-]

[deg]

θ

c

1.0

μ

d

d

θ

[deg]

θ

c

1.01.0

μ

d

d

θ

Figure 7: PMF for a goal point.

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1

θ

[deg]

p[-]

()

mix out

μθ

[deg]

θ

out

θ

1.0

μ

mix

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1

θ

[deg]

p[-]

()

mix out

μθ

[deg]

θ

out

θ

1.01.0

μ

mix

Figure 8: Mixed PMF.

where

,rd

r is an absolute value of the position

vector of the goal relative to the robot.

ε

is

constant. If

,rd

r is below

ε

, c is defined. The

shorter the distance between the obstacle and the

robot is, the smaller

c becomes. Therefore the robot

can decelerate and stop stably.

3.2 Calculation of Command Velocity

Vector by Fuzzy Inference

The proposed method employs fuzzy inference to

calculate the current command velocity vector.

Specifically, The PMF

o

μ

, which considers the

velocity of obstacle relative to the robot, and the

PMF

d

μ

, which is to head to the goal, are integrated

by fuzzy operation into a mixed PMF

mix

μ

as shown

in Figure 6.

mix

μ

is an algebraic product of

o

μ

and

d

μ

as following equation:

mix d o

μ

μμ

=

⋅ (13)

Finally, by defuzzifier, the command velocity

vector is calculated as a traveling direction

out

θ

and

an absolute value of the reference speed of the robot

base on the mixed PMF

mix

μ

.

out

θ

is decided as the

direction

i

θ

which makes a following function

()f

θ

maximum.

() ( )

jn

mix i

ijn

f

θ

μθ

+

=−

=

∑

(14)

where

n is the parameter to avoid choosing

undesirable

i

θ

caused by such as noises on the

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

302

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1.0

theta[deg]

u[-]

μ

direction [deg]

Robot PMF

Desired direction

Robot PMF

Desired direction

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1.0

theta[deg]

u[-]

μ

direction [deg]

-180 -120 -60 0 60 120 180

0

0.2

0.4

0.6

0.8

1.0

theta[deg]

u[-]

μ

direction [deg]

Robot PMF

Desired direction

Robot PMF

Desired direction

Figure 9: Visualization of PMF.

sensor data. Based on

out

θ

,

out

v is calculated as

following equation:

()

(

)

out mix out max min min

vvvv

μθ

=−+ (15)

where

()

mix out

μθ

is the mixed PMF

mix

μ

corresponding to the

out

θ

,

max

v and

min

v are

configured in advance respectively as higher and

lower limit of the robot speed.

3.3 Visualization for PMF on

Two-dimension Surface

It would be convenient to have a visualizer that

show us why the robot will go on to the direction. In

the proposed method, we can see aspects of the PMF

on two dimension surface and understand easily the

reason for choice of the direction. For example, a

PMF described on polar coordinate shown in Figure

9(a) is comparable to the PMF described on x-y

coordinate shown in Figure 9(b).

4 SIMULATION RESULTS

The radius of robot and obstacle are supposed to be

both 0.3m, therefore,

,

0.6m

ro

R = .

α

in equation

(8) is 1.6m.

γ

in equation (4) is 0.7.

ε

in equation

(12) is 1.0m.

Figure 10, 11 and 12 show the simulation results

when the robot passes the obstacle. Initial positions

of the robot and the obstacle are respectively

(0m,0m) and (5.0m, 0.3m) . The goal position of

the robot is

(7.0m,0m) . In the situation in Figure 10,

the higher limit of robot speed is

max

0.5m/sv = , the

lower one is

min

0.0m/sv = . The higher limit of

acceleration of the robot is

2

1.0m/s

r

a = . The

simulations have done with three different obstacle

speed

0.0, 0.5m/s

o

v = , that the direction is negative

on

x

-axis. Figure 10(a) and (b) show respectively

the trajectory of the robot that the PMF for obstacle

avoidance is generated without considering the

relative velocity and that with considering the

relative velocity, when

0.0m/s

o

v

=

. In Figure 10(a),

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Robot : 10.8s

Robot : 15.0s

Robot : 0.0s

Robot : 19.0s Robot : 19.5s

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Robot : 10.8s

Robot : 15.0s

Robot : 0.0s

Robot : 19.0s Robot : 19.5s

(a) not using PMF considering relative velocity

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Robot : 3.1s Robot : 12.6s

Robot : 0.0s

Robot : 15.0s Robot :20.6s

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Robot : 3.1s Robot : 12.6s

Robot : 0.0s

Robot : 15.0s Robot :20.6s

(b) using PMF considering relative velocity

Figure 10: Simulation results of an obstacle avoidance

going by each other when speed of obstacle (

o

v )

is

0.0m/s

and of a robot (

r

v ) is

0.5m/s

.

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Robot : 1.9s Robot : 8.5s

Robot : 0.0s

Robot : 10.8s Robot :13.2s

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Robot : 1.9s Robot : 8.5s

Robot : 0.0s

Robot : 10.8s Robot :13.2s

Figure 11: Simulation results of an obstacle avoidance

going by each other when speed of obstacle (

o

v )

is

0.0m/s and of a robot (

r

v ) is 0.8m/s.

the robot gets close to the obstacle because the

relative velocity is not considered. On the other

hand, in Figure 10(b), the early starting of avoidance

behaviour due to generating PMF by use of

predicted information based on the relative velocity.

In addition to the situation as in Figure 10(b), in

Figure 11, the higher limit of the robot speed has

been changed:

max

0.8m/sv

=

. Even if the robot

speed becomes more rapid, the robot succeed in

efficient avoidance. In Figure 12(a) and (b), the

trajectories of the robot, with PMF considering the

relative velocity and not considering that, when the

obstacle speed

0.5m/s

o

v

=

. In (a), due to delay of

starting avoidance behaviour, the robot collided with

the obstacle. On the other hand, in (b), due to the

early starting of the avoidance behaviour, the robot

succeeded at the obstacle avoidance.

From these simulation results, it is confirmed that

by an associating the PMF for avoidance with the

relative velocity, faster the obstacle speed is, earlier

the timing of the avoidance behaviour of the robot is,

therefore the ability of avoiding obstacle can be

enhanced.

OBSTACLE AVOIDANCE FOR AUTONOMOUS MOBILE ROBOTS BASED ON POSITION PREDICTION USING

FUZZY INFERENCE

303

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Obstacle : 0.0s

Obstacle : 4.1sObstacle : 5.3s

Robot : 4.1s Robot : 5.3s

Robot : 0.0s

Robot : 15.0s

Robot : 18.8s

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Obstacle : 0.0s

Obstacle : 4.1sObstacle : 5.3s

Robot : 4.1s Robot : 5.3s

Robot : 0.0s

Robot : 15.0s

Robot : 18.8s

(a) not using PMF considering relative velocity

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Obstacle : 0.0s

Obstacle : 1.8sObstacle : 6.7sRobot : 0.0s

Robot : 1.8s Robot : 6.7s Robot : 15.0s Robot : 20.4s

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

-1.0

0

1.0

x-coordinate [m]

y-coordinate [m]

Obstacle : 0.0s

Obstacle : 1.8sObstacle : 6.7sRobot : 0.0s

Robot : 1.8s Robot : 6.7s Robot : 15.0s Robot : 20.4s

(b) using PMF considering relative velocity

Figure 12: Simulation results of obstacle avoidance going

by each other when speed of an obstacle (

o

v ) is 0.5m/s

and of a robot (

r

v ) is 0.5m/s.

5 EXPERIMENTAL RESULTS

To verify the effectiveness of the proposed method

that employs PMF considering the velocity of the

obstacle of the robot, a ball is supposed to be a

moving obstacle and is rolled toward the robot. The

robot recognizes the environment by the omni-

directional camera. A position of a goal and that of

an obstacle relative to the robot are calculated by

extracting features based on objects’ colours. The

robot size is L 0.4

×

W 0.4

×

H 0.8m and the ball

diameter is 0.2m. The radius of robot and obstacle

are supposed to be 0.3m and 0.1m respectively,

therefore,

,

0.4m

ro

R = .

α

is set to 1.4m when the

robot uses the proposed PMF which is considering

relative velocity. When the robot doesn’t use the

proposed PMF,

α

is set to 2.4m.

γ

is 0.7.

ε

is

1.0m.

max

v is 0.5m/s,

min

v is 0.0m/s.

r

a is

2

1.0m/s .

When the robot used the proposed PMF, which was

considering relative velocity, as shown in Figure 13

(a), it succeeded in avoiding the moving ball with

smooth trajectory. On the other hand, in the situation

Figure 13 (b), the robot with the PMF, which was

not considering relative velocity, diverged once.

(a) (b)

Figure 13: Trajectories of the obstacle (ball) and the robot

with the PMF considering relative velocity (a) and not

considering relative velocity (b).

6 CONCLUSIONS

In this paper, design method of the potential

membership function (PMF), which is considering

the velocity of the obstacle relative to the robot for

the purpose of avoiding the moving obstacle safely

and smoothly, has been presented. In the proposed

method, the proposed PMF for an obstacle and PMF

for a goal are unified by fuzzy inference. By

defuzzification, the command velocity vector of the

robot is calcu lated and the obstacle avoidance has

realized. A numerical simulation, which assumes an

obstacle avoidance of autonomous omni-directional

mobile robot, has done. As the result of the

comparison between the design method of PMF

using relative velocity and not using, it is confirmed

that the ability of avoiding the moving obstacle can

be enhanced. In addition, thorough simplified

experiments, the real robot can avoid an obstacle

using proposed method.

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