ENHANCEMENT OF MANEUVERABILITY OF A POWER ASSIST

OMNI-DIRECTIONAL WHEELCHAIR BY APPLICATION OF

NEURO-FUZZY CONTROL

Kazuhiko Terashima and Juan Urbano

Department of Production Systems Engineering, Toyohashi University of Technology

Hibarigaoka 1-1, Toyohashi, 441-8580, Japan

Hideo Kitagawa

Department of Electronic Control Engineering, Gifu National College of Technology

Kamimakuwa, Motosu, Gifu, 501-0495, Japan

Keywords:

Omni-directional wheelchair, power assistant, neuro-fuzzy systems, operability.

Abstract:

A power assist system has been added to an Omni-directional Wheelchair (OMW) for helping attendants of

handicapped people and elderly people, . With this addition it is possible for the attendants to deal with heavy

loads, but there is a problem of operability when the attendants want to easily move OMW laterally or rotate

around OMW’s Gravity Center (CG). To solve the present problem, this paper provides a fuzzy reasoning

method for estimating the navigation direction according to the force added by the attendants to the handgrips

of the handle of OMW. A neuro-fuzzy system (ANFIS) is used for auto-tuning of the membership functions

of the fuzzy system according to each attendant’s characteristics, by using input data of attendants.

1 INTRODUCTION

In order to satisfy the demand for higher mobility,

designers have created new driving concepts such as

omni-directional movement which allows any com-

bination of forward, sideways, and rotational move-

ment, thus ensuring users much more freedom and

safety in wide or narrow spaces. A variety of wheel-

chairs with different options and special add-on fea-

tures have been developed to meet a wide range of

needs (Wada and Asada, 1999)-(West and Asada,

1992).

In the author’s laboratory, a holonomic Omni-

directional Wheelchair (OMW) which can act as

an autonomous (Kitagawa et al., 2002) or semi-

autonomous (Kitagawa et al., 2001) omni-directional

wheelchair has been developed.Comfort has been a

subject of study in the case with and without the joy-

stick (Kitagawa et al., 2002), (Terashima et al., 2004).

For handicapped people or elderly people that can

use their arms freely, many power assisted wheel-

chairs have been developed such as (Seki et al., 2005),

(FrankMobilitySystems, 2002), for example. How-

ever, it is necessary to consider that some elderly peo-

ple or handicapped people can not use their arms be-

cause they are damaged or they are so weak. These

people needs the help of an attendant. Considering

this background, a power assist system that helps at-

tendants to move a heavy load has been designed

and developed in author’s laboratory (Kitagawa et al.,

2004). Application of power assist for supporting the

attendant of an omni-directional wheelchair is one of

a novel research. To the authors knowledge, no other

report about this topic has appeared yet. However,

there is some research about power system for omni-

directional vehicles, but it is related to carts (Maeda

et al., 2000), not to wheelchairs. Moreover, it still has

some problems in rotation and in occupant’s comfort

since this system was developed for a food tray carry

vehicle in a hospital.

However, there is a problem related to the operabil-

ity of the OMW. Due to the application of the power

assist system, operability of the OMW degrades, es-

pecially when the attendant tries to rotate in clockwise

(CW), or counter-clockwise (CCW) direction around

the center of gravity (CG) of the OMW.

It was impossible to ﬁnd general rules that ex-

plained all cases, but a relationship was found be-

tween lateral and rotational movements. These re-

lationships were used as the base for constructing a

fuzzy reasoning system (MathWorks, 2002)-(Harris

et al., 1993) that helped to improve the operability of

the OMW.

Nevertheless, when the system was tested by dif-

67

Terashima K., Urbano J. and Kitagawa H. (2006).

ENHANCEMENT OF MANEUVERABILITY OF A POWER ASSIST OMNI-DIRECTIONAL WHEELCHAIR BY APPLICATION OF NEURO-FUZZY

CONTROL.

In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics, pages 67-75

DOI: 10.5220/0001213700670075

Copyright

c

SciTePress

Figure 1: Omni-directional wheelchair (OMW).

ferent attendants, it was found that a complete sat-

isfactory result was not obtained by every attendant.

It is because each person has its own tendencies and

the fuzzy inference system must be tuned to respond

to them. Tuning of the fuzzy inference system by

trial and error thus has been tried in (Kitagawa et al.,

2004). However it is a time consuming and needs a

lot of trials of the attendants, then these can become

tired and bored.

Thus, a better tuning method, a method that allows

tuning of the fuzzy inference system, is needed. It

can be obtained by adding Neural Networks (NN) to

the fuzzy inference system, obtaining what is known

as a neuro-fuzzy system. There is a lot of research

in this topic (Jang, 1993)-(Lin and Lee, 1991), being

the basic difference the kind of NN that is used in

combination with the fuzzy inference system.

Jang (Jang, 1993) developed ANFIS: Adaptive-

Network-based Fuzzy Inference Systems, a neuro-

fuzzy system in which the fuzzy inference system is

tuned by using the input data of the system.

Hence, in this paper, a method for improving the

operability of a power assist omni-directional wheel-

chair is presented.

2 OMNI-DIRECTIONAL

WHEELCHAIR

A holonomic omni-directional wheelchair (OMW)

using omni-wheels has been built, as is described in

(Kitagawa et al., 2002)-(Kitagawa et al., 2001). Fig-

ure 1 shows an overview of the OMW.

The OMW is able to move in any arbitrary direc-

tion without changing the direction of the wheels.

In this system, four omni-directional wheels are in-

dividually and simply driven by four motors. Each

wheel has passively driven free rollers at their circum-

ference. The wheel that rolls perpendicularly to the

direction of movement does not stop its movement

because of the passively driven free rollers. These

wheels thus allow movement that is holonomic and

omni-directional.

In semi-autonomous mode, a joystick is used as

the input device. The OMW’s direction of movement

depends on the orientation of the joystick, while the

speed of the OMW is proportional to the inclination

of the joystick in the direction of movement. More-

over, eight ultrasonic sensors and eight PSD sensors

are distributed around the OMW’s base in order to ac-

quire information regarding the environment.

The OMW is also equipped with a handle and a six-

axis force sensor, as shown in Fig. 1, that allows the

OMW’s use in power-assist mode. The force that the

attendant inputs to the grips of the handle is measured

by this force sensor.

3 POWER ASSIST SYSTEM

3.1 Second Order Controller for

Power Assist

When a ﬁrst order controller is used for the transfor-

mation from force to velocity (Kitagawa et al., 2004),

a big jerk (derivative of acceleration) appears if the in-

put force changes suddenly. Jerk is considered as the

factor that dominates the riding comfort. For the rid-

ing comfort’s improvement, jerk must be decreased.

A second order controller

G

i

(s) =

V

i

(s)

F

i

(s)

=

K(ω

n

)

2

i

s

2

+ 2ζ

i

(ω

n

)

i

s + (ω

n

)

2

i

, (1)

is chosen as a power assist controller which can pro-

vide compatibility for both operability and riding

comfort. Here, ζ is the attenuation factor. Even when

the force added by attendant is ﬁxed, if overshoot O

s

occurs, certain amount of time is required for the ve-

locity to achieve convergence and therefore operabil-

ity is deteriorated during this period. Then, in order

to avoid overshoot, ζ

i

(i = x, y, m) is chosen as ζ

x

=

1, ζ

y

= 1, ζ

m

= 1. In addition, T

x

= 0.4, T

y

= 0.4 and

T

m

= 0.4, is used.

On the other hand, in the case of second order con-

troller, ω

n

is determined such that the system is not in-

ﬂuenced by the noise included in the input and good

operability of OMW is also obtained. Then, in this

case, (ω

n

) is chosen, by trial and error, as (ω

n

)

x

= 4,

(ω

n

)

y

= 4, (ω

n

)

m

= 4.

Experimental comparison of the jerk produced in x

direction by a ﬁrst order controller and a second or-

der controller, for the same reference velocity, was

conducted. The experimental parameters were: K

x

=

0.02, T

x

= 0.4, ζ

x

= 1.0, (ω

n

)

x

= 4.0, sampling time

t

s

= 0.03[s]. OMW was moved in automatic mode

with an input help force given as:

f

x

=

(

0 (0 ≤ t < 1, 4 ≤ t < 7, t ≥ 10)

50 (1 ≤ t < 4)

−50 (7 ≤ t < 10)

Jerk was evaluated by differentiating the output of

the encoders of OMW’s motors. Experimental results

are shown in Fig. 2. v

x

is the reference velocity, j

omw

x

ICINCO 2006 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

68

0 2 4 6 8 10 12

1st-order controller

2nd-order controller

-5

0

5

jx [

m/s

]

3

omw

0 2 4 6 8 10 12

-1

0

1

vx [

m/s

]

jerk

velocity

time t [s]

Figure 2: Experimental result of jerk.

-2 -1 0 1 2

point

1st-order controller

2nd-order controller

3-3

swing

feeling

security

comfort

stability

reliability

ride quality

Figure 3: Questionnaire result of x-axis.

Figure 4: Working force.

shows the actual jerk that was calculated by using the

encoders output.

In addition, as riding comfort is something that de-

pends on the subjective judgement of the OMW’s oc-

cupant, riding comfort was evaluated by using Se-

mantic Differential (SD) method. The mean value of

the results obtained in each item of the SD question-

naire are shown in Fig. 3 for x direction. It is possible

to see that the values obtained by the second order

controller are much better than that obtained by the

ﬁrst order controller. Then a second order controller

will be used as power assist controller because it can

improve riding comfort.

3.2 Direction Estimator of

Navigation for Input Force

When the user tries to rotate OMW around its grav-

ity center, OMW begins to slide and the radius of ro-

tation sometimes becomes very big. Then, rotation

around the center is very difﬁcult (Kitagawa et al.,

2004). A survey was conducted among various at-

tendants trying to discover some relationships in the

way they realized forwards-backwards, lateral and ro-

6axis force

sensor

2nd-order

controller

f

R

directional

reasoning

f

L

f

x

f

y

m

v

x

v

y

d

d

v

y

d

Sensor

input

Sensor

output

Transfer

to velocity

Command input by

direction estimator

Figure 5: Block diagram of power assist system.

Table 1: Fuzzy reasoning rules.

Rule Antecedent Consequent

1 v

y

> 0 and ω < 0, v

d

y

> 0 (Right Slide)

2 v

y

< 0 and ω > 0, v

d

y

< 0 (Left Slide)

3 v

y

≈ 0 and ω ≈ 0, v

d

y

≈ 0 (Not Slide)

4 v

y

≥ 0 and ω > 0, ω

d

> 0 (CCW Turn)

5 v

y

≤ 0 and ω < 0, ω

d

< 0 (CW Turn)

6 v

y

≈ 0 and ω ≈ 0, ω

d

≈ 0 (Not Turn)

tational movements. The goal of the survey was to

ﬁnd general rules that related the three mentioned mo-

tions. Even when it was impossible to ﬁnd general

rules that explained all cases, a relationship was found

between lateral and rotational movements. These re-

lationships were used as the base for constructing a

fuzzy reasoning system (MathWorks, 2002)-(Harris

et al., 1993) that helped to improve the operability

of the OMW. These rules, in which just lateral mo-

tion and rotational motion are considered, are shown

in Table 1. The block diagram of the system that con-

siders power assist and fuzzy reasoning is shown in

Fig. 5.

In order to establish the rules of direction inference,

ﬁrst, the force applied to the grips of the force sensor

are changed to the center of OMW, as shown in Fig. 4.

Note that the input of the direction estimator is veloc-

ity V

omw

, not force F . It may seem more reasonable

to use F for the estimation of the attendant’s inten-

tion, however, it is very difﬁcult to derive transform

equations from F , because of an effect of vibration of

input force or noise. v

x

is not included since forward

and backward motion can be realized without direc-

tion estimation. Features of slide motion is expressed

by Rules 1 and 2 in Table 1, and that of rotation by

Rules 4 and 5. Rules 3 and 6 are added not to gener-

ate the reference velocity when input velocity is zero.

The reason of these rules is shown in Table 1. Ta-

ble 1 is described in detail in (Kitagawa et al., 2004),

and hence the explanation is omitted due to the paper

space.

Figure 6 shows the graph of membership functions

of the ﬁrst rule. The membership function of the an-

tecedent of 1, 2, 4 and 5 is

µ

name

= tan

−1

{a

name

(β

i

− b

name

)} /π +0.5, (2)

where β

i

is input (β

1

= v

y

, β

2

= ω) and a

name

and

b

name

are tuning parameters. ‘name’ is replaced

by the name of each membership function. The

ﬁrst letter of ‘name’ of antecedents indicates sensor

output(v

d

y

:Y, ω

d

:O), the second letter indicates sign

ENHANCEMENT OF MANEUVERABILITY OF A POWER ASSIST OMNI-DIRECTIONAL WHEELCHAIR BY

APPLICATION OF NEURO-FUZZY CONTROL

69

Table 2: Parameters of menbership functions.

Rule Number

Antecedent

name a b c

1

YPS 7 0.3 -

ONS 7 -0.3 -

2

YNS 7 -0.3 -

OPS 7 0.3 -

3

YZS - - 1000

OZS - - 1000

4

YPT 7 0.3 -

OPT 7 0.3 -

5

YNT 7 -0.3 -

ONT 7 -0.3 -

6

YZT - - 1000

OZT - - 1000

-1 0 1

0

1

-1 0 1

0

1

0

1

0

1

[rad/s]

Antecedent 1

ConsequentAntecedent 2

Rule 1

YPS

ONS

vy [m/s]

yRS

RS

Figure 6: Membership functions of rule 1.

(Positive:P, Negative:N, Zero:Z), and the third letter

indicates the realized motion (Slide:S, Turn:T).

The membership function of the antecedent of 3

and 6 is

µ

name

= exp(−c

name

· β

2

i

), (3)

where c

name

is a tuning parameter.

3.3 Experimental Results

In order to verify the effectiveness of the control sys-

tem, laboratory experiments were conducted. The re-

sults shown correspond to a ﬁrst order controller. Pa-

rameters of the membership function of Fig. 6 are

shown in Table 2. These parameters are given by trial

and error method. The details are described in the for-

mer paper (Kitagawa et al., 2004).

The trajectory and velocity v

d

omw

of slide motion

to right are shown in Fig. 7 and Fig. 8, respectively.

As seen in the trajectory of v

d

y

, vibration of the ve-

locity was reduced. The trajectory and velocity v

d

omw

of rotation around its center in counter-clockwise are

shown in Fig. 9 and Fig. 10, respectively. As seen

in Fig. 9, the rotation around its center was realized

by using the direction estimator. The effectiveness of

the direction estimator is shown especially in case of

rotation. In this case, the gain of the controller for

the velocity in the direction X, Vx, was reduced to

very small value in order to tes the goodness of the

approach.

0 1 2 3

-1

0

1

y

G

[m]

x

G

[m]

0 2 4 6 8 10

-1

0

1

x

G

[m]

0 2 4 6 8 10

0

1

2

3

y

G

[m]

0 2 4 6 8 10

-10

0

10

q

G

[deg]

Time [s]

No-reasoned

Reasoned

Figure 7: Trajectory of right

slide.

0 2 4 6 8 10

-1

0

1

v

y

d

[m/s]

0 2 4 6 8 10

-1

0

1

w

d

[rad/s]

Time[s]

0 2 4 6 8 10

-1

0

1

v

x

d

[m/s]

No-reasoned

Reasoned

Figure 8: Velocity v

d

omw

of right slide.

0 5 10

-1

0

1

x

G

[m]

0 5 10

-1

0

1

y

G

[m]

0 5 10

0

200

400

q

G

[deg]

Time[s]

-0.5 0 0.5

-0.5

0

0.5

y

G

[m]

x

G

[m]

No-reasoned

Reasoned

Trajectory of the

CG of OMW

Figure 9: Trajectory of rota-

tion (CCW).

0 5 10

-1

0

1

v

y

d

[m/s]

0 5 10

-1.5

0

1.5

w

d

[rad/s]

Time[s]

0 5 10

-1

0

1

v

x

d

[m/s]

No-reasoned

Reasoned

Figure 10: Velocity v

d

omw

of rotation (CCW).

4 TUNING OF FUZZY SYSTEM

Figure 11 shows attendant’s intention representing di-

rection to make OMW move using v

y

and ω added by

attendant. In the present fuzzy parameters given by

the previous section, the attendant such as examinee

1 can operate OMW well. On the other hand, the

attendant such as examinee 2 wants to make OMW

move towards right in the region of v

y

> 0 and ω ≈

0.

Then, when fuzzy membership function is ﬁxed

based on examinee 1 for all examinees, the attendant

with having the tendency like examinee 2 feels the dif-

ﬁculty to operate OMW. Therefore, it is necessary to

adjust the parameters of fuzzy membership functions

according to the driving characteristics of individual

attendants.

The fuzzy system must be tuned to respond to the

particular characteristics of each attendant. As the

tuning by trial and error is a time consuming and cer-

tainly not optimal, the tuning of the fuzzy system by

using a neuro-fuzzy system is proposed in this pa-

per. In the literature there are many neuro-fuzzy sys-

tems. ANFIS(Adaptive-Network-Based Fuzzy Infer-

ence System) (Jang, 1993) was chosen for this re-

search. The details of the implementation of ANFIS

are not presented here. For further information refer

to (Jang, 1993).

According to the rules shown in Table 1, the range

ICINCO 2006 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

70

Table 3: Fuzzy rules for ANFIS.

R Antecedent Consequent

1 If V

N

and ω

N

, y

1

= A

1

× V

N

+ B

1

× ω

N

+ C

1

2 If V

Z

and ω

N

, y

2

= A

2

× V

Z

+ B

2

× ω

N

+ C

2

3 If V

P

and ω

N

, y

3

= A

3

× V

P

+ B

3

× ω

N

+ C

3

4 If V

N

and ω

Z

, y

4

= A

4

× V

N

+ B

4

× ω

Z

+ C

4

5 If V

Z

and ω

Z

, y

5

= A

5

× V

Z

+ B

5

× ω

Z

+ C

5

6 If V

P

and ω

Z

, y

6

= A

6

× V

P

+ B

6

× ω

Z

+ C

6

7 If V

N

and ω

P

, y

7

= A

7

× V

N

+ B

7

× ω

P

+ C

7

8 If V

Z

and ω

P

, y

8

= A

8

× V

Z

+ B

8

× ω

P

+ C

8

9 If V

P

and ω

P

, y

9

= A

9

× V

P

+ B

9

× ω

P

+ C

9

right

slide

ccw

turn

vy

right

slide

ccw

turn

examinee 1

examinee 2

vy

Figure 11: Attendant’s intention.

Figure 12: Partition of the ranges of V

y

and ω.

of V

y

and ω is divided in three Membership Functions

(MF), Negative (V

N

and ω

N

), Zero (V

Z

and ω

Z

) and

Positive (V

P

and ω

P

), as shown in Fig. 12. The func-

tions used for the partitions of the range of V

y

and ω,

shown in Fig. 12, are called the dsigmoidal (Math-

Works, 2002) functions, and are deﬁned as the differ-

ence of two sigmoidal functions. That is, if Eq. (4) is

a sigmoidal function, with parameters a and c,

f(x, a, c) =

1

1 + e

−a(x−c)

(4)

A dsigmoidal function can be deﬁned as

f(x, a

1

, c

1

)−f (x, a

2

, c

2

)=f(x, [a

1

, c

1

, a

2

, c

2

]) (5)

As there are 6 membership functions, and each with

4 parameters, there must be 24 parameters that are

denoted as (a

1

...a

12

), (c

1

...c

12

).

Then, as there are three partitions in each variable,

the total number of rules must be 3 × 3 = 9 rules,

Figure 13: ANFIS system.

which are shown in Table 3. The odd rules correspond

to those shown in Table 1, while the even rules are

used for completeness. In the rules shown in Table 3

the consequents are a function of the inputs because

a Takagi-Sugeno-Kang (TSK) (Takagi and Sugeno,

1985) system is being used, instead of the Mamdani

(Mamdani and Assilian, 1985) system used for the

rules of Table 1. The coefﬁcients of the consequents

are denoted by (A

1

...A

9

), (B

1

...B

9

) and (C

1

...C

9

), as

shown in Table 3. The ANFIS equivalent of this sys-

tem is shown in Fig. 13. ANFIS has 5 layers:

• 1

st

Layer: Here the inputs Vy and ω are subjected

to the action of the membership functions of Fig.

12, that are represented by its parameters (a

1

... a

12

)

and (c

1

... c

12

).

• 2

nd

Layer: In the 2

nd

Layer the fuzzy rules shown

in Table 3 are constracted. As the antencedents are

jointed by a logic ”AND”, this relationship is math-

ematically obtained by the product (Π) of the two

antecedents. The output of each node represents

the ﬁring strength of a rule, that is represented by

ω

i

(i = 1 ... 9).

• 3

rd

Layer: This is a normalization layer, where the

ratio of the i

th

rules’ ﬁring strength to the sum of

all rules ﬁring strength is calculated.

• 4

th

Layer: Here the normalized ﬁring strength that

comes from the 3

rd

Layer is multiplied by the out-

put functions of the fuzzy reasoning system.

• 5

th

Layer: The overall output of the system is com-

puted as the sum of all the incoming signals.

For using ANFIS, the structure of the block labeled

as ”directional reasoning” in Fig. 5 is shown in Fig.

14. It is clear that two fuzzy systems, one for Vy, and

the other for ω are used.

For the off-line training of ANFIS system of the

OMW, the following approach was followed:

ENHANCEMENT OF MANEUVERABILITY OF A POWER ASSIST OMNI-DIRECTIONAL WHEELCHAIR BY

APPLICATION OF NEURO-FUZZY CONTROL

71

Figure 14: Contents of the block directional reasoning.

Figure 15: Input data and results of teaching for the case of

lateral movement((a)-(b): input data, (c): teaching data and

(d): estimated output data).

(i) An attendant is asked to conduct ﬁve kind

of movements composed of: (1) forward and

backward movement, (2) lateral movement, (3)

counter-clockwise (CCW) rotation, (4) clock-

wise (CW) rotation and (5) forwards and back-

wards diagonal movement, for ﬁve times. For

taking this data just power assistance is used.

Three groups of data will be used for the training

of ANFIS and the remaining two for the testing

of the obtained results.

(ii) ANFIS is trained and tested by using a simula-

tion program developed in Matlab. The validity

of this simulator has been tested by comparing

the results obtained from simulation and experi-

ments.

(iii) The obtained parameters are saved in the com-

puter of the OMW and the system is tested by

experiments.

In this paper, the simulation results will correspond

to one attendant called ”Attendant 1”. Fig. 15 shows

the input data (a)-(b), the teaching data (c), and the

estimated output data (d) after the training by ANFIS

for ”Attendant 1” for the case of lateral movement.

In Fig. 16 the same information is shown for the case

of rotational movement. The teaching data was con-

structed following the logic of Table 3. The ANFIS

systems was trained by using the input and teaching

data shown in Fig. 15 and Fig. 16. The total error in

each epoch was calculated as:

J = Σ

N

n=1

E

n

, (6)

Figure 16: Input data and results of teaching for the case of

rotational movement((a)-(b): input data, (c): teaching data

and (d): estimated output data).

Figure 17: Results of training of Vy system.

where,

E

n

= (y

i

(n) − y

d

i

(n))

2

, (7)

with n being the n

th

data and N the total number of

data used for the training. Tuning is performed by

minimizing the output error of the NN used in combi-

nation with the fuzzy inference system. For achieving

this goal, the NN is trained by using a hybrid method

that combines least squares and the Backpropagation

algorithm (BP law). This method is thus thought to be

an effective method for tuning the parameters of the

OMW’s fuzzy inference system. In the case shown in

Fig. 15 and Fig. 16, N = 8530. According to the re-

sults obtained from different trials, it has been found

that, in order not to lose the generality, the miminum

total error allowed should be around 0.05 for both sys-

tems. The time needed for the training of the ANFIS

system is around 1 [min], and the convergence to the

desired values of error is reached after 20 epochs. The

results of the training are shown in Fig. 17 and Fig.

18. It is possible to note that the shape of the member-

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72

Figure 18: Results of training of ω system.

ship functions almost does not change for any of the

systems, Vy or ω. However, the change in the output

function is easily seen. By the change in the output

functions the system adjust to the input data of the

attendant.

Results for one case of testing data, that the training

of ANFIS did not include, are shown in Fig. 19. The

trajectory of the OMW when ”Attendant 1” rotates

the OMW in CCW direction and moves the OMW in

lateral direction by using just power assist, are shown

in Fig. 19 (a) and Fig. 19 (b). It is possible to see that

CCW rotation is inﬂuenced by the lateral velocity and

the velocity in direction X. The lateral movement is

almost a perfect horizontal line. Fig. 19 (c) and Fig.

19 (d) show the result for CCW rotation and lateral

movement after ANFIS was applied. As lateral move-

ment is almost the same as desired, from now the dis-

cussion will be centered in the rotational movement in

CCW direction. As expected from the results shown

in Fig. 16 the rotational movement in CCW direction

has been improved by reduction of the lateral velocity.

However, as in this case the gain of the controller for

Vx has not been reduced as it happened in the cases

shown in Fig. 7 - Fig. 10, there is some displacement

in direction X. Just reducing the gain of the controller

in the direction X, as before, could be a good solution.

However, it will inﬂuence the movement of the OMW

when the attendant wants to easily move forwards or

backwards. Then, some relationship must be estab-

lished between the different movements studied here:

rotation, lateral and forwards and backwards, that al-

lows to reduce the velocity in direction X, Vx, when

rotating and let it pass almost untouched when mov-

ing forwards or backwards. The inﬂuence of Vx in the

lateral movement is almost irrelevant, and for that rea-

son is not considered any action in the case of lateral

movement.

After the reasoning system has been trained with

Figure 19: Trajectory of the OMW in CCW rotation and lat-

eral movement. (a) and (b) show the cases in which power

assist only is used, and (c) and (d) the result by ANFIS.

Figure 20: Vx, Vy and ω for a case of forwards and back-

wards movement of the OMW, by”Attendant 1”.

ANFIS, in the case when the movement of the OMW

is not a rotational movement, ω is reduced according

to the training described in previous paragraphs. It

happens in the case of lateral movement and in the

case of forwards and backwards movement too. By

studying the value of ω when ”Attendant 1” moves

the OMW forwards and backwards, it has been found

that it is always less than 0.3 [rad/s]. Fig. 20 shows

one case of forwards and backwards movement. Es-

tablishing a rule in which for all the cases in which

ω is less than 0.3 [rad/s] was considered in principle.

However it will ignore cases like the one shown in

Fig. 21.

In Fig. 21 it is possible to see that for a rotational

movement the value of ω is greater than 0.2 [rad/s]

and it happens in all the cases studied for ”Attendant

1”. Then a rule is established such as Vx must be mul-

tiplied by a Reducing Multiplicative Factor (RMF) if

the value of ω is greater than 0.2 [rad/s]. The value

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Figure 21: Vx, Vy and ω for a case of rotational movement

of the OMW, by ”Attendant 1”.

Figure 22: Trajectory of the OMW in CCW rotation when

the Reduction Multiplicative Factor (RMF) is (a) RMF = 0,

(b) RMF = 0.1, (c) RMF = 0.2 and (d) RMF = 0.3.

of RMF is decided by trial and error, by trying mul-

tiples of 0.1. Fig. 22 shows the cases in which RMF

= 0, 0.1, 0.2, 0.3. As it is seen there, a value greater

than 0.2 is not so good. Then it is decided that the

range of variation of RMF must be [0 ∼ 0.2], and the

mean value, 0.1, is chosen for this research. Results

the reduction of Vx are shown in Fig. 23 for CCW ro-

tation, lateral movement and forwards and backwards

movement, when RMF = 0.1. It is possible to see that

operability has been improved by the application of

the fuzzy reasoning system tuned by ANFIS. In this

paper, the threshold of ω is 0.2 [rad/s] and RMF = 0.1.

But these values may change by attendant. Therefore,

it is a future problem to generalize how to determine

these values such as RMF and threshold.

5 CONCLUSIONS

A power assist system for omni-directional wheel-

chairs considering both attendant’s manipulability

Figure 23: Improvement of the trajectory of the OMW in

CCW rotation when Vx is multiplied by a factor 0.1.

and rider’s comfort has been developed. The refer-

ence velocity of the omni-directional wheelchair was

derived from attendant’s input force. Operability of

rotation was improved greatly by using the fuzzy di-

rection estimator. The membership functions of the

fuzzy systems are tuned using attendant’s input data

by applying a neuro-fuzzy system (ANFIS).

ACKNOWLEDGEMENTS

This work was partially supported by The 21

st

Cen-

tury COE (Center of Excellence) Program ”Intelligent

Human Sensing”

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