Hybrid Controller Design for Power Assisted Wheel-chair
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Hybrid Controller Design for Power Assisted Wheel-chair
SEMINAR REPORT

Submitted by
SHERINE JESNA V.A.
First Semester
M.Tech, Control System , Roll no - 10 CS 09

DEPARTMENT OF ELECTRICAL ENGINEERING
COLLEGE OF ENGINEERING
TRIVANDRUM
2010

ABSTRACT
Welfare robotics means to provide technical assistance at initial stages of recovery
from disabilities .The concept of power assistance for manual wheelchair is relatively
new and represents a viable alternative for individuals who are unable to generate suf-
ficient propulsion force to use a manual wheelchair, but do not wish to use a traditional
powered mobility device. The power assisted wheel chair have wide spread acceptance.
But the conventional power-assist controllers only focus on the amplification of the hu-
man input force using torque sensor and assist leaving much to be improved. The design
of a hybrid controller for power assisted wheelchair with human co-operative control
is being discussed here.
This controller does not use a torque sensor but an electromyogram sensor to es-
timate the driver’s intention. The design also use a disturbance observer to compensate
for the lack of propelling torque information since it is difficult to simply regard the
myoelectric signals as propelling torque. Then the hybrid controller analyses both data
and produces the assist torque. The early detection of human will for a positive motion
is the main advantage of the system . Smooth control and ride , less burden for driver
as well as caregiver , feel of safety are the other added advantages . The proposed
controller can be considered as an excellent tool in self rehabilitation.


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TABLE OF CONTENTS
INTRODUCTION
1 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Conventional Power Assisted Wheel-chair . . . . . . . . . . . . . . 2
1.3 Experimental Results of Conventional Method . . . . . . . . . . . . 3
OBJECTIVE
2 4
DESIGN OF THE HYBRID CONTROLLER
3 5
3.1 Sensing and Processing of EMG signal . . . . . . . . . . . . . . . . 5
3.1.1 EMG Signal . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1.2 EMG Sensor . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1.3 Signal processing of EMG signals . . . . . . . . . . . . . . 7
3.2 FSPAC- Force Sensorless Power Assistance Controller . . . . . . . 9
3.2.1 Functions of each block . . . . . . . . . . . . . . . . . . . 9
3.2.2 Analysis of Generalised FSPAC . . . . . . . . . . . . . . . 10
3.2.3 Functions of Two Force Observers . . . . . . . . . . . . . . 10
3.2.4 Decision of Parameters . . . . . . . . . . . . . . . . . . . . 11
3.3 Design of Acceleration Controller . . . . . . . . . . . . . . . . . . 12
3.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.5 Direction Discrimination Function . . . . . . . . . . . . . . . . . . 14
3.6 Final Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
i
3.6.1 Design and Block Diagram . . . . . . . . . . . . . . . . . . 15
3.6.2 Experimental Results of Proposed Power Assistance . . . . 16
ADVANTAGES OF HYBRID CONTROLLER
4 17
CONCLUSION
5 18
ii
LIST OF FIGURES
1.1 Yamaha JW 2 Wheelchair . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Conventional Power Assist Wheelchair . . . . . . . . . . . . . . . . 2
1.3 Power assist result of the Conventional Method . . . . . . . . . . . 3
2.1 Outline Of Proposed Control Method . . . . . . . . . . . . . . . . . 4
3.1 Dry surface Electrode . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Measurement Set up of EMG signal . . . . . . . . . . . . . . . . . 7
3.3 Amplified EMG signals from pollicis muscle and the wheel-velocity 7
3.4 Flow diagram of EMG signal processing . . . . . . . . . . . . . . . 8
3.5 Comparison between filtered EMG and input torque via the torque sen-
sor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.6 Generalized structure of Force Sensorless Power Assist Control . . . 9
3.7 Feedback Controller in Velocity Control Type . . . . . . . . . . . . 10
3.8 Analysis of FSPAC Structure . . . . . . . . . . . . . . . . . . . . . 10
3.9 The Functions of Two Observers . . . . . . . . . . . . . . . . . . . 11
3.10 Block diagram of the acceleration controller with controller highlighted 12
3.11 The output of disturbance observer and the input torque . . . . . . 13
3.12 Power-assistance of the proposed method (forward) and input torque 13
3.13 A joint and two muscles . . . . . . . . . . . . . . . . . . . . . . . 14
3.14 Internal structure of a hybrid controller block with direction discrimi-
nation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
iii
3.15 Block diagram of the proposed power-assist method . . . . . . . . . 15
3.16 Power-assist result of the proposed power-assist method (in two direc-
tions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
iv
CHAPTER 1
INTRODUCTION

1.1 Overview
According to demographic forecasts by WHO, the ratio of elderly people at
least 65 years old is expected to top 40 percent in 2050. Therefore, there are needs for
technical assistance for elderly people from the aspect of welfare engineering based on
the coming aging society with fewer children. The term welfare robotics is coined to
develop technical assistance to support the independent lives of disabled and elderly
people. The welfare robotics provide technical assistance at initial stages of recovery
from disabilities .The concept of power assistance , in welfare robotics , represents a
viable alternative for individuals who do not wish to use a traditional powered mobility
device . For them technology is an assistance in self rehabilitation.
Figure 1.1: Yamaha JW 2 Wheelchair
There are many researches and applications which uses power assistance system ,
for example, power steering in vehicles. Besides conventional applications , more daily
life applications such as power assisted wheelchairs and wearable electro-mechanical
suits are highlighted recently as new applications of power assistance system. We focus
on power-assisted wheelchairs (shown in fig.1.1), which are self-propelled wheelchairs
with an electrical motor. The power assisted wheelchairs have wide spread acceptance
due to the following reasons. First, they reduce fatigue when going long distances. Sec-
ond, they aid in maintaining the present abilities of the operators as well as rehabilita-
tion. In other words, power-assisted wheelchairs have advantages of both self-propelled
wheelchairs and electric powered wheelchairs.
Since the operational environment makes the control difficult and unique to the
power assisted wheelchairs , the design methodology of the control part needs to be
investigated .The conventional power-assisted wheelchairs on the market only amplify
the power through the handrims and assist, leaving much to be improved.
1.2 Conventional Power Assisted Wheel-chair
The block diagram of a conventional power assisted wheelchair is given below
fig 1.2. The widely implemented control method simply amplifies the manual inputs
from the push rims with first order delay .
Figure 1.2: Conventional Power Assist Wheelchair
The wheelchair dynamics can be simplified as ( eqn (1))
1
Tassist = α Thuman (1.1)
1 + τs
where α is the power-assist-ratio, Thuman is the input torque from the push han-
drim, Tassist is the amplified torque from the push handrim, and τ is the time constant of
the first-order delay. τ should be a suitable value to realize an inertia for the wheelchair.
Therefore, τ should be a small value when the differential value of the input torque
is positive (which means the wheelchair is accelerated) and τ should be a large value
when the differential value of the input torque is negative (which means the wheelchair
2
is decelerated), as shown by the following relations:

̇
 τ
f ast Thuman > 0
τ= (1.2)
̇
 τ
slow Thuman < 0
For example, our experiments adopt the following values, respectively:
τf ast = 0.08[s] τslow = 1[s] (1.3)
1.3 Experimental Results of Conventional Method
The real time experiment is carried out with a Yamaha JW - 2 and Art Linux PC,
with a torque sensor, a gyrosensor and two rotary encorders . The behaviour of the
controller is shown in fig 1.3
Figure 1.3: Power assist result of the Conventional Method
Analysing the results shows that there are two possible problems to be improved
in the acceleration phase. First, the rising time of the wheel speed is long. Second,
the acceleration is too sudden. These problems tend to cause driver discomfort and
dangerous feeling. The need of implementation of a human co-operative control method
is now revealed.
3
CHAPTER 2
OBJECTIVE

The problems of delay in response of the system and jerky acceleration could be
solved with a haptic compliance. A hybrid controller is proposed to serve the pur-
pose. The proposed wheelchair do not use any torque sensor or joystick ; rather, an
electromyogram (EMG) sensor is used for input interface, considering developing co-
operative control between human and machine. Also a disturbance observer is used to
compensate for the lack of propelling torque information since it is difficult to simply
regard the myoelectric signals as propelling torque. Then, the assist torque is decided
by combining the filtered myoelectric signals and the estimated human torque signal
calculated by the disturbance observer.
EMG records action potential of the muscle fibres, which causes contraction of
the muscles. Ideally, the magnitude of an EMG sensor attached to a muscle should be
proportional to the force exerted by the muscle. However, it is not so; the magnitude
of the EMG sensor output differs depending on people, and even for the same person,
the magnitude becomes different depending on the fatigue of muscle and the conditions
of the skin the EMG sensor is located on. Thus, it is difficult to simply consider that
input torque and myoelectric signal are proportional. For this reason, the disturbance
observer is introduced to detect the exerted human force and to determine how much
torque should be provided by motors to assist the user. Moreover, both the EMG signal
and the estimated force are combined to provide more safe and comfortable assistance.
Figure 2.1: Outline Of Proposed Control Method
CHAPTER 3
DESIGN OF THE HYBRID CONTROLLER

Now let us discuss the step-by-step design of the hybrid controller. The discussion
involves ;
1. The sensing and processing of the EMG signal ;
2. The concept and development of Force Sensorless Power Assist Control (FS-
PAC);
3. The direction detection algorithm;
4. The final design.
The working of the new controller consist of two phases namely ; i) Grasping
phase and ii) Propelling phase . At the grasping phase, the filtered EMG signals
are regarded as the intensity of the driver’s intention of forward movement, and at the
propelling phase, the propelling torque is estimated based on the disturbance observer.
3.1 Sensing and Processing of EMG signal
3.1.1 EMG Signal
EMG records action potential of the muscle fiber, which causes contraction of the
muscles. EMG is established as an evaluation tool for applied medical rehabilitation .
The advantages of introducing an electromyography signal for the power-assist control
of the wheelchair are as follows:
1. able to assist people who do not have enough power to propel handrims;
2. able to detect how much power is applied;
3. able to estimate the driver’s motion.
First, by using an EMG sensor, the power assistance and the effective rehabilitation is
expected: Elderly people with little grip force or having difficulty in propelling han-
drims because of a disorder of the hands can drive a wheelchair by themselves.
Second, a myoelectric signal enables measurement of how much power is applied by
the operator.
Third, a myoelectric signal measures a signal that occurs when the brain orders the
muscle to propel the wheelchairs before the wheels rotate.
3.1.2 EMG Sensor
A dry surface electrode shown in fig 3.1 is used as it is non-invasive and easy to
apply.
Figure 3.1: Dry surface Electrode
The measurement set up is given fig 3.2. The measurement is carried out by
applying 2.5 V to a reference electrode and having a surface electrode attached to the
adductor pollicis muscle. EMG measured by the surface electrode on the skin is called
surface electromyogram (sEMG). It is suitable for measuring entire muscle activation
because it is a temporal and spatial summation of the action potential of the muscle
fiber under the surface electrode. The sMEG is 1200 times amplified by the differential
amplifier as the raw EMG signals are between a few microvolt and 2-3 millivolt. The
sampling rate is 1 kHz through a 12-bit A/D converter.
The raw signals of EMG and encoder signals when a driver propels the handrims
twice are shown in fig.3.3. The high frequency EMG signals are detected before the
driver propels the handrims. This is an advantage of the EMG sensor; human’s will can
be detected very quickly.
GRASPING PHASE OF POWER ASSISTANCE
The grasping phase is defined as the range of about 0.5 s before and after pro-
6
Figure 3.2: Measurement Set up of EMG signal
Figure 3.3: Amplified EMG signals from pollicis muscle and the wheel-velocity
pelling the handrims. Also the propelling phase is defined as the range during which
the driver propels the handrims and wheel velocity is increasing.
3.1.3 Signal processing of EMG signals
To extract the grasping phase from EMG signals, it is necessary to apply signal
processing to the EMG signals of the adductor pollicis muscle. the sEMG signals are
digitally high-pass filtered as in the following equation:
1
(EM Ghpf [k − 1] + sEM G[k] − sEM G[k − 1])
EM Ghpf [k] = (3.1)
1 + ωT
7
Figure 3.4: Flow diagram of EMG signal processing
where ω is the cutoff frequency of 100 rad/sec, T is the sampling time of 1 ms,
and EM Ghpf [k] is the high-pass filtered EMG signal.
Next, the signals are full-wave rectified. Then, the signals are smoothed by taking
a moving average per 50 points as in the following equation:
49
1
EM Ghpf [k − 1])
EM Gf iltered [k] = ( (3.2)
50 i=0
The processing is effective in reducing the impulsive noise that is generated by
the disconnection between the human skin and the EMG sensor. Finally, subthreshold
signals are cut to zero so that the steady noise is eliminated. The flow diagram of
signal processing of EMG signals is shown in fig 3.4 The filtered EMG signal of the
adductor pollicis muscle is shown in fig 3.5. Compared with input torque signals from
the torque sensor, there is a large rise in the filtered EMG signal before the rise of the
measured input torque, which means the suggested filtering captures the grasping phase
successfully.
Figure 3.5: Comparison between filtered EMG and input torque via the torque sensor
8
3.2 FSPAC- Force Sensorless Power Assistance Controller
At the propelling phase, the main assisting torque is determined by the estimated
human torque. Therefore, the assist torque calculated by using a disturbance is used
at the propelling phase. The disturbance observer used is a linear disturbance observer
. Let us review the FSPAC. The generalised structure of FSPAC ; two disturbance
observers, model impedance, and feedback gain; is given below in fig 3.6.
Figure 3.6: Generalized structure of Force Sensorless Power Assist Control
3.2.1 Functions of each block
Inner disturbance observer is the conventional disturbance observer which aims
to reject all the external force. The outer disturbance observer which is usually called
a reaction force observer or force observer is for the estimation of the force to assist. The
linear disturbance observer utilizes the known model dynamics and the system output
and input . It calculates the external force to the system based on them. The accuracy
of modelling determine the quality of estimated force. To be free from modelling error
neural network learning or sliding mode approach is adopted to estimate the force.
The modelling impedance decides the extent of power assistance. If the impedance
in the model is smaller than that of the original plant; which means, Jm < J , Bm < B
then the model impedance achieves power assistance.
In the power assist control, the output behaviours such as position or velocity of
9
the target plant are more important states to be controlled. The feedback controller
which produces the control input proportional to the error determines the tracking char-
acteristics. The velocity feedback controller shown in fig 3.7 consist of conventional
PID controller . The higher the gain is , the better the tracking performance will be.
Figure 3.7: Feedback Controller in Velocity Control Type
3.2.2 Analysis of Generalised FSPAC
For simple and general description, the control blocks in is characterized like fig
3.8. Q filters in two disturbance observers are illustrated as Qi and Qo , the inverse
−1
dynamics model is described as Pn , the model impedance is described as PM , P is
the real plant, and the feedback controller is described as A. This notation is used in the
following analysis.
Figure 3.8: Analysis of FSPAC Structure
3.2.3 Functions of Two Force Observers
There are three signal paths as in fig 3.9 : (1) is the original path which affects
the output through the plant itself, (2) is through the inner disturbance observer, and (3)
10
is through the outer power assist control loop .
P (1 − Qi + Qo APM )
TF = (3.3)
−1 −1
1 + Qi (P Pn − 1) + A(P + Qo PM (1 − P Pn ))
Three terms in the numerator represent three paths described above. The first term P
corresponds to the first path (1) in fig 3.9, the second term −P Qi to the path (2) and the
last term P Q0 APM to the path (3). The inner disturbance observer can improve model
matching performance of the FSPAC. The second term −P Qi can eliminate the effect
of the first term P, if Qi = 1. This is conventional usage of the disturbance observer;
this elimination of the effect of the path (1) can help the controlled plant to follow the
model impedance PM . Besides this model matching characteristics, two observers
Figure 3.9: The Functions of Two Observers
can distinguish the disturbances to be assisted and to be rejected by setting different
processing between the two observers.
3.2.4 Decision of Parameters
With high gain A on the condition of Qi ∼ 1 and under the assumption Pn ∼ P ,
−1
= =
the transfer function becomes :
P (Qo PM )
TF = (3.4)
−1
P + Qo PM (1 − P Pn )
This illustrates that Qo determines the frequency bandwidth where the model impedance
is realized. In the frequency band where Qo ∼ 1, the transfer function from the external
=
force to the system output will be PM , and in the frequency band where Qo ∼ 0, the
=
impedance will be zero and the force will not be assisted.
11
The idea how to design Qi and Qo are made clear; Qi determines to what fre-
quency the undesirable external force should be rejected and model matching charac-
teristics should be kept. Qo determines the frequency bandwidth where the assistance
is effective. Usually, these two time constants are set as same value.
3.3 Design of Acceleration Controller
At the grasping phase,the filtered EMG signals are regarded as the intensity of
the driver’s intention of forward movement, and at the propelling phase, the propelling
torque is estimated based on the disturbance observer. Then, both the filtered EMG sig-
nals and estimated torque signals are combined using a weighting function of velocity.
The illustration of the whole algorithm is shown in fig. 3.10. K1 and K2 are constant
values and F1 and F2 are variables that indicate the effect extent of power assistance.
These values change according to the wheel velocity. At the grasping phase, when the
wheel velocity is under vα , set F1 to a large value and set F2 to a small value so that
power assistance is based on the filtered EMG signals. On the other hand, at the pro-
pelling phase, when the wheel velocity is over vβ , set F1 to a small value and set F2 to
a large value so that power assistance is decided based on the estimated torque signals.
At the transition phase from grasping to propelling, F1 decreases and F2 increases in
proportion to acceleration to realize smooth acceleration. At the coasting phase, the
1
conventional method is adopted. ie ; Tassist = α 1+τ s Thuman from eqn 1.1
Figure 3.10: Block diagram of the acceleration controller with controller highlighted
vα and vβ are used as parameters, which indicate the effect between filtered EMG
signals and estimated torque signals. For example, vα is set to a large value when the
driver is a severely disabled person who has a weak grip. When the proposed method is
12
used for rehabilitation, vβ is gradually reduced according to the degree of recovery. In
this way, it can realize acceleration according to the driver’s taste by changing vα and
vβ .
3.4 Experimental Results
Experiments where the human subject propels handrims two times using the pro-
posed acceleration method are performed. The results are shown in fig(3.11) and fig
3.12. Comparing fig 3.12 with fig 1.3 shows that the assist torque of the proposed
method is generated earlier than that of the conventional method.
Figure 3.11: The output of disturbance observer and the input torque
Figure 3.12: Power-assistance of the proposed method (forward) and input torque
The fig 3.11 shows that the wheel velocity accelerates smoothly before the driver
propels the handrims so that the driver can propel with less power. When the wheelchair
runs at the dirt road or lawn, it may need strong power for the driver to propel the
wheelchair. The proposed method has a beneficial effect on these situations.
13
3.5 Direction Discrimination Function
So as to ensure power assist in both forward and backward direction a new
direction-detection algorithm is developed.
A model of a joint and two muscles : There is generated only tension in a muscle.
The angle of a joint is controlled by two types of muscles that are located on opposite
sides of the joint and move in a complementary manner. One type is called an extensor
muscle and tightens the joint, while the other is called a flexor muscle and flexes the
joint. Stretching or bending movements are performed by the combined action of these
two types of muscles.
Figure 3.13: A joint and two muscles
At forward movement, a driver flexes his arms and then extends his arms. On
the other hand, the driver extends his arms and then flexes his arms at backward move-
ment. In consideration of the aspect of this driver’s movement, focus is on the flexor
muscle and the extensor muscle of the upper arm to determine the direction.A surface
electrode is attatched to the triceps brachii muscle and the biceps brachii muscle. Then,
a direction-discrimination function is added to the acceleration controller given in fig
3.10.
In fig 3.14, the direction is controlled by the sign of the torque, which is decided
by the direction discrimination function. .
The direction-discrimination function makes positive torque by a positive gain when
filtered EMG signals of the biceps brachii muscle is stronger than those of the triceps
brachii muscle at the beginning time of the grasping phase. On the other hand, when the
filtered EMG signals of the triceps brachii muscle is stronger than those of the biceps
brachii muscle at the beginning time of the grasping phase, the direction discrimination
14
Figure 3.14: Internal structure of a hybrid controller block with direction discrimination
function
function makes the assist-torque negative.
3.6 Final Design
3.6.1 Design and Block Diagram
The integrated block diagram of the proposed power-assist method is shown in
fig 3.15.
Figure 3.15: Block diagram of the proposed power-assist method
The input torque is added to the handrim by the command of the driver through
the upper skeletal muscle. The disturbance observer estimates this input torque as the
estimated torque signals and carries these signals to the hybrid controller as the feedback
signal. At the same time, the dEMG filter estimates filtered EMG signals as the intensity
of driver’s intention of propelling movement and carries these signals to the hybrid
controller as the feedforward signal. In addition, the direction-discrimination function
estimates whether the driver wants to propel forward or backward. Then, the hybrid
15
controller combines feedforward and feedback signals and decides the assist torque.
3.6.2 Experimental Results of Proposed Power Assistance
Experiments where the human subject propels handrims forward and backward,
respectively, using the proposed power assist method are performed. The results are
shown in fig 3.16.
Figure 3.16: Power-assist result of the proposed power-assist method (in two directions)
Figure shows that the proposed power-assist method can assist the wheelchair
smoothly in both forward and backward direction. Here, we set K1 and K2 smaller
at the backward movement than at the forward movement since too much assist in the
backward direction cause dangerous situations such as rollover of the driver.
16
CHAPTER 4
ADVANTAGES OF HYBRID CONTROLLER

The advantages of surface myoelectric based power assisted wheelchair over the
conventional controller based wheelchair are listed below:
1. A human friendly wheelchair system is developed.
2. Using of EMG signals helps in
(a) Assisting people who do not have enough power to propel handrims.
(b) Able to detect how much power is applied.
© Able to estimate the driver’s motion.
3. Early detection of human will is possible and can have early switching on of
assistance , preventing jerky acceleration.
4. Lightens the burden of driver as well as caregiver.
5. Avoiding torque sensors will reduce sensor noise in the system.
CHAPTER 5
CONCLUSION

The new controller for the power-assisted wheelchair combines filtered EMG sig-
nal and estimated torque signals calculated by the disturbance observer. At the grasping
phase, the assistance of the wheelchair is by using the filtered EMG signal so that the
wheelchair can move before the driver propels the handrims. The power-assisted di-
rection is decided depending on the relative strength of filtered EMG signals between
the extensor muscle and the flexor muscle. This lightens the driver’s burden when he
starts to propel the handrims. At the propelling phase, the assistance of the wheelchair
is by using the estimated torque signals so that a caregiver’s pushing force can be also
amplified. This, on the other hand, lightens the caregiver’s burden.
From the viewpoint of the welfare application, smooth control and ride quality
are important. More detailed discussion on the analysis of the control system is re-
quired limiting the modelling errors , trade off between performance assistance and
weak robustness etc .
REFERENCES
[1] S. Oh, N. Hata, and Y. Hori, “New Control Method For Power Assisted Wheelchair
Based on the Surface Myoelectric Signal, ”IEEE Tranactions on Industrial Elec-
tronics, vol. 57, no. 1, pp. 3191-3196, Sep. 2010.
[2] S. Oh and Y. Hori, “discussion on design of force-sensor-less Power Assist Con-
trol,”in Proceedings IEEE International Workshop on Advanced Motion Control,
pp. 492-497,2008.
[3] J. Miyata, Y. Kaida, and T. Murakami,“υ − φ-coordinate-based power assist control
of electric wheelchair for a caregiver”, IEEE Transactions on Industrial Electronics,
vol. 55, no. 6, pp. 2517-2524, Jun. 2008.
[4] 4. S. Oh, N. Hata, and Y. Hori,“Integrated motion control of a wheelchair in the
longitudinal, lateral and pitch directions,”,IEEE Transactions on Industrial Elec-
tronics, vol. 55, no. 4, pp. 1855-1862, Apr. 2008.
[5] S. Katsura and K. Ohnishi,“Human cooperative wheelchair for haptic interaction
based on dual compliance control,”IEEE Transactions on Industrial Electronics,
vol. 51, no. 1, pp. 221-228, Feb. 2004.


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