17 i5 ijaet0511556 intelligent inverse kinematic copyright ijaet

International Journal of Advances in Engineering & Technology, Nov 2011.

©IJAET ISSN: 2231-1963

158 Vol. 1, Issue 5, pp. 158-169

INTELLIGENT INVERSE KINEMATIC CONTROL OF

SCORBOT-ER V PLUS ROBOT MANIPULATOR

Himanshu Chaudhary and Rajendra Prasad

Department of Electrical Engineering, IIT Roorkee, India

ABSTRACT

In this paper, an Adaptive Neuro-Fuzzy Inference System (ANFIS) method based on the Artificial Neural

Network (ANN) is applied to design an Inverse Kinematic based controller forthe inverse kinematical control of

SCORBOT-ER V Plus. The proposed ANFIS controller combines the advantages of a fuzzy controller as well as

the quick response and adaptability nature of an Artificial Neural Network (ANN). The ANFIS structures were

trained using the generated database by the fuzzy controller of the SCORBOT-ER V Plus.The performance of

the proposed system has been compared with the experimental setup prepared with SCORBOT-ER V Plus robot

manipulator. Computer Simulation is conducted to demonstrate accuracyof the proposed controller to generate

an appropriate joint angle for reaching desired Cartesian state, without any error. The entire system has been

modeled using MATLAB 2011.

KEYWORDS: DOF, BPN, ANFIS, ANN, RBF, BP

I. INTRODUCTION

Inverse kinematic solution plays an important role in modelling of robotic arm. As DOF (Degree of Freedom) of

robot is increased it becomes a difficult task to find the solution through inverse kinematics.Three traditional

method used for calculating inverse kinematics of any robot manipulator are:geometric[1][2] ,

algebraic[3][4][5] and iterative [6] methods. While algebraic methods cannot guarantee closed form

solutions. Geometric methods must have closed form solutions for the first three joints of the

manipulator geometrically. The iterative methods converge only to a single solution and this solution

depends on the starting point.

The architecture and learning procedure underlying ANFIS, which is a fuzzy inference system

implemented in the framework of adaptive networks was presented in [7]. By using a hybrid learning

procedure, the proposed ANFIS was ableto construct an input-output mapping based on both human

knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs.

Neuro-Genetic approach for the inverse kinematics problem solution of robotic manipulators was

proposed in [8]. A multilayer feed-forward networks was applied to inverse kinematic problem of a 3-

degrees-of freedom (DOF) spatial manipulator robot in [9]to get algorithmic solution.

To solve the inverse kinematics problem for three different cases of a 3-degrees-of freedom (DOF)

manipulator in 3D space,a solution was proposed in [10]usingfeed-forward neural networks.This

introduces the fault-tolerant and high-speed advantages of neural networks to the inverse kinematics

problem.

A three-layer partially recurrent neural network was proposed by [11]for trajectory planning and to

solve the inverse kinematics as well as the inverse dynamics problems in a single processing stage for

the PUMA 560 manipulator.

Hierarchical control technique was proposed in[12]for controlling a robotic manipulator.It was based

on the establishment of a non-linear mapping between Cartesian and joint coordinates using fuzzy

logic in order to direct each individual joint. Commercial Microbot with three degrees of freedom was

utilized to evaluate this methodology.

Structured neural networks based solution was suggested in[13] that could be trained quickly. The

proposed method yields multiple and precise solutions and it was suitable for real-time applications.



159 Vol. 1, Issue 5, pp. 158-169

To overcome the discontinuity of the inverse kinematics function,a novel modular neural network

system that consists of a number of expert neural networks was proposed in[14].

Neural network based inverse kinematics solution of a robotic manipulator was suggested in[15]. In

this study, three-joint robotic manipulator simulation software was developed and then a designed

neural network was used to solve the inverse kinematics problem.

An Artificial Neural Network (ANN) using backpropagation algorithm was applied in [16]to solve

inverse kinematics problems of industrial robot manipulator.

The inverse kinematic solution of the MOTOMAN manipulator using Artificial Neural Network was

implemented in [17]. The radial basis function (RBF) networks was used to show the nonlinear

mapping between the joint space and the operation space of the robot manipulator which in turns

illustrated the better computation precision and faster convergence than back propagation (BP)

networks.

Bees Algorithm was used to train multi-layer perceptron neural networks in [18]to model the inverse

kinematics of an articulated robot manipulator arm.

This paper is organized into four sections. In the next section, the kinematicsanalysis (Forward as well

as inverse kinematics) of SCORBOT-ER V Plus has been derived with the help of DH algorithm as

well as conventional techniques such as geometric[1][2], algebraic[3][4][5] and iterative [6] methods.

Basics of ANFIS are introduced in section3. It also explains the wayfor input selection for ANFIS

modeling. Simulation results are discussed in section 4. Section 5 gives concluding remarks.

II. KINEMATICS OF SCORBOT-ER V PLUS

SCORBOT-ER V Plus [19] is a vertical articulated robot, with five revolute joints. It has a Stationary

base, shoulder, elbow, tool pitch and tool roll. Figure 1.1 identifies the joints and links of the

mechanical arm.

2.1. SCORBOT–ER V PLUS STRUCTURE

All joints are revolute, and with an attached gripper it has six degree of freedom. Each joint is

restricted by the mechanical rotation its limits are shown below.

Joint Limits:

Axis 1: Base Rotation: 310°

Axis 2: Shoulder Rotation: + 130° / – 35°

Axis 3: Elbow Rotation: ± 130°

Axis 4: Wrist Pitch: ± 130°

Axis 5: Wrist Roll Unlimited (electrically 570°)

Maximum Gripper Opening: 75 mm (3") without rubber pads 65 mm (2.6") with rubber pads

The length of the links and the degree of rotation of the joints determine the robot’s work envelope.

Figure 1.2 and 1.3 show the dimensions and reach of the SCORBOT-ER V Plus. The base of the robot

is normally fixed to a stationary work surface. It may, however, be attached to a slide base, resulting

in an extended working range.



160 Vol. 1, Issue 5, pp. 158-169

2.2. FRAME ASSIGNMENT TO SCORBOT–ER V PLUS

For the kinematic model of SCORBOT first we have to assign frame to each link starting from base

(frame {0}) to end-effector (frame {5}). The frame assignment is shown in figure 1.4.

Here in model the frame {3} and frame {4} coincide at same joint, and the frame {5} is end– effector

position in space.

Joint i �� (��) �� (��) �� Operating range

1 − �/2 16 349 �1 −155° � + 155°

2 0 221 0 �2 −35° � + 130°

3 0 221 0 �3 −130° � + 130°

4 �/2 0 0 �/2 + �4 −130° � + 130°

5 0 0 145 �5 −570° � 570°

2.3. FORWARD KINEMATIC OF SCORBOT–ER V PLUS

Once the DH coordinate system has been established for each link, a homogeneous transformation

matrix can easily be developed considering frame {i-1} and frame {i}. This transformation consists of

four basic transformations.

0 0 1 2 3 45 1 2 3 4 5* * * *T T T T T T= (1)

0 *1 1 1 1

0 *0 1 1 1 11 0 1 0

1

0 0 0 1

C S a C

S C a ST

d

−

= −

(2)



161 Vol. 1, Issue 5, pp. 158-169

2 2 2 2

2 2 2 212

0 *

0 *

0 0 1 0

0 0 0 1

C S a C

S C a ST

− =

(3)

3 3 3 3

3 3 3 323

0 *

0 *

0 0 1 0

0 0 0 1

C S a C

S C a ST

− =

(4)

4 0 4 0

4 0 4 034 0 1 0 0

0 0 0 1

S C

C ST

− =

(5)

5 5 0 0

5 5 0 045 0 0 1 5

0 0 0 1

C S

S CT

d

− =

(6)

Finally, the transformation matrix is as follow: -

1 5 1 5 234 5 1 1 5 234 1 234 1 1 2 2 3 23 5 234

1 5 1 5 234 1 5 1 5 234 1 234 1 1 2 2 3 23 5 2340

5

5 234 5 234 234 1 2 2 3 23 5 234

( )

( )

( )

0 0 0 1

S S C C S C S C S S C C C a a C a C d C

C S S C S C C S S S S C S a a C a C d CT T

C C S C S d a S a S d S

− − − + + + +

− + + + += =

− − − − −

(7)

Where, � = (��), �� = (��) �� = (�� + � + ��), �� = (�� + � + ��). The T is all over transformation matrix of kinematic model of SCORBOT-ER V Plus, from this we

have to extract position and orientation of end –effector with respect to base is done in the following

section.

2.4. OBTAINING POSITION IN CARTESIAN SPACE

The value of �, �, � is found from last column of transformation matrix as: -

1 1 2 2 3 23 5 234( )X C a a C a C d C= + + + (8)

1 1 2 2 3 23 5 234( )Y S a a C a C d C= + + − (9)

1 2 2 3 23 5 234( )Z d a S a S d S= − − − (10)

For Orientation of end-effector frame {5} and frame {1} should be coincide with same axis but in our

model it is not coincide so we have to take rotation of −90° of frame {5} over y5 axis, so the overall

rotation matrix is multiplied with ��−90° as follow: -

cos( 90 ) 0 sin( 90 )

0 1 0

sin( 90 ) 0 cos( 90 )

yR

− −

= − − −

o o

o o

0 0 1

0 1 0

1 0 0

yR

−

=

(11)

The Rotation matrix is: -

1 5 1 5 234 5 1 1 5 234 1 234

1 5 1 5 234 1 5 1 5 234 5 234

5 234 5 234 234

0 0 1

0 1 0

1 0 0

S S C C S C S C S S C C

R C S S C S C C S S S S C

C C S C S

− − − − +

= × − + − −



162 Vol. 1, Issue 5, pp. 158-169

5 234 5 234 234

1 5 1 5 234 1 5 1 5 234 5 234

1 5 1 5 234 5 1 1 5 234 1 234

C C S C S

R C S S C S C C S S S S C

S S C C S C S C S S C C

−

= − + − − − + (12)

Pitch: Pitch is the angle of rotation about y5 axis of end-effector

2 3 4 234pitchβ θ θ θ θ= + + = (13)

2 2234 a tan 2( 13, 23 33 )r r rθ = ± + (14)

Here we use atan2 because its range is [−�, �], where the range of atan is [−�/2, �/2].

Roll: The �� = �5 is derived as follow: -

5 234 234tan 2( 12 / , 11/ )a r C r Cθ = (15)

Yaw: Here for SCORBOT yaw is not free and bounded by �1.

2.5. HOME POSITION IN MODELING

At home position all angle are zero so in equation (1.7) put �1 = 0, �2 = 0, �3 = 0, �4 = 0, �5 = 0

So the transformation matrix reduced to:-

1 2 3 5

1

0 0 1 0 0 1 603

0 1 0 0 0 1 0 0

1 0 0 1 0 0 349

0 0 0 1 0 0 0 1

Home

a a a d

Td

+ + + = = − −

(16)

The home position transformation matrix gives the orientation and position of end-effector frame.

From the 3×3 matrix orientation is describe as follow, the frame {5} is rotated relative to frame {0}

such that �5 axis is parallel and in same direction to �0 axis of base frame; �5is parallel and in same

direction to �0 axis of base frame; and �5axis is parallel to �0but in opposite direction. The position is

given by the 3 × 1 displacement matrix 1 2 3 5 10 .T

a a a d d+ + +

2.6. INVERSE KINEMATICS OF SCORBOT-ER V PLUS

For SCORBOT we have five parameter in Cartesian space is x, y, z, roll (�), pitch (�).For joint

parameter evaluation we have to construct transformation matrix from five parameters in Cartesian

coordinate space. For that rotation matrix is generated which is depends on only roll, pitch and yaw of

robotic arm. For SCORBOT there is no yaw but it is the rotation of first joint �1.

So the calculation of yaw is as follow: -

1 tan 2( , )a x yα θ= = (17)

Now for rotation matrix rotate frame {5} at an angle – � about its x axis then rotate the new frame {5′

} by an angle � with its own principal axes �′ , finally rotate the new frame {5′′} by an angle � with

its own principal axes � ''.

�� = ��( −�) ∗��( �) ∗��(�)

1 0 0 0 0

0 0 1 0 0

0 0 0 0 1

C S C S

C S S C

S C S C

γ γ α α

β β α α

β β γ γ

−

= × × − −



163 Vol. 1, Issue 5, pp. 158-169

C C C S S

C S C S S C C S S S C S

S S C C S S C S C S C C

α γ γ α γ

β α α β γ β α β γ α γ β

β α α β γ β α α β γ β γ

−

= − + − − − + (18)

Now rotate matrix by 90° about y axis: -

(90 ) 0 (90 )

( 90 ) 0 1 0

(90 ) 0 (90 )

y

COS SIN

R

SIN COS

− = −

o o

o

o o

0 0 1

( 90 ) 0 1 0

1 0 0

yR

− = −

o

(19)

After pre multiplying the equation 19 with equation 18, one will get following rotation matrix: -

S S C C S S C S C S C C

C S C S S C C S S S C S

C C C S S



α γ γ α γ

− − − +

= − + − − (20)

So, the total transformation matrix is as follows: -

0 0 0 1

S S C C S S C S C S C C X

C S C S S C C S S S C S YT

C C C S S Z



α γ γ α γ

− − − +

− + = − − (21)

After comparing the transformation matrix in equation (7) with matrix in equation (21), one can

deduce: -

�1 = �,

�234 = �,

�5 = �,

Now, we have �1 and �5 directly but �2, �3��4 are merged in �234 so we have separate them, to

separate them we have used geometric solution method as shown in Figure 1.6

Here for finding �2, �3, �4, we have X, Y, Z in Cartesian coordinate space from that we can take:-

2 21 1( )X X Y andY Z= + = (22)

We have pitch of end-effector �234 = �, from that we can find point �2, �2 is calculated as follows: -

2 1 5 234

2 1 5 234

cos

sin

X X d

Y Y d

θ

θ

= −

= + (23)



164 Vol. 1, Issue 5, pp. 158-169

Now the distance �3and �3can be found: -

3 2 1

3 2

X X a

Y Y

= −

=

From the low of cosines applied to triangle ABC, we have: - 2 2 2 23 3 2 3

32 3

( )cos

2

X Y a a

a aθ

+ − −=

23 3 3tan 2( 1 cos , cos )aθ θ θ= ± −

(24)

From figure 1.6 �2 = −∅ − � or

2 3 3 3 3 2 3tan 2( , ) tan 2( sin , cos )a Y X a a aθ θ θ= − − + (25)

Finally we will get: -

4 234 2 3θ θ θ θ= − − (26)

III. INVERSE KINEMATICS OF SCORBOT-ER V PLUS USING ADAPTIVE

NEURO FUZZY INFERENCE SYSTEM (ANFIS)

The proposed ANFIS[7][20][21] controller is based on Sugeno-type Fuzzy Inference System (FIS)

controller.The parameters of the FIS are governed by the neural-network back propagation method.

The ANFIS controller is designed by taking the Cartesian coordinates plus pitch as the inputs, and the

joint angles of the manipulator to reach a particular coordinate in 3 dimensional spaces as the output.

The output stabilizing signals, i.e., joint angles are computed using the fuzzy membership functions

depending on the input variables. The effectiveness of the proposed approach to the modeling is

implemented with the help of a program specially written for this in MATLAB. The information

related to data used to train is given inTable 1.2.

Sr.

No.

Manipulator

Angles

No. of

Nodes

No. of Parameters Total No. of

Parameters

No. of

Training

Data Pairs

No. of

Checking

Data Pairs

No. of

Fuzzy

Rules Linear Nonlinear

01. Theta1 193 405 36 441 4500 4500 81

02. Theta2 193 405 36 441 4500 4500 81

03. Theta3 193 405 36 441 4500 4500 81

04. Theta4 193 405 36 441 4500 4500 81

The procedure executed to train ANFIS is as follows:

(1) Data generation: To design the ANFIS controller, the training data have been generated by using

an experimental setup with the help of SCORBOT-ER V Plus. A MATLAB program is written to

govern the manipulator to get the input –output data set. 9000 samples were recorded through the

execution of the program for the input variables i.e., Cartesian coordinates as well as Pitch. Cartesian

coordinates combination for all thetas are given in Fig.1.7



165 Vol. 1, Issue 5, pp. 158-169

(2) Rule extraction and membership functions: After generating the data, the next step is to estimate

the initial rules. A hybrid learning algorithm is used for training to modify the above parameters after

obtaining the Fuzzy inference system from subtracting clustering. This algorithm iteratively learns the

parameter of the premise membership functions and optimizes them with the help of back propagation

and least-squares estimation. The training is continued until the error minimization..The input as well

as output member function used was triangular shaped member function.The final fuzzy inference

system chosen was the one associated with the minimum checking error, as shown in figure 1.8.it

shown the final membership function for the thetas after training.

-0 . 5 0 0 . 5

0

0 . 5

1

in p u t 1

De

gre

e o

f m

em

be

rsh

ip

in 1 m f1 in 1 m f2 in 1 m f3

-0 . 4 -0 . 2 0 0 . 2 0 . 4

0

0 . 5

1

in p u t 2

De

gre

e o

f m

em

be

rsh

ip


-0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8

0

0 . 5

1

in p u t 3

De

gre

e o

f m

em

be

rsh

ip

i n 3 m f1 in 3 m f2 in 3 m f3

-4 -2 0 2 4

0

0 . 5

1

in p u t 4

De

gre

e o

f m

em

be

rsh

ip


-0 . 5 0 0 . 5

0

0 . 5

1

in p u t 1

De

gr

ee

of

me

mb

er

sh

ip


-0 . 4 -0 . 2 0 0 .2 0 . 4

0

0 . 5

1

in p u t 2

De

gr

ee

of

m

em

be

rs

hip


-0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8

0

0 . 5

1

in p u t 3

De

gre

e o

f m

em

be

rsh

ip

i n 3 m f1 in 3 m f2 i n 3 m f3

- 4 -2 0 2 4

0

0 . 5

1

in p u t 4

De

gre

e o

f m

em

be

rsh

ip


- 0 . 5 0 0 . 5

0

0 . 5

1

i n p u t 1

De

gr

ee

o

f

me

mb

er

sh

ip

i n 1 m f 1 i n 1 m f 2 i n 1 m f 3

- 0 . 4 - 0 . 2 0 0 . 2 0 . 4

0

0 . 5

1

i n p u t 2

De

gr

ee

o

f

me

mb

er

sh

ip

i n 2 m f1 i n 2 m f2 i n 2 m f 3

- 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8

0

0 . 5

1

i n p u t 3

De

gr

ee

o

f

me

mb

er

sh

ip

i n 3 m f1 i n 3 m f 2 i n 3 m f 3

- 4 - 2 0 2 4

0

0 . 5

1

i n p u t 4

De

gr

ee

o

f

me

mb

er

sh

ip

i n 4 m f1 i n 4 m f2 i n 4 m f 3

- 0 . 5 0 0 . 5

0

0 . 5

1

i n p u t 1

De

gr

ee

o

f

me

mb

er

sh

ip

i n 1 m f 1 i n 1 m f 2 i n 1 m f 3

- 0 . 4 - 0 . 2 0 0 . 2 0 . 4

0

0 . 5

1

i n p u t 2

De

gr

ee

o

f

me

mb

er

sh

ip

i n 2 m f 1 i n 2 m f 2 i n 2 m f3

- 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8

0

0 . 5

1

i n p u t 3

De

gr

ee

o

f

me

mb

er

sh

ip

i n 3 m f1 i n 3 m f2 i n 3 m f 3

- 4 - 2 0 2 4

0

0 . 5

1

i n p u t 4

De

gr

ee

o

f

me

mb

er

sh

ip

i n 4 m f1 i n 4 m f 2 i n 4 m f3

θ1

θ2

θ3θ4

(3) Results: The ANFIS learning was tested on a variety of linear and nonlinear processes. The

ANFIS was trained initially for 2 membership functions for 9000 data samples for each input as well

as output. Later on, it was increased to 3 membership functions for each input. To demonstrate the

effectiveness of the proposed combination, the results are reported for a system with81 rules and a

system with an optimized rule base. After reducingthe rules the computation becomes fast and it also

consumes less memory. The ANFIS architecture for θ1 is shownin Fig. 1.9.



166 Vol. 1, Issue 5, pp. 158-169

Five angles have considered for the representation of robotic arm. But as the �5 is independent

of other angles so only remaining four angles was considered to calculate forward kinematics. Now,

for every combination of �1, θ2, θ3 andθ4 values the x and y as well as z coordinates are deduced using

forward kinematics formulas.

IV. SIMULATION RESULTS AND DISCUSSION

The plots displaying the root-mean-square error are shown in figure 1.10. The plot in blue represents

error1, the error for training data. The plot in green represents error2, the error for checking data.

From the figure one can easily predict thatthere is almost null difference between the training error as

well as checking error after the completion of training of ANFIS.

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00 . 5 5

0 .6

0 . 6 5

0 .7

0 . 7 5

0 .8

0 . 8 5

0 .9

E p o c h s

RM

SE

(R

oo

t M

ea

n S

qu

are

d E

rro

r)

E r ro r C u rve s

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00 . 2 2

0 . 2 4

0 . 2 6

0 . 2 8

0 .3

0 . 3 2

0 . 3 4

E p o c h s

RM

SE

(R

oo

t M

ea

n S

qu

are

d E

rro

r)

E rro r C u rve s

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00 . 4 5

0 .5

0 . 5 5

0 .6

0 . 6 5

0 .7

E p o c h s

RM

SE

(R

oo

t M

ea

n S

qu

are

d E

rro

r)

E r ro r C u rve s

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 00 . 3 2

0 . 3 4

0 . 3 6

0 . 3 8

0 . 4

0 . 4 2

0 . 4 4

E p o c h s

RM

SE

(R

oo

t M

ea

n S

qu

are

d E

rro

r) E r r o r C u rve s

θ1 θ2

θ3 θ4

In addition to above error plots, the plot showing the ANFIS Thetas versus the actual Thetasare given

in figures1.11,1.12,1.13 and 1.14 respectively. The difference between the original thetas values and

the values estimated using ANFIS is very small.

0 50 100 150 200 250 300 350-4

-3

-2

-1

0

1

2

3

Time (sec)

Theta1 and ANFIS Prediction theta1

Experimental Theta1

ANFIS Predicted Theta1

0 50 100 150 200 250 300 350-1

-0.5

0

0.5

1

1.5

2

Time (sec)

Theta2 and ANFIS Prediction theta2

Experimental Theta2




167 Vol. 1, Issue 5, pp. 158-169

0 50 100 150 200 250 300 350-3

-2

-1

0

1

2

3

Time (sec)

Theta3 and ANFIS Prediction Theta3

Experimental Theta3


0 50 100 150 200 250 300 350-3

-2

-1

0

1

2

Time (sec)

Theta4 and ANFIS Prediction Theta4

Experimental Theta4


The prediction errors for all thetas appear in the figures 1.15, 1.16, 1.17, 1.18 respectively with a much finer

scale. The ANFIS was trained initially for only 10 epochs. After that the no. of epochs were increased to 20 for

applying more extensive training to get better performance.

0 50 100 150 200 250 300 350-3

-2

-1

0

1

2

3

Time (sec)

Prediction Errors for THETA 1

Prediction Error Theta1

0 50 100 150 200 250 300 350-1.5

-1

-0.5

0

0.5

1

Time (sec)

Prediction Errors for THETA2


0 50 100 150 200 250 300 350-3

-2

-1

0

1

2

Time (sec)





168 Vol. 1, Issue 5, pp. 158-169

0 50 100 150 200 250 300 350-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time (sec)



V. CONCLUSION

From the experimental work one can see that the accuracy of the output of the ANFIS based inverse

kinematic model is nearly equal to the actual mathematical model output, hence this model can be

used as an internal model for solving trajectory tracking problems of higher degree of freedom (DOF)

robot manipulator. Asingle camera for the reverse mapping from camera coordinates to real world

coordinateshas been used in the present work, if two cameras are used stereo vision can be achieved

andproviding the height of an object as an input parameter would not be required. The methodology

presented herecan be extended to be used for trajectory planning and quite a few tracking applications

with real world disturbances. Thepresent work did not make use of color image processing; making

use of color image processing can helpdifferentiate objects according to their colors along with their

shapes.

ACKNOWLEDGEMENTS

As it is the case in almost all parts of human endeavour so also the development in the field of robotics has been

carried on by engineers and scientists all over the world.It can be regarded as a duty to express the appreciation

for such relevant, interesting and outstanding work to which ample reference is made in this paper.

REFERENCES

[1] F. R, "Position and velocity transformation between robot end-effector coordinate and joint angle,"

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Authors

Himanshu Chaudhary received his B.E. in Electronics and Telecommunication from

Amravati University, Amravati, India in 1996, M.E. in Automatic Controls and Robotics

from M.S. University, Baroda, Gujarat, India in 2000.Presently he is a research scholar in

Electrical Engineering Department, IIT Roorkee, India. His area of interest includes

industrial robotics, computer networks and embedded systems.

Rajendra Prasad received B.Sc. (Hons.) degree from Meerut University, India in 1973. He

received B.E.,M.E. and Ph.D. degree in Electrical Engineering from the University of

Roorkee, India in 1977, 1979 and 1990 respectively. . He also served as an Assistant

Engineer in Madhya Pradesh Electricity Board (MPEB) from 1979- 1983. Currently, he is a

Professor in the Department of Electrical Engineering, Indian Institute of Technology

Roorkee, Roorkee (India).He has more than 32 years of experience of teaching as well as

industry. He has published 176 papers in various Journals/conferences and received eight

awards on his publications in various National/International Journals/Conferences Proceeding papers. He has

guided Seven PhD’s, and presently six PhD’s are under progress. His research interests include Control,

Optimization, System Engineering and Model Order Reduction of Large Scale Systems and industrial robotics.

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