final msd project

8/13/2019 Final MSD Project

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University Of Jordan

Fuzzy Control

0908541

Robot Manipulator Task Control UsingFuzzy Behavior-Based Strategy

Liana Abu-Alsoud 0080270

Anas Odeh 0081555

Omar Othman 0085157


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Abstract

In this project, the concept of fuzzy behavior-based control is used toconstruct a fuzzy generator that generates the desired positions and

orientations of a robot manipulator in the Cartesian space. The aim of this

project is to give a solution to manipulation control problem. Manipulation

requires identifying the target acquired from vision system mounted on the

manipulator, and grasping it by the end-effector. The control law used here is

based on fuzzy logic. The controller determines the parameters of the target.

After studying the behavior of the system, fuzzy rule was built.


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Introduction

A behavior-based control system, which can intelligently construct acontrolled system for a robot manipulator according to the interaction

between the robot and the environment, is now becoming attractive in the

field of robotics; that is why we chose a subject that is related to that, which

is Robot Manipulator Task Control Using Fuzzy Behavior-based Strategy.

In the field of Cartesian control vision system two methods have been

proposed: Position-based visual servo control and Image-based visual

servo control, but these methods suffer from singularities, complicatedcalculation process and inaccuracy.

On the other hand, Fuzzy Logic, which was initially introduced by Dr. Lutfi

Zadeh, was found to be the perfect solution to minimize the complications

and challenges faced earlier.It is used to detecteasily the situation-action

mapping.

Therefore the objective of this work is for a six-link, six degree-of-freedom

PUMA robot to reach a target from an initial point while avoiding obstacleusing behavior-based approach.The application of fuzzy logic control in

robotics is to produce an intelligent robot with the ability of autonomous

behavior and decision.

Fuzzy Vs. Other Methods

Two methods (Vision Systems) have been proposed previously:1) Position-based visual servo control:

-Calculated and estimated position.-Calibration errors.

2) Image-based visual servo control:

-The inaccuracy in the position of the end-effector.

-Jacobian matrix is difficult to calculate.

-Singularities.


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While designing control system using Fuzzy Control rules gives us :-High quality.

-Minimized calculations complexity.

Thats why we preferred to use Fuzzy Logic in this work

Components

1)Vision System:CCD Camera sensor.2)Target:Sphere with (x, y) as center coordinates, and (r) as any point

on the circumference of the sphere.

3)Manipulator:PUMA 560.

1.CCD Camera

CCD (Charge-Coupled Device) is an analog device. When light strikes the

chip it is held as a small electrical charge in each photo sensor, the chargesare converted to voltage one pixel at a time as they are read from the chip.

Additional circuitry in the camera converts the voltage into digital

information. Its role is to keep catching pictures and compare it with the

original photo saved on it, to identify the target.

Why CCD?A.Low noise (noiseless charge transfer).B.Linear and easy to calibrate.C.Commercially produced.

2.Spherical Target


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Fig1. Camera-laser coupling with a sphere.

3.PUMA Manipulator

1. The controller of the manipulator has several roles (Fig2):1) Information role:collecting and processing info provided by sensor.

2) Decision role:planning the geometric motion.

3) Communication role:organizing info between robot and environment.

2. PUMA(Programmable Universal Machine for Assembly): is one of themost common assembly robots. Six-links 6-DOF robot (Fig3).


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Fig3: PUMA Manipulator

3. Note: These axes are determined based on DH parameters that will be discussed indetails later (Refer to table 1).

Rotation Module:

For the 1stjoint (J1), the input data is represented by (x, r) which are the x

coordinate and the radius of the spherical target. The output data is the angle

(1).

Reaching Target Module:

For the 2nd

and 3rd

joints (J2, J3), which will move the gripper to grasp the

target. The Input data is represented by (y, r) which are the y coordinated and

the radius of the spherical target. The output data are the angles (2, 3).

Equation of Motion

= M() + h(, ) + g() + m + f .. (1)

; Where:

M(): inertia matrix.

h(, ):Coriolis and centrifugal force vector.g():gravitational vector.

:is the torque vector.

, and :joint angle vector, angular velocity vector, angular acceleration vector respectively.


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m , f:torques required to overcome the motor armature inertia and friction of the joints

respectively. (Refer to Appendix A)

DH Parameters

Joint i i [deg] ai [m] di [m] Joint Range i

[deg]

1 90 0 0 160 to 160

2 0 0.4318 0.14909 225 to 45

3 90 0.02032 0 45 to 225

4 -90 0 0.43307 110 to 170

5 90 0 0 100 to 100

6 0 0 0.05625 266 to 266

Table1: DH Parameters (Refer to Appendix B)

Fuzzy Logic Controller


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CAD Model

Control system design

Three stages of Fuzzy Logic Control are used:1. Fuzzification: A process of transforming crisp values into grades of

membership for linguistic terms (ie: Near, Far,..) of fuzzy sets.Its role

is to activate If-Then rules.

2. Inference:Isconsidered to be the core of the fuzzy system whichcombines the facts obtained from the fuzzification with the rule base


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and conducts a fuzzy reasoning process(the process of concluding new

facts from already existing facts).

3. Defuzzification:Translate results back to real world values.

Fuzzy Sets

X(Pixel)

F-= [-62, 85]QN-= [42, 94]

N-= [85, 103.5]

VN-= [94, 112]N+= [103, 121]

QN+= [112, 165]

F+= [122, 261]

Y(Pixel)

F-= [-62, 69]N-= [24, 78]

VN= [69, 87]N+= [78, 122]

F+= [87, 212]

R(Pixel)

F-= [-67 85]

QN-= [42.04 93.98]

N-= [85 103.5]VN-= [94 112]

N+= [103.1 121.6]

QN+= [112 165]

F+= [122 261]


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J1VB-= [ -6 -1]

B-= [-5 -0.5]

S-= [-1 -0.15]

VS-= [-0.5 0]

Z= [-0.15 0.15]

VS+= [0 0.5]S+= [0.15 1]

B+= [0.5 4]

VB+= [1 6]

J2VB-= [ -25 -6]B-=[-15 -1.8]

S-= [-6 -0.5]

VS-= [-1.8 0]

Z=[-0.461 0.539]

VS+= [0 1.8]

S+= [0.5 6]

B+= [1.8 15]VB+= [6 25 ]

J3VB-= [ -20 -4.97]

B-= [-12 -1.5]

S-= [-5 -0.4]

VS-= [-1.5 0]

Z= [-0.4 0.4]VS+= [0 1.5]

S+= [0.4 5]B+= [1.5 12]

VB+= [5 20 ]


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Linguistic Variables

Linguistic Variables Linguistic Values

(Primary terms)

Linguistic Hedges

(Secondary terms,modifiers)

x-coordinate

Near,

Very near

Quite near,Far

Positive (+)

Negative (-)y-coordinate

r-circumference

Table2: Input linguistic terms

Linguistic Variables Linguistic Values

(Primary terms)

Linguistic Hedges(Secondary terms,

modifiers)

1

Big

Very bigSmall

Zero

Positive (+)Negative (-)2

3

Table2: Output linguistic terms

Notes:a. For x and y: (+) means that the center of circumference is greater than the

goal position, while (-) means smaller than.b.For r:(+) means approaching, while (-) means thatthe manipulator is very

close to the target.c. For : (+) means positive angle, while (-) means negative


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Simulation

Fig 4: Inputs and Outputs.


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1.Fuzzification

Fig5: (X-Coordinate).

Fig6: (Y-Coordinate).


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Fig7: (Circumference r).

Fig8: (1).


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Fig9: (2).

Fig.10: (3).


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2.Fuzzy Rule Base

The first step is to evaluate the antecedent (fuzzifying the input andapplying any necessary fuzzy operators).

The second is the implication (applying the result of antecedent toconsequent).

Joint1 rules (R1-R42):R1: If (x is F-) and (r is F+) then (is B+)

R2: If (x is F-) and (r is QN+) then (is B+)

R3: If (x is F-) and (r is N+) then (is VB+)

R4: If (x is F-) and (r is VN) then (is VB+)

R5: If (x is F-) and (r is N-) then (is VB+)

R6: If (x is F-) and (r is QN-) then (is VB+)

R7: If (x is QN-) and (r is F+) then (is VB+)

R8: If (x is QN-) and (r is QN+) then (is VB+)

R9: If (x is QN-) and (r is N+) then (is VB+)

R10: If (x is QN-) and (r is VN) then (is VS+)

R11: If (x is QN-) and (r is N-) then (is VS+)

R12: If (x is QN-) and (r is QN-) then (is VS+)

R13: If (x is N-) and (r is F+) then (is VS+)

R14: If (x is N-) and (r is QN+) then (is S+)


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R15: If (x is N-) and (r is N+) then (is S+)

R16: If (x is N-) and (r is VN) then (is S+)

R17: If (x is N-) and (r is N-) then (is S+)

R18: If (x is N-) and (r is QN-) then (is S+)

R19: If (x is VN) and (r is F+) then (is Z)

R20: If (x is VN) and (r is QN+) then (is Z)

R21: If (x is VN) and (r is N+) then (is Z)

R22: If (x is VN) and (r is VN) then (is Z)

R23: If (x is VN) and (r is N-) then (is Z)

R24: If (x is VN) and (r is QN-) then (is Z)

R25: If (x is N+) and (r is F+) then (is VS-)

R26: If (x is N+) and (r is QN+) then (is S-)

R27: If (x is N+) and (r is N+) then (is S-)

R28: If (x is N+) and (r is VN) then (is S-)

R29: If (x is N+) and (r is N-) then (is S-)

R30: If (x is N+) and (r is QN-) then (is S-)

R31: If (x is QN+) and (r is F+) then (is VB-)

R32: If (x is QN+) and (r is QN+) then (is VB-)

R33: If (x is QN+) and (r is N+) then (is VS-)


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R34: If (x is QN+) and (r is VN) then (is VS-)

R35: If (x is QN+) and (r is N-) then (is VS-)

R36: If (x is QN+) and (r is QN-) then (is VS-)

R37: If (x is F+) and (r is F+) then (is B-)

R38: If (x is F+) and (r is QN+) then (is B-)

R39: If (x is F+) and (r is N+) then (is VB-)

R40: If (x is F+) and (r is VN) then (is VB-)

R41: If (x is F+) and (r is N-) then (is VB-)

R42: If (x is F+) and (r is QN-) then (is VB-)

Joint2 rules (R43-R72):R43: If (y is F-) and (r is F+) then (is B-)

R44: If (y is F-) and (r is QN+) then (is VB-)

R45: If (y is F-) and (r is N+) then (is VS-)

R46: If (y is F-) and (r is QN) then (is VS-)

R47: If (y is F-) and (r is N-) then (is S+)

R48: If (y is F-) and (r is QN-) then (is VS+)

R49: If (y is N-) and (r is F+) then (is B-)

R50: If (y is N-) and (r is QN+) then (is VB-)

R51: If (y is N-) and (r is N+) then (is VS-)


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R52: If (y is N-) and (r is VN) then (is Z)

R53: If (y is N-) and (r is N-) then (is VS+)

R54: If (y is N-) and (r is QN-) then (is VB+)

R55: If (y is QN) and (r is F+) then (is B-)

R56: If (y is QN) and (r is QN+) then (is VB-)

R57: If (y is QN) and (r is N+) then (is VS-)

R58: If (y is QN) and (r is VN) then (is Z)

R59: If (y is QN) and (r is N-) then (is VS+)

R60: If (y is QN) and (r is QN-) then (is VB+)

R61: If (y is N+) and (r is F+) then (is B-)

R62: If (y is N+) and (r is QN+) then (is VB-)

R63: If (y is N+) and (r is N+) then (is S-)

R64: If (y is N+) and (r is VN) then (is Z)

R65: If (y is N+) and (r is N-) then (is VS+)

R66: If (y is N+) and (r is QN-) then (is VB+)

R67: If (y is F+) and (r is F+) then (is B-)

R68: If (y is F+) and (r is QN+) then (is VB-)

R69: If (y is F+) and (r is N+) then (is S-)


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R70: If (y is F+) and (r is VN) then (is S-)

R71: If (y is F+) and (r is N-) then (is VS-)

R72: If (y is F+) and (r is QN-) then (is VB+)

Joint3 rules (R73-R102):R73: If (y is F-) and (r is F+) then (is B+)

R74: If (y is F-) and (r is QN+) then (is VB+)

R75: If (y is F-) and (r is N+) then (is VS+)

R76: If (y is F-) and (r is VN) then (is VS+)

R77: If (y is F-) and (r is N-) then (is VS+)

R78: If (y is F-) and (r is QN-) then (is VS+)

R79: If (y is N-) and (r is F+) then (is VB+)

R80: If (y is N-) and (r is QN+) then (is VS+)

R81: If (y is N-) and (r is N+) then (is S+)

R82: If (y is N-) and (r is VN) then (is S+)

R83: If (y is N-) and (r is N-) then (is Z)

R84: If (y is N-) and (r is QN-) then (is VS-)

R85: If (y is QN) and (r is F+) then (is VB+)

R86: If (y is QN) and (r is QN+) then (is VS+)

R87: If (y is QN) and (r is N+) then (is S+)


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R88: If (y is QN) and (r is VN) then (is Z)

R89: If (y is QN) and (r is N-) then (is S-)

R90: If (y is QN) and (r is QN-) then (is VS-)

R91: If (y is N+) and (r is F+) then (is VB+)

R92: If (y is N+) and (r is QN+) then (is VS+)

R93: If (y is N+) and (r is N+) then (is S-)

R94: If (y is N+) and (r is VN) then (is S-)

R95: If (y is N+) and (r is N-) then (is S-)

R96: If (y is N+) and (r is QN-) then (is VS-)

R97: If (y is F+) and (r is F+) then (is VB+)

R98: If (y is F+) and (r is QN+) then (is S-)

R99: If (y is F+) and (r is N+) then (is VS-)

R100: If (y is F+) and (r is VN) then (is VS-)

R101: If (y is F+) and (r is N-) then (is VS-)

R102: If (y is F+) and (r is QN-) then (is VB-)


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3.Fuzzy Inference

Generalized Modus Ponens (GMP) inference procedure, which usesan if-then rule that implicitly represents fuzzy relation.

Mamdani reasoning type

For Joint1:

R1: If (x is A1) and (r is B1) then ( is C1).

.

R42: If (x is A42) and (r is B42) then ( is C42)

Observations: , Conclusion: C*=Combine (C1*,.,C42*) Firing strength:

= ( (

.

.= ( (

Rules Conclusion:

(= ( w.

.

(= ( w

The overall joint1 conclusion:

(=

( v

( v .. v

( w

For Joint2:


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R1: If (y is A43) and (r is B43) then ( is C43).

.

R42: If (y is A72) and (r is B72) then ( is C72)

Observations: , Conclusion: C*=Combine (C43*,.,C72*) Firing strength:

= ( (

.

.

= ( (

Rules Conclusion:

(= ( w..

(= ( w


(=

( v

( v .. v

( w

For Joint3:

R1: If (y is A73) and (r is B73) then ( is C73).

.

R42: If (y is A102) and (r is B102) then ( is C102)

Observations: , Conclusion: C*=Combine (C73*,.,C102*)


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Firing strength:= ( (

.

.

= ( (

Rules Conclusion:

(= ( w.

.

(= ( w


(=

( v

( v .. v

( w

4.Defuzzification

Center of gravityW*=


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Fig10: If-Then Rules


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Manipulator Control

= M()+ h(, ) + g() + + Where:

M(

) is the inertia matrix,h(, ) is the Coriolis and centrifugal force vector

g() is the gravitational vector. is the torque vector

is torques required to overcome the motor armature inertia

istorques required to overcome the motor friction

=

= +sgn( )

i = 1,,6

at joint i, is the armature inertia of the motor

is the ith joint reduction gear ratio defined by motor speed/link speedis viscous friction

is the Coulomb friction


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Control system block diagram


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Step1: the sphere object is far from the manipulator

Step2: first joint is rotated to face the object


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Step3: joint 2 and joint 3 approaching the object

Step4: the end effector caught the object


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Step5: moving the object to the desired location

Controller specifications

The system controlled by a PC. The software interface between the controller

and the physical manipulator is constituted by an high level language and

connected through RS232 serial line.

Manipulator Control

= M()+ h(, ) + g() + + Where:

M() is the inertia matrix,

h(, ) is the Coriolis and centrifugal force vector

g() is the gravitational vector. is the torque vector

is torques required to overcome the motor armature inertia

istorques required to overcome the motor friction

=

= +sgn( )

i = 1,,6

at joint i, is the armature inertia of the motoris the ith joint reduction gear ratio defined by motor speed/link speed

is viscous friction

is the Coulomb friction


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Conclusion

In this project, a system has been designed using fuzzy behavior-based

strategy which gave us the advantage of moving towards a particular point

without knowing the inverse kinematics or any prior knowledge of how to

avoid obstacles or an algorithm to avoid obstacle.

The simulation proved that the proposed method was effective for complex

manipulators like PUMA robot.

Fuzzy logic is easy, practical and effective control method, with the help of

Mamdanis rule and Matlab (fuzzy tool boxes).


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final msd project

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