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OTKA* HUNGARIAN SCIENTIFIC RESEARCH FUND

INTELLIGENT CONTROL of MANUFACTURING SYSTEMS

(OTKA T 037525)

Professor J.SOMLO, Academical Doctor of Engineering

Budapest University of Technology and Economics

TOPIC:

Scientific leader:

*OTKA – Országos Tudományos Kutatási Alapprogramok

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Research covers:

Optimization Problem of Manufacturing Systems

Hybrid Dynamical Approach for FMS Scheduling

Optimal Robot Motion Planning

The present demonstration material covers the last two topics

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Hybrid Dynamical Approach for FMS Scheduling Literature Survey

Basic Results published in: Perkins J.R., Kumar P.R. “Stable, Distributed, Real-Time Scheduling of Flexible Manufacturing (Assembly) Disassembly Systems,” IEEE Transactions on Automatic Control. Vol. 34, No:2. February 1989, pp. 139-148.

Mathematical theories provided in: Matveev A.S., Savkin A.V., “Qualitative Theory of Hybrid Dynamical Systems,” Birkhauser 2000, pp. 348.

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Hybrid Dynamical Approach for FMS Scheduling

DiscussionsThe good solution of scheduling is a key issue of the goodness of FMS actions effectiveness.

Today's practice of solution is usually based on heuristic methods giving GANTT diagrams determining processing times for series.

Hybrid Dynamical Approach changes the formulation of tasks. Demand rates are formulated for the inputs. Dynamic nonlinear determination of the process based on switching policies is possible.

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Hybrid Dynamical Approach for FMS SchedulingResearch results

The results of the present research are:

hybrid dynamical approach provides effective, overlapping production for practical tasks

the proposed demand rate determination method makes possible to met practical goals

the developed computing and simulation systems make possible to determine the goodness of planning parameters (demand rates, initial auxiliary buffer contents, etc.)

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New Ways in FMS Scheduling

By Prof. János SOMLO

Budapest University of Technology and Economics,

e-mail: somloj@eik.bme.hu

Demonstration of Hybrid Dynamical Approach

for FMS Scheduling

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Content

1. What is the Hybrid Dynamical Approach for FMS Scheduling

2. Scheduling Problem for FMS

3. Determination of Demand Rates

4. The Active Buffer Technique

5. Conclusions

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1. What is the Hybrid Dynamical Approach to FMS Scheduling

Let us outline some basic points of HDA use. Consider a system given on Figure at the next page. This is a continuous analog of a part of a Flexible Manufacturing System. There are a number of tanks which are supplied with fluid. The incoming fluid flow rates are d1, d2, d3 ..etc. The servers are intelligent. It means that they

drop the content of tanks in different rate. That is, from every tank the fuel is dropped with some specific rate qi, (i =1,2,3,…. I). The

fuel may arrive from the central buffer, or from other servers. The fluid from a server may go to any of the tanks of the other servers, or to the output of the system which can be represented by the final product store.

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q1 q2 q3

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Equations of the Motions

I n p u t

)0()( iii utdtu

O u t p u t

tpty ii )( o r0)( ty i

B u f f e r C o n t e n t)()()( tytutz iii

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CLB (Clear the Largest Buffer Level) CAF (Clear A Fraction) ETC.

Switching Policies

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Stability of Switching Policies

,)]([sup)]()([sup iit

iit

Mtztytu

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2. The Scheduling Problem for FMS

One has: n jobs (J1, J2,..., Jn), to be processed on m machines (M1, M2,..., Mm). On machines we understand an equivalent group of machines, which can be in practice one machine, too. Sometimes instead of word machine we use server. For all of the jobs the number of parts ni the due date ddi , the release date ri (ri- is the time at which Ji becomes available for processing) is given. Tsch is the scheduling period.

The CAPP subsystem determines for every job Ji (a job Ji is ni parts of type i ) the operation sequence oij ,where j=1,2,..., jl (jl- is the number of operation sequences), oij –is an integer showing in which machine the given operation is performed. Very important information are the processing times qij . The processing times are determined by the operation planning subsystem of CAPP including the manufacturing data determination section. We note that the engineering database for scheduling is generated from CAPP results. But, it needs proper modification. In engineering database for scheduling it is convenient to apply , where is the number of machines in the equivalent group.

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The GANTT diagrams

ti1

tilast Tsch t

tj-1

t

tjτi(j-1)

τij

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Determination of Demand Rates

iup

h

i

j

iilos

i d

h

n

ij

ddT

n

tMaxMaxMin )(,1

)(ch

Tsch0

thh-th server

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t

demand rate di

il

Part demand ui

i2i1

3. Determination of Demand Rates at Hybrid Dynamical Approach

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4. The Controlled Buffer Technique

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Application of Auxiliary Buffer to Supply the Parts According to the Demand Rate

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Conclusions

The idea to use switching server (hybrid dynamical) approach to the solution of FMS Scheduling problems opens high horizons. Realizing overlapping production, this approach may give significant economical effects. Determining the demand rates as proposed in the present material, or in more detail (and for multiple-machine case) in

Somló [4], simulation studies (based on LabVIEW, Taylor, Simple++ or others) are possible to clear the real nature of the processes.

Somlo. J., Hybrid Dynamical Approach Makes FMS Scheduling More Effective - Periodica Politechnika Budapest University of Technology and Economics, 2001

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Simulation Based Investigation

By Alexander ANUFRIEV

Ph.D. studentBudapest University of Technology and Economics,

e-mail: avanv007@hotmail.com

Demonstration of Hybrid Dynamical Approach

for FMS Scheduling

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Warning!Warning!

You should install the AVI codec to view following slides correctly.

Install Now

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• The simulation model is developed in Taylor ED discrete event simulation software.

Introduction

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Work with Model

Simulation system gives possibility to change parameters before and under the simulation run.

Parameters: Demand Rate Set up time of Server Cycle time of Server Number of Parts for every Part Type Maximum Capacity of Buffers

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Excel Connection

The system writes down the History of the production process to Excel.

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Another simulation system was developed by Koncz Tomas.

(Diploma work at BUTE)

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Optimal Robot Motion Planning

(Research also supported by OTKA T029072)

By Prof. János Somló

and Ph.D. students: Alexey Sokolov

Zoltán Nagy

Vladimir Lukanyin

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Introduction

For practical application of robots the motion planning has key role. The optimization of robot motion has special importance for FMS.

New research results were obtained in the field of: time-optimal, process-optimal, force effective, optimal trapezoidal motion planning. In the following demonstration the results are given.

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Content

1. Parametric Method for Path Planning

2. Trajectory Planning Methods

3. Intelligent, 5-th Generation, LabVIEW Based Robot Control Device

4. The AUTRAP (Automatic Trajectory Planning) System

5. Conclusion

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1. Parametric Method for Path Planning

Literature survey:

Shin K.G., McKay N.D. (1985), “Minimum-time control of robotics manipulators with geometric path constraints” IEEE of Automatic Control, AC-30, 6, pp. 531-541.

J. Somló - B. Lantos - P.T. Cat (1997), “Advanced Robot Control” pp. 430, Akadémiai Kiadó, Budapest.

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ni

hx

hx

ii

,...2,1

),(

)(

Direct geometry

Initialpoint

X

B0B

run out

Y

Z

Xn

YnZn

λCruising part

Finalpoint

Transient part

A

A0

B0

B

A0A

run in

v

Inverse geometry

mi

fqq

hq

iii

,...2,1

)()(

)(1

Parametric Method for Path Planning

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Differential Equation of the Motion From Euler-Lagrange Equation

mj

QQhvgad

dt

da

dt

dv

jextjjjj

,...2,1

;),()()(

;

;

.2

2

2

Parametric Method for Path Planning

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2. Trajectory Planning Methods2. Trajectory Planning Methods

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Trajectory Planning Trajectory Planning MethodsMethods

2.1 Time-Optimal Cruising 2.2 Optimal Robotized

Manufacturing 2.3 Force Effective Trajectory

Planning 2.4 Optimal Trapezoidal Velocity

Profile

Content

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2.2 Optimal Robotized Manufacturing

J. Somlo (1997), “Robotized Manufacturing Process Optimisation”, RAAD’97 Conference, Cassino, Italy, June 26-28, 1997

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Optimal Robotized Manufacturing

u [m/min]velocity

milling tool

s [mm/rot] feed

A

B

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Mathematical Model for Optimization

1.) System of Constraints

2.) Performance Index (cost)

3.) Tool Life Equation

},{ ..max proptiiopt vvMinv

.. proptvis obtained

Optimal Robotized Manufacturing

The extremal Tool Life Point Conception

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Optimal Robotized Manufacturing

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2.3 Constant Kinetic Energy or 2.3 Constant Kinetic Energy or Force Effective MotionForce Effective Motion

Somló J., Loginov A. (1997), “Energetically optimal cruising motion of robots”, 1997 IEEE International Conference on Intelligent Engineering Systems INES’97, Budapest, September 15-17

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222

21

22221

211

212

222

211

211

)(2

12

1

qmqqmIIrm

qIVmqIVmT

Kinetic Energy

Force Effective Motion

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Force Effective Motion

2q12qq

V

tg

tg

122

12

2

qqq

qq

q

)]([

2)(

tg2

1

21

21

2222

22221

211

IS

Tq

qqmqmIIrmT

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Constant Kinetic Energy General Case (Podurajev J., Somlo J. (1993), “ A New Approach to the Contour Following Problems in Robot Control (Dynamic

Model in Riemann Space) )”, Mechatronics (GB) Vol. 3. N2.)

- the momentary power developed by the drives; - the power given by the end-effector to the object of the work – the overall kinetic energy

texNtmN

dtdT

tmN

texN

T

Force Effective Motion

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Dynamic model in the Riemann space

11

2/11

2

JIJH

kgSHds

dlR

TS

RFS

T

T

NV

Force Effective Motion

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Constant overall kinetic energy

constSS 0

The constant kinetic energy motion of given position and velocity provides the highest external force

Force Effective Motion

0)( SR

SR

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2.4 Optimal Trapezoidal 2.4 Optimal Trapezoidal Velocity ProfileVelocity Profile

J. Somló - B. Lantos - P.T. Cat (1997), “Advanced Robot Control”, pp. 430, Akadémiai Kiadó, Budapest

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Optimal Trapezoidal Velocity Profile

• Time-Optimal motion has been determined • Trajectory is non-special

Motion with a constant acceleration (deceleration) on the transient part

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START CR STOP

Sa Ea

ES max

crv

Optimal Trapezoidal Velocity Profile

a) )(sa touches )( START at 0 point

b) )(sa goes through the point where)( START and )( CR crosses,and

c) )(sa touches )( START between the above two cases.

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3. . Intelligent, 5-th Generation, Intelligent, 5-th Generation, LabVIEW Based Robot Control DeviceLabVIEW Based Robot Control Device

Personal computer: Pentium II 400 MHz

Control servo drive cards PCL-832 „ADVANTECH”

Multifunctional card ACL-8112PG

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Main features of control servo Main features of control servo card PCL-832card PCL-832

Independent 3-axis servo control Proportional control Built-in F/V converter Servo update time 2ms..2s

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PCL-832PCL-832 Operational principlesOperational principles

DDA PULSEBUFFER

buffer

DDAGENERATOR

CONTROLLOGIC

SUMMINGCIRCUIT

GAIN &OFFSETCIRCUIT

GAINBUFFER

ERRORCOUNTER

12-BITDAC

SERVOMOTORDRIVER

MOTORVELOCITY

BLOCKF/V

CONVERTER

ENCODER FEEDBACK

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Multifunctional cardMultifunctional cardACL-8112PGACL-8112PG

ADC, 16 channels – potentiometer sensors voltage (manipulator

calibration)– voltage current sensor– information about velocity

Programming timer– measure of time system

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DrivesDrives

Power supply Amplifiers 12A8

„ADVANCED MOTION”– PWM– information about

current

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IndustrialIndustrial robot PUMA 560 robot PUMA 560

6 joints Drives DC-motors Position sensors

– encoders (motion control)

– potentiometer sensors (manipulator calibration)

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The main characteristics of this The main characteristics of this control device:control device:

Flexibility Cheap Great possibilities for system monitoring Software module structure Nevertheless, sophisticated

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4. The AUTRAP (Automatic 4. The AUTRAP (Automatic Trajectory Planning) System Trajectory Planning) System The developed LabVIEW based robot control system make possible to realize automatic robot trajectory planning. Recently, we develop such a system named AUTRAP. The AUTRAP system realizes all of the 4 methods for trajectory planning as described in the present paper. The different methods are activated as the user gives one of the commands: TIME-OPT, PROCESS-OPT, FORCE-EF, OPT-TRAP. Override facility is provided for all of the 4 methods. It proportionally decreases the velocities as the override value is given by the user.

Parametric Method for Path Planning

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ConclusionsConclusions

Earlier, almost exclusively, constant velocity or trapezoidal velocity profiles were used in robot motion planning. Recently, as it was outlined in the paper, at least 4 different, rather sophisticated approaches are possible for this problem. The experimental LabVIEW based system developed by us, which uses open system architecture principles, make possible to realize sophisticated control laws. The AUTRAP system, which is under development, implements the outlined methods in an automatic way.