study and implementation of industrial robots dynamic controllers in real-time

PUMA 560 Architecture

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Núria Rosillo Guerrero

References Trajectories

Control of manipulators Robots

Opened Control Architecture

Obtaining of Robots dynamic model by Gibbs-

Appell formulation

Movement simulation through the Dynamic

Model

Study and Implementation of Industrial Robots Dynamic Controllers

in Real-Time

Name:Núria Rosillo Guerrero

Faculty:Computer Science Engineering

Department:Mathematics Science and Computation

Universidad Cardenal Herrera CEUHalmstad, 21 de abril de 2023


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Appell formulation


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PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture

Robot Arm

Control Wardrobe

Original Architecture


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Appell formulation


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Robot Arm


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Appell formulation


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Control Wardrobe

• Power Tray.

• Control Panel.

• Control Module.

• I/O Module.

•Amplifier Module.


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Appell formulation


Model

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Motorde

Articulación

Potenciómetro

Encoder

LSI-11/02 Interfaz

ServoDigital

6503

D/AServo

Analógico

Amp.

A/D

28 ms

875 s

Controlador PUMA


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Appell formulation


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• LSI –11/02 Processor.

• Digital Servos.

• Analogical Servos.

• Amplifiers.

• Incremental encoders.

• Potentiometers.

...


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Appell formulation


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Motorde

Articulación

Potenciómetro

Encoder

LSI-11/02 Interfaz

ServoDigital

6503

D/AServo

Analógico

Amp.

A/D

28 ms

875 s

Controlador PUMA


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Appell formulation


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Opened Control ArchitectureOpened Control ArchitectureOpened Control ArchitectureOpened Control Architecture

...


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Appell formulation


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Hardware Original

Motorde

Articulación

Encoder

PC

Tarjetasde

Adquisiciónde

Datos

Amplificadoresde Potencia

PUMA

Potenciómetro

Ordenador


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Appell formulation


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• PCL-812.

• PCL-833.

• PCL-726.

...


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Appell formulation


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...


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Appell formulation


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Brake circuit

• Original braking system.

• Brake control by computer.


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Appell formulation


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Obtaining of Robots dynamic model by Obtaining of Robots dynamic model by Gibbs-Appell formulationGibbs-Appell formulationObtaining of Robots dynamic model by Obtaining of Robots dynamic model by Gibbs-Appell formulationGibbs-Appell formulation

...


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Appell formulation


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Solve the Inverse Dynamic Problem Gibbs’s Function :

Gibbs’s function for the solid i is given by

2

1

1

2

n

i ii

G m a

T T T1 1( ) ( ) ( )

2 2i i i ii i G G i G i i i G iG m r r I I


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Appell formulation


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Solve the Inverse Dynamic Problem

If we express the tensorial and vectorial magnitudes considering a reference system located in the iesim bar.

For a system consisting of n bodies, Gibbs’s function could be given by:

T T T1 1( ) ( ) ( )

2 2i i i i

i i i i i i i i ii i G G i G i i i G iG m r r I I

1

( 1,2 )n

ii

G G i n


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Appell formulation


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...

Solve the Inverse Dynamic Problem The Gibbs-Appell’s movements equations are obtained leading respect to the generalized accelerations , of that way we obtain the inertial forces that correspond to the generalized external forces j

Operating:

jq

( 1, 2 )

ni

ji j j

Gj n

q

T

( )

i

i i i

Tiin nGi i i i i ii

j G i i G i i Gi j i jj j

j j

rm r

q q

A B

I I


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Appell formulation


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Complexity n algorism

From D-H and off-line:

With a recursive way:

A term:

B term:

T

( )

i

i i i

Tiin nGi i i i i ii

j G i i G i i Gi j i jj j

j j

rm r

q q

A B

I I

1ii

R1

1,i i

iO Or

ii

iq

i

iω

i

iOr

i

iGr

Tiii

i ii

i i iTiii

i ii

A q

A B

Bq

...


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Appell formulation


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Complexity n algorism

Algorism Complexity n=6

Luh, Walker and Paul

(x) 121n -112

(+) 90n - 82

614

458

Proposed algorism (x) 121n –136

(+) 91n - 116

590

430

...


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Appell formulation


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Direct Dynamic Problem

Algorism that simulate the dynamic behavior of industrial robot.General form of the movement equation:

Obtaining BIAS vector:

Obtaining gravity vector:

)(),()( qGqqqCqqM ),()( qqbqqM

0q

0 , 0q q


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Appell formulation


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Direct Dynamic Problem

Obtaining the system inertias matrix.

i

ii

iiT

ii

i

iCi

T

iCi

iii q

wEw

q

rrmM

i

jj

jjT

ii

j

jCj

T

jCj

jij q

wEw

q

rrmM


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Appell formulation


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Movement simulation through the Dynamic Movement simulation through the Dynamic ModelModelMovement simulation through the Dynamic Movement simulation through the Dynamic ModelModel

Dynamic equation:

DDP: IDP

System to solve:

Controller Simulator

q, v, aqd

)=+G(q,q),q+C(q,q)M(q,

)M(q,

b)(q,=Mq

1 q qdt dt

q

...


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Appell formulation


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Movement simulation through the Dynamic Movement simulation through the Dynamic ModelModelMovement simulation through the Dynamic Movement simulation through the Dynamic ModelModel

Results


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Appell formulation


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Control of manipulators RobotsControl of manipulators RobotsControl of manipulators RobotsControl of manipulators Robots

...

Development of a general expression to the controllers by passiveness and inverse dynamic

= Mâ + C + G


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Appell formulation


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...

Control by passiveness

The control based in the passiveness with point to point strategies can be seen as particular cases of this control law.

We obtain the gravitational term a partir de:

doing that and

e p dK e K v g

),(),,(),( qGqqqCqqM

0q 0q


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Appell formulation


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Control g v

PD + G(q)

PD + G(qd)

Compensador Lineal + G(q)

Compensador Lineal + G(qd)

Diferenciación Aproximativa + G(q)

Diferenciación Aproximativa + G(qd)

PID

PI2D


...

q

G qd( , ) q

G q( , )

eKLxx d

eKLxx d

diagb p

p aqi

i

diagb p

p aqi

i

q

i

i

b pdiag q

p a

G q( , )

G qd( , )

G q( , )

G qd( , )

K ei

t

0 dt

0

( )t

ii

i

b pK e diag q dt

p a


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Appell formulation


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Control by passiveness

...


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Appell formulation


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Control by inverse dynamic

We start from this equation

We will establish a control over the trajectory, calculating a of that way

M(q, )a+C(q,q, )q+G(q, )

vKdeKp **

veKdeKpqd **

1

0

·*** dteKivKdeKp

Type of control over the trajectory a

Point to point

Follow-up of the trajectory

Follow-up of the trajectory with integral action

...


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Appell formulation


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Control by inverse dynamic


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Appell formulation


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Reference TrajectoriesReference TrajectoriesReference TrajectoriesReference Trajectories

Ramp entry Natural cubic spline

...

_ _

errorAp

n p m

2 3( )i i i i iY t a b t c t d t


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Appell formulation


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Reference TrajectoriesReference TrajectoriesReference TrajectoriesReference Trajectories

Fourier Series

01

( ) sin(2 ) cos(2 )2 2

iN i il l

i f f ii f f

a bq t f lt f lt q

f l f l

...


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Appell formulation


Model

ConclusionsConclusionsConclusionsConclusions

study and implementation of industrial robots dynamic controllers in real-time

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