PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by

PUMA 560 Architecture

Main Page

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, 18 de abril de 2023


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Appell formulation


Model

PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture

Robot Arm

Control Wardrobe

Original Architecture


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Appell formulation


Model


Robot Arm


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Appell formulation


Model


Control Wardrobe

• Power Tray.

• Control Panel.

• Control Module.

• I/O Module.

•Amplifier Module.


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Appell formulation


Model

...



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


Model



• LSI –11/02 Processor.

• Digital Servos.

• Analogical Servos.

• Amplifiers.

• Incremental encoders.

• Potentiometers.

...


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Appell formulation


Model



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


Model

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


Model


• 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


Model

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


Model

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

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PUMA 560 Architecture Main Page References Trajectories Control of manipulators Robots Opened Control Architecture Obtaining of Robots dynamic model by