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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
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
PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture
Robot Arm
Control Wardrobe
Original Architecture
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
PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture
Robot Arm
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
PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture
Control Wardrobe
• Power Tray.
• Control Panel.
• Control Module.
• I/O Module.
•Amplifier Module.
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
...
PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture
Original Architecture
Motorde
Articulación
Potenciómetro
Encoder
LSI-11/02 Interfaz
ServoDigital
6503
D/AServo
Analógico
Amp.
A/D
28 ms
875 s
Controlador PUMA
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
PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture
Original Architecture
• LSI –11/02 Processor.
• Digital Servos.
• Analogical Servos.
• Amplifiers.
• Incremental encoders.
• Potentiometers.
...
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
PUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 ArchitecturePUMA 560 Architecture
Original Architecture
Motorde
Articulación
Potenciómetro
Encoder
LSI-11/02 Interfaz
ServoDigital
6503
D/AServo
Analógico
Amp.
A/D
28 ms
875 s
Controlador PUMA
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
Opened Control ArchitectureOpened Control ArchitectureOpened Control ArchitectureOpened Control Architecture
...
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
Opened Control ArchitectureOpened Control ArchitectureOpened Control ArchitectureOpened Control Architecture
...
Hardware Original
Motorde
Articulación
Encoder
PC
Tarjetasde
Adquisiciónde
Datos
Amplificadoresde Potencia
PUMA
Potenciómetro
Ordenador
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
Opened Control ArchitectureOpened Control ArchitectureOpened Control ArchitectureOpened Control Architecture
• PCL-812.
• PCL-833.
• PCL-726.
...
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
Opened Control ArchitectureOpened Control ArchitectureOpened Control ArchitectureOpened Control Architecture
...
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
Opened Control ArchitectureOpened Control ArchitectureOpened Control ArchitectureOpened Control Architecture
Brake circuit
• Original braking system.
• Brake control by computer.
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
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
...
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
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
...
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
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
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
...
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
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
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
...
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
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
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
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
...
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
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
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
...
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
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
...
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
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
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
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
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
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
...
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
Movement simulation through the Dynamic Movement simulation through the Dynamic ModelModelMovement simulation through the Dynamic Movement simulation through the Dynamic ModelModel
Results
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
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
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
Control of manipulators RobotsControl of manipulators RobotsControl of manipulators RobotsControl of manipulators Robots
...
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
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
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
Control of manipulators RobotsControl of manipulators RobotsControl of manipulators RobotsControl of manipulators Robots
...
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
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
Control of manipulators RobotsControl of manipulators RobotsControl of manipulators RobotsControl of manipulators Robots
Control by passiveness
...
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
Control of manipulators RobotsControl of manipulators RobotsControl of manipulators RobotsControl of manipulators Robots
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
...
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
Control of manipulators RobotsControl of manipulators RobotsControl of manipulators RobotsControl of manipulators Robots
Control by inverse dynamic
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
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
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
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
...
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
ConclusionsConclusionsConclusionsConclusions
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