tuhh im nächsten jahrtausend · pdf filerobotic and medicine robot-, hand-eye- relation...
TRANSCRIPT
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.1 04.05.2015
Lecture Topics
1. Introduction
2. Sensor Guides Robots / Machines
3. Motivation Model Calibration
4. 3D Video Metric (Geometrical Camera Model)
5. Grey Level Picture Processing for Position Measurement
6. Light and Perception as well as Black-and-White- and Colour
Pictures
7. Model Calibration
8. Video Metric Sensor Calibration (Geometrical Camera Model)
9. Video Metric Camera Model (Fourier 2D)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.2 04.05.2015
Motivation
Model Calibration
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.3 04.05.2015
Video der Firma Volvo
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.4 04.05.2015
Applications
Transportation- and Flight Systems
R ö n tg e n q u e lle
R ö n tg e n g e rä t
sc h e m a tisc h
S tra h le n k e g e l
B ild p la t te
Z e n tra ls tra h l
Measuring Techniques,
Robotic and Medicine
Robot-, Hand-Eye-
Relation und
Work Piece Frame
Kuka Ahlers
Tool Machine
Work Piece Frame
SHW
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.5 04.05.2015
Accuracy Behavior of the Robot before and
after the Model Calibration
Calibrated Model
Non calibrated
Model
/ 100 µm
/ 1 mm
RMS x / m y / m
x / m y / m
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.6 04.05.2015
Positionsfehler
-5,00E-04
-4,00E-04
-3,00E-04
-2,00E-04
-1,00E-04
0,00E+00
1,00E-04
2,00E-04
3,00E-04
4,00E-04
5,00E-04
1 3 5 7 9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
Pose-Nr.
[m]
y
Accuracy behavior of the Sensor and
Robot Model Calibration in x/y Direction
Position Error
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.7 04.05.2015
Research Center CFK-Nord (Stade)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.8 04.05.2015
Load change
Aging and Attrition
as well as
Changed Environmental Condition
Operating
point change
Time Variance of the System Properties
Kuka
Boeing
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.9 04.05.2015
Adaptive Production Technology
Pose Error
Assembly
(5 – 10 mm)
Pose and Shape
Error Linear Axis
at TCP
(5 – 20 mm)
Pose Error
Robot
(1 – 5 mm)
Process Pose
Error at TCP
(0,5 – 1 mm)
Process Force
influenced
Pose Error
(0,5 – 1 mm)
Accuracy
(0,1mm auf
10 to 20 m
-> 5µm/m)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.10 04.05.2015
Assembly Shape and Pose Correction I
• Flexible controlled Shape
• Non expensive Gripper
• 6D Controlled Forces
• Multi dimensional elasticity model
• Shape and Pose accuracy converge after
2 – 4 Iterations to machine repeatability
(50 to 100 µm)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.11 04.05.2015
Assembly Shape and Pose Correction II
Multi-Frames with separate and
cooperating Movements
(Adaptive hierarchical control process)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.12 04.05.2015
Absolute PositionierAbsolute Positionier--
fehlerfehler der Großder Groß--
bauteilebauteile
0,05 bis 0,1 mm0,05 bis 0,1 mm
(nach typisch 2-4 Iterationen)
Preiswerte Greifer,Preiswerte Greifer,
StandardStandard--IndustrieIndustrie--
roboterroboter und preisund preis--
werte Hallenwerte Hallen--
fundamentefundamente
Fotos:
Roman
Jupitz
Experimental Field for Wide Body Shape and
Pose Automatic Control Loop
Inexpensive
gripper,
robots and
hall foundations
Absolute
positioning errors
0,05 – 0,1 mm (after typically 2-4
iterations)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.13 04.05.2015
Absolute PositionierfehlerAbsolute Positionierfehler
der Großbauteile der Großbauteile
0,1 bis 0,2 mm0,1 bis 0,2 mm
(nach typisch 2-4 Iterationen)
Preiswerte Greifer, StandardPreiswerte Greifer, Standard--
Industrieroboter und preiswerte Industrieroboter und preiswerte
HallenfundamenteHallenfundamente
Fotos: Roman Jupitz Symposium 2004Symposium 2004
Wide Body handling with Cooperating Robots
Inexpensive gripper,
robots and
hall foundations
Absolute positioning
errors 0,1 – 0,2 mm (after typically 2-4 iterations)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.14 04.05.2015
Laser Scanner Remote Welding
Laser-Scanner
Laser-Scanner Mirror Movements
are to be derived from Constructional Data (No Teaching!)
TRUMPF
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.15 04.05.2015
Sensor guided Remote Laser Welding
Emmelmann
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.16 04.05.2015
Fixateur Extern, Robotic und Picture Processing
R ö n tg e n q u e lle
R ö n tg e n g e rä t
sc h e m a tisc h
S tra h le n k e g e l
B ild p la t te
Z e n tra ls tra h l
a b
Medicinal 3D Picture Processing
Fixateur Extern /
Robotic
3D x-Ray Technology
K u g e lg e le n k
S te l lsc h ra u b e
D is tr a k to r I l is a ro w -R in g
Video Metric to Measure Pose of
x-Ray Source and Picture Plane
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.17 04.05.2015
Machine Off Line Programming
Separation from plant enterprise and programming
B lu m e
Absolute pose errors require time consuming teaching
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.18 04.05.2015
System Approach in Mechanical Engineering
Computer
Aided Manufacturing
Computer
Aided Design
Off-Line-
Programmig
Sensor-TCP Calibration Body
Palette System
with Index
Tool
Gripper
Option
Machines x
yz
w
Sensor
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.19 04.05.2015
Examples
System Identification
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.20 04.05.2015
System Identification at the Ohm's Resistance
u
i
Structure
Identification ?
Parameter Identification ?
u R i
Ru
i
Measure Voltage u and Current i ,
than Calculate Parameter R !
x
p
yy = f (x ,p )
P a ra m e te r
S te u e r-
w e rte
A u s g a n g s -
w e rte
concentrated
Element
Input
Values
Parameter
Output
Values
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.21 04.05.2015
, {1, , }i i
i I y A p B x
1 1i I i I y y y A p B x x x
Y A p B X
A p Y B X
1
, R an k D im
p A Y B X A p
System Identification of Linear Vector Maps
x
p
yy = f (x ,p )
P a ra m e te r
S te u e r-
w e rte
A u s g a n g s -
w e rte
Input
Values
Parameter
Output
Values
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.22 04.05.2015
System Identification with Linearization I
( , ) , {1, , }i i
i I y f p x
0 0( , ) ,
i i
py J p x p R 0 R 0
0 0 0 0, ( , ) ,
i i i i i y y y y f p x p p p with
Linearization
Vector Map
, {1, , }i i
i I y A p
, {1, , }i i
i Ix y
Measured Data
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.23 04.05.2015
0 1
0
0
( , )
( , )
( , )
i
I
p
p
p
J p x
Α J p x
J p x
1
' , R an k D im ,
p A y A p with
t
t t t
1'
i Iy y y y
and
System Identification with Linearization II
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.24 04.05.2015
The system identification appears
to be very simple.
What do you mean, are this is in
principle like that?
Why not?
System Identification I
x
yz
w
Kuka
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.25 04.05.2015
• Structure of the model admits not from the beginning
• Spatially distributed non linear systems
• Spatially concentrated non linear systems
• Spatially distributed or concentrated features of the
systems not sufficiently known
System Identification II
• Input and output values must be measurable.
Therefore principle sensors are needed.
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.26 04.05.2015
Potentials of the System Identification
• Static and dynamic parametric models
Control, Regulation as well as Sensor Models
• Accuracy increase of the stationary and dynamic behavior by
model calibration
(Positioning and Path error, Automatic Controller Optimization,
Adaptive Automatic Controllers etc..)
• Calibration, Quality Assurance, Error-, Aging- as well as Attrition-
Recognition (In the manufacturing process and at the customer in the
service)
• Linear Independence Parameters makes Hierarchical as well as
Sub Set Parameter Calibrations possible
(Pre- and Re-Calibration at the manufacturer and customer)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.27 04.05.2015
Linear approximation in one and
multidimensional case
Base for Iterative
Optimization Procedures
(Regula falsi
Newton Method)
Base for Computation
of the
inverse Mapping
Base for Iterative
Identification
Algorithms
Analysis
Analysis
Base for Error
Propagation Analyses
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.28 04.05.2015
Learning
by
Use and Repetition
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.29 04.05.2015
Hand Eye Coordination
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.30 04.05.2015
W a h rn e h m u n g
M o d e llb ild u n g
P la n u n g
A k tio n
M o to r is c h e
S te u e ru n g
Long Time Memory and
neuronal Catenations needs
Repetitions
Lerning and Remembering
Perception
Modeling
Scheduling
Action
Neuromuscular
Movement
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.31 04.05.2015
Memory Quota
2 0 %
3 0 %
5 0 %
7 0 %
9 0 %
H ö re n
S e h e n
H ö re n u n d S e h e n
H ö re n , S e h e n u n d D is k u tie re n
H ö re n , S e h e n , D is k u tie re n u n d Tu n
H a n d b u c h H o c h s c h u l le h re
Hearing
Seeing
Hearing and seeing
Hearing, seeing and discuss
Hearing, seeing, discuss and doing
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.32 04.05.2015
Matlab-Class-Room-License to Practicing
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.33 04.05.2015
Hand Eye Calibration
Movement
Measure
Iterative Model Calibration
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.34 04.05.2015
System Analysis
and
Calibration
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.35 04.05.2015
Annahmen zurVereinfachung
VereinfachungAufstellen derGleichungen
TheoretischesModell
- Struktur- Parameter
Vereinfachtes theoretisches
Modell
A-priori-Kenntnisüber das System
Struktur unbe-bekannt kannt
Experiment
Identifikation
parame-tr isch
nicht parame-trisch
parame-trisch
nicht parame-trisch
Experim. ModellVergleich
TheoretischeAnalyse
ExperimentelleAnalyse
Qualität
neinja
Ende
Methodology Systems Analysis
Theoretical
Analysis
Experimental
Analysis
Assumption
Simplification
Set up the
Equations
Theoretical
Model Structure/Param.
Simplification
Experiment
A priori Knowledge
Structure known / unknown
Identification
Experiment
Model
compare
Q
Simplified Theoretical
Model
no yes Q := Quality
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.36 04.05.2015
Model Quality and Process Knowledge
M := Model Quality
K := Process Knowledge Isermann
ME := Mechanical Electrical
Systems
ET := Energy-Technical
Systems
VT := Process Engineering
systems
Theoretical
Model Design Identification
Attainable
Model
Quality
Knowledge of
Internal Processes
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.37 04.05.2015
Isermann
Model Quality and Investment
Expenditure
(Costs)
Expenditure
(Costs)
Attainable
Model
Quality
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.38 04.05.2015
Problem Definition Robot I
Decrease of the manufacturing tolerances of the
construction components technically and economically
limited.
Repetition Accuracy
50 - 100 µm
Absolute PositioningAaccuracy
2 - 10 mm
Robot frame is indicated approximately or not
Angle error of 0.1° of 1 m length results in a arc length error of 1.7 mm
zero errors of the sensors and
arc errors between world and robot frame
=> problem:
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.39 04.05.2015
x
z
x
z
o h n e e rw e ite r te R e g e lu n g
S o llb a h n
Is tb a h n
0 ,5 m0
,5m
0 ,10 ,8 0 ,9
t/s
0 ,5 m /s
x
z
e rw e ite r te r R e g le r
Weber
Problem Definition Robot II (Path Error)
Without extended regulation Extended regulation
Destination Path
Actual Path
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.40 04.05.2015
Robot Model
Pose Error
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.41 04.05.2015
0 5 5 4 3 2 1 1 2 3 4 5 5, 6
I I I I I I i I I I I I II
r D D R R R R r t t t t t t
Kinematics Transformation II
3 3 3 3
1 1 1 1 1, w ith , ,
x
i i i i i i i r R r t R t r
Coordinates Transformation (classical)
Si
Si+ 1
i- te s G e le n k
SR
Ti
SG
S0
W K S
R o b o te r -
K S
T C P
( + 1 )- te s
G e le n k
i
i- te s
G e le n k
ti
x i+ 1
y i+ 1z
i+ 1
x i
y i z
i
p := Parameter Vector
x := Ideal Machine Coordinates
i-th Joint
i-th
Joint
(i+1)-th
Joint World-FR
Robot-
FR
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.42 04.05.2015
( , ) ( , )j j j
j
x T T p f p x
Transformation T with an open Kinematics Chain
Products of the homogeneous
Matrices Tj
Kinematics Transformation IV
Advantages of
Homogeneous Coordinates
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.43 04.05.2015
Kinematics Transformation V
p := constant joint parameter of the cinematic model
x := ideal variable drive coordinates also
ideal machine coordinates called
xS := variable sensor coordinates of the internal
position measuring systems and/or real variable
machine coordinates
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.44 04.05.2015
Internal Sensor
Measured Machine
Coordinates
A S S A( )x f x
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.45 04.05.2015
T f p , x m xk k kS
'
S
'
S0d i d ie j
Kinematics Transformation with Sensor Coordinates
Sensor zero position errors and sensor
gradient errors can be interpreted as
parameters of the model.
f m x p x f p x' ' '( , , , ) ( , )
S
'
S
'
S S0
FH
IKf p x p p
' ' '( , ) ,
S S
't
S
't
t
t
m xk kd i d i0
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.46 04.05.2015
ST C P
TT C P
A
SA
T C P
rT i
di( )p
T C P
A
A
rB i
Wikipedia
A T C P T C P
B A TE
( )i i i
d r T p r
D 0i i i id d d D
{1, .. . , 6}i
Parallel Kinematic I
Analytic Inverse Kinematic Transform
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.47 04.05.2015
T C P
A 0
D
0
:= N u ll P o se
:= - th D r iv e D is ta n c e
:= - th C a rd a n Jo in t D is ta n c e
:= - th O f f se t in N u ll P o se (S e n so r O f f se t)
:= - th D is ta n c e P a r t
i
i
i
i
d i
d i
d i
D i
p
Parallel Kinematic II
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.48 04.05.2015
Causes for Absolute Positioning Errors
x
yz
w
1. Kinematics Parameters: (zero position, alignment and length)
2. Relation from Machine FR
to World FR
3. Variations
Temperature
4. Joint
Elasticity
5. Element
Elasticity 6. Transmission Error (Linearity, Backlash … Error)
7. Bearing
Backlash
8. Position
Sensor
9. Friction
10. Controller: (rounding and numeric
procedural errors)
Kuka
FR := Frame
= coordinate system
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.49 04.05.2015
J u d d ‘8 7 , B e rg ‘9 0 ,
M e y e r ‘9 1 , T ra d t ‘9 1
T h e o d o lite n -
M e ß v e r fa h r e n T ra d t ‘9 1 , B e y e r ‘9 5 ,
G e u e n s ‘9 7
V id e o m e tr is c h e
V e r fa h re n
T C P - F la n s c h
L E D -
P a n e l
C C D -S e n s o r-
s y s te m
W a ts o n ‘8 5 , L a u ‘8 5 ,
M a y e r ‘8 6 , P re n n in g e r ‘9 2
In te r fe ro m e tr is c h e
L a s e r -T ra c k in g -V e r fa h re n
M e ß k o p f-V e r fa h re n
P o s e - u n d P o s it io n s -
s e n s o re n
in d u k tiv , ta s te n d :
u ltra s c h a ll:
v id e o m e tr is c h :
W a rn e c k e ‘8 6 , S c h ie le ‘8 7 ,
G o s s e l ‘9 6
S to n e ‘8 6 , B e rg ‘9 0
D a in is ‘8 5 , Z h u a n g ‘9 6 ,
R o o s ‘9 6 , W o lln a c k ‘9 6
K a lib r ie rk ö rp e r
Theodolites
Laser-Tracking
Measuring Head
(TCP-Sensor)
Calibration body
TCP Flange CCD/CMOS 3D Sensor Videometric
Inductively, tactile:
Ultrasonic:
Videometric:
External 3D Position Sensors
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.50 04.05.2015
SM
S
TM
T
T
MesswerteMesswerte ModellwerteModellwerte
Measured Values Model Values
Homogeneous Error Transformation I
1 MΔT T T
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.51 04.05.2015
2 t
E E EM in = M in ,p p p
M 1
E( ) ( ) ( )
T T p T p T p I
M
E p p p
Principal ambiguities of the pose and periodicity
ambiguities are not present here (See inverse RPY-Transform).
The minimization of the pose instead of the
homogeneous matrix T generates the orthogonal
rotation matrix correctly.
Homogeneous Error Transformation II
These approach is very important for pose calibration.
with
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
MMC.52 04.05.2015
END