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TRANSCRIPT
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.1 10.04.2015
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
SGR.2 10.04.2015
Sensor Guided
Robots / Machines
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.3 10.04.2015
Mounting Task I
TCP
ATWanted:
Known: OA
OB ( )tTS
A
TTCP
A
SG
6D Pose 6D
6D
6D
6D
6D
6D
STCP
SG
SOB
SO
SOA
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.4 10.04.2015
6D
6D
6D
6D
6D
6D
STCP
TTCP
A( )t
TO
A
TOB
G
TG
TCP
TOA
O
TOA
OB( )t
SG
SOA
SO
SOB
SA
1 1 1
TCP O OA OA OB G
A A O OB G TCP( ) ( )t t
T T T T T T
Mounting Task II
Poses from CAD model lead to
relatively big systematic assembly
pose errors.
Therefore the poses must be
taught
or we realize sensor guided
robots/machines. see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.5 10.04.2015
S =SR C0 S
C1
SL
xL
Θy
SO
an
am
ai
a1,2,3
a
r
:= Richtungsvektoren freie Vektoren := Ortsvektoren
KS := Koordinatensystem
ri rk
rj
2 Punkte aufObjektkanten(nicht parallele Geraden)
Jeweils 3 Punkte auf2 Objektebenen definieren2 Normalenvektoren undSchnittgerade(nicht parallele Ebenen)
Jeweils 3 Punkte auf3 Objektebenen definieren3 Normalenvektoren, 2 Schnittgerade und1 Punkt(nicht parallele Ebenen)
3 Punkte einesMerkmals(Kreis, Ellipse)(nicht auf einer Gerade liegend)
Methods for pose measurement
3 Points of feature
(circle, ellipse)
(not lying on a straight line)
2 points on
object edge
(non-parallel straight lines)
Each 3 points on
2 object planes define
2 normal vectors and
Intersections
(non-coplanar planes)
Each 3 points on
3 object planes define
3 normal vectors,
2 intersection lines and
1 point
(non-coplanar planes)
a := Direction vector
free vectors
r := Position vector
CS:= Coordinate system
3D Measurement
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.6 10.04.2015
The positioning errors grows with the movement or joint
path length.
This is valid both for teaching and absolute positioning of
calibrated robots/machines.
Preliminary Considerations I
How can we use these facts for the attainment of high
precisions?
With measuring of local poses in the environment of the
production or assembly task increase the precisions !!!!!
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.7 10.04.2015
φS φ
x
xS
xI
real
destinationabsolut positioning error
machine coordinates calculated via debitmodel
Preliminary Considerations II
Analogue for complex robot models
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.8 10.04.2015
x
ΔxxT
xTS
xTI
φφTSφT
Δφ
local absolut positioning error
machine coordinatecalculated viadebit model
Advantages of teaching and local sensor guiding
Preliminary Considerations III
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.9 10.04.2015
Spatial Eyesight and Measurement
A spatial eyesight
needs at least two
or more eyes
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.10 10.04.2015
Hand eye coordination
is in robotics
equal to
tool or gripper sensor calibration.
This means that the external parameters or
transformations must be calibrated between
sensor and working frame.
External Sensors at the TCP I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.11 10.04.2015
External Sensors at the TCP II
STCP
STCP
SI
SOA
SOB
SG
SO
SA
TC0
M
TOA
O
T p( ( ))OA
OB t
TC0
TCP
SC0
SC1
TC0
C1
T p( ( ))TCP
A t
TM
O
TO
A
SM C0;O
ri
12
3
6D
6D
6D
6D6D
6D
6D
6D
6D
6D6D
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.12 10.04.2015
C0
S S S( , ) Parametric Sensor Modeln nr f p x
TCP
A A A A( ) ( , ) Parametric Actuator Modelm mT p f p x
External Sensors at the TCP III
4 4 Homogeneous Transform1
R tT
0
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.13 10.04.2015
pC0TCP := Pose sensor (C0) to TCP (coordinate system),
pGTCP := Pose gripper to TCP,
pOA := Pose object to actuator,
C0;Orm := Measurement frame coordinates in SC0 and SO,
pOBG := Pose object B to gripper,
pGI := Pose gripper to mechanical interface,
pITCP := Pose mechanical interface to TCP,
pMC0 := Pose measure frame to sensor (Using three 3D Points),
pRO := Pose reference to object (Using three 3D Points form CAD),
pOBOA := Assembly Pose,
pOAO := Local object Pose Pose := Position and Orientation (6D)
External Sensors at the TCP IV
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.14 10.04.2015
SR
SD
TR
TD
TR
D
R := real
D := destination
C0 R M -1 M
C0 D C0 D C0 RT T T
Error pose measure frame
M C0 -1 OB OA OA -1 M
C0 D TCP TCP OB D O OT T T T T T
Destination pose
OB I G OB
TCP TCP I GT T T T
Tool transform
Correction pose C0 C0 R -1
V C0 DT T
C0 C0 C0
1 Vi i T T T
Relative Pose movement
External Sensors at the TCP V
Measured Data
CAD Data
CAD Data or better identified
via measurement
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.15 10.04.2015
STCP
SC0
6D6D
6D
TC0
V
TC0
TCP TC0
TCP
TTCP
V
6D
6D
6D
6DC0
TCP TCP
C0
TCP
V ?T
TCP C0 C0 C0 -1
V TCP V TCPT T T T
External Sensors at the TCP VI
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.16 10.04.2015
Small pose modifications results too low absolute pose
errors. We obtain this behavior for teaching and the sensor
guided systems.
TCP
Vp
External Sensors at the TCP VII
A calibrated robot model enhanced maximum possible
changes in the pose getting the same destination
precision.
TCP
Vp
The constant transformations
and
must be known or better calibrated.
C0
TCPT
OB I G OB
TCP TCP I GT T T T
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.17 10.04.2015
Adaptive Milling Cell I
Y
X
Z
6D-Kraftmessung
6D-Werkzeug-korrektur
6D-Lage-messung
6D-Bauteillage
6D Force
Measurement
6D Pose
Measurement
6D Tool
Correction
6D Body
Pose
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.18 10.04.2015
6D
TI
TCP
TTCP
A
TB
A
TW
I
TM
TCP
TW
B
TMB
WB
TMB
S
TS
TCP
6D
6D
6D
6D
6D
6D Pose
Bauteil
Bauteil-mess-stelle
Adaptive Milling Cell II
Body
Body
Measure
Point
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.19 10.04.2015
A := Actuator Base Frame
D := Destination
B := Body Frame
I := Interface Frame
M := Measure Frame (Laser Tracker)
MB := Measure Frame Body
R := Real
S := Sensor Frame
TCP := TCP Frame
W := Work Frame
Adaptive Milling Cell III
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.20 10.04.2015
Calculate the sensor guided homogeneous Transform
Analyze what we must measure or identify
Use the measured information to move to the correct
working pose
TCP
AT
MB
SRT
Sensor guided Robots I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.21 10.04.2015
11TCP B W MB MB S
A A B WB S D TCP
1MB S I W MB
S D TCP TCP I WB
, with
Τ Τ Τ Τ Τ Τ
Τ Τ Τ Τ Τ
1
MBR MB MB
S D S D S R
T T T
Sensor guided robot equation
Sensor real to destination Transform S
R
SD
TR
TD
TR
D
1
R
D D R
T T T
Sensor guided Robots II
Data comes from CAD
Identification problem
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.22 10.04.2015
6D
TI
TCP
TTCP
A
TB
A
TW
I
TM
TCP
TW
B
TMB
WB
TMB
S
TS
TCP
6D
6D
6D
6D
6D
6D Pose
Bauteil
Bauteil-mess-stelle
Body
Body
Measure
Point
Which Transform are
constant and
which are depend on
time ?
constant
depend on time
Sensor guided Robots III
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.23 10.04.2015
How we can calculate the robot movement transform
via the known sensor movement Transform ? MBR
S DT
TCPR
A DT
Sensor guided Robots IV
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.24 10.04.2015
6D6D
TM
B
TM
P
TM
P
TM2
M1 TM3
M2
TM
P
TP
A
TP2
P1
TP3
P2
6D
6D
6D
6D
A B
M
P
6D
Sensor guided Robots V
1
M2 M P2 M
M1 P P1 P
T T T T
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.25 10.04.2015
M 1 P
M C P C
j j
i i
T T T T
Tensor Transform
M 1 P
M C P C C
M P 1
C M P C C
P M 1
P C M C
from left
from right
j j
i i
j j
i i
j j
i i
T T T T T
T T T T T
T T T T
Sensor guided Robots VI
Identification
problem
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.26 10.04.2015
M 1 P 1 M
V C V C V
1 M 1 P
V C V C
( ) ( ) ( ) ( ) ( ) from left
( ) ( ) ( ) ( ) ( )
T p T p T p T p T p
T p T p T p T p T p I
Sensor guided Robots VII
C
t
COpt
1
Min , 2N
N
p p p p
Interpretation as a minimization problem
Use orthogonal Translations and Rotation Movements
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.27 10.04.2015
SC
Sn
SB
SS
p
k-te Kugel
6D
6D
TS
MTCP
TMTCP
R
Applications Adaptive Milling Cell I
Tensor Transform
Identification
via
Movements
Eye/Sensor
Calibration
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.28 10.04.2015
6D
6D
6D
6D
TMCB
R
TMTCP
R
TMCB
MTCP
TMCB
I
TI
MTCP
Applications Adaptive Milling Cell II
Tensor Transform
Identification
via
Movements
Hand/Tool Calibration
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.29 10.04.2015
I MTCP -1 MCB MCB -1
MTCP R R IT T T T
Applications Adaptive Milling Cell III
Mechanical
Interface
W I W
MTCP MTCP IT T TTool Correction
MTCP
TCPT
Measurement
to Movement
Frame
Tensor
Identification
via movements
Interface Cal.
Tool
Tool
Measurement
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.30 10.04.2015
HSK Interface
Calibration Tool for
HSK Interface
Applications Adaptive Milling Cell IV
Tool Measurement
DT
LT
5D
5D
Rotation Symmetry around z-Axis
z
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.31 10.04.2015
Applications Adaptive Milling Cell V
Tool
Correction
Reference
Measure Frame
to TCP
Tensor Transform
Identification
via
Movements Hand/Tool Eye/Sensor Calibration
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.32 10.04.2015
Analytical
closed
Identification
Measure to TCP-Frame (Eye-Hand Calibration with analytical closed solution)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.33 10.04.2015
Identification Measurement to TCP Frame
Known as well as
via Measurement:
Actuator Poses TTCPA
Measurement Poses TRM
STCP
SA
TR
M
TM
TCP
SM;C0
SC1
TC0
C1
TTCP
A
TR
A
SR r
M
i
12
3
Unknown:
Measurement to TCP Pose TTCPA
Reference to Actuator Pose TRM
Condition:
Calibrated Sensor System
R TCP M R
A A TCP MT T T T
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.34 10.04.2015
Transformations with Movements
T T T TM SI TCP C
M
TCP SI TCP C
Mc h 1
T T T TTCP SI TCP C
M
M SI TCP C
Mc h 1
SA
STCP
I
SR
STCP
S
TTCP
ASTTCP
AITM
RI
TM
RS
TM SI
TM
TCP CT
M
TCP C
TTCP SI
SM
SSM
I
1
M M M M
R S R I TCP C TCP SI TCP C
T T T T T
Changing Pose M- und TCP frame
Changing Pose Reference frame
Constant Transformation
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.35 10.04.2015
SR
SM
STCP
SA
TM
R
TM
TCP
TTCP
A
TCP2 t
TCP1 1 1 1 1(0 0 0 0) , , ] 0, [w w p
TCP3 t
TCP2 a 2 2(0 0 0 0) , , ] 0, [w w p
TCP3 t
TCP2b 2 2(0 0 0 0) , , ] 0, [ p
Identification Measurement to TCP Frame I
Non linear Translation and
non linear depended
rotations (orthogonal)
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.36 10.04.2015
1M2 M TCP2 M
M1 TCP TCP1 TCP
1M3 M TCP3 M
M2 TCP TCP2 TCP
T T T T
T T T T
M M2 TCP2 M
TCP M1 TCP1 TCP
M M3 TCP3 M
TCP M2 TCP2 TCP
T T T T
T T T T
M M2 TCP2 M
TCP M1 TCP1 TCP
M M3 TCP3 M
TCP M2 TCP2 TCP
TCP1 TCP2 M1 TCP2 TCP
TCP2 TCP1 M2 TCP1 M
TCP2 TCP3 M2 TCP3 TCP
TCP3 TCP2 M3 TCP2 M
( )
( )
D D D D
D D D D
t D t D E t
t D t D E t
tM TCP
M TCP M 1 2 3TCP
1 1
x
D t x x x tT
0 0
Rotation
Translation
Identification Measurement to TCP Frame II
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.37 10.04.2015
TCP2 M2 t TCP2 TCP2
TCP1 11 M1 TCP1 12 TCP1 13
TCP2 TCP2 M2 t TCP2
TCP1 21 TCP1 22 M1 TCP1 23
TCP2 TCP2 TCP2 M2 t
TCP1 31 TCP1 32 TCP1 23 M1
TCP3 M3 t TCP3 TCP3
TCP2 11 M2 TCP2 12 TCP2 13
TCP3 TCP3
TCP2 21 TCP2 22
d d d
d d d
d d d
d d d
d d
E D E E 0
E E D E 0
E E E D 0
E D E E 0
E EM3 t TCP3
1M2 TCP2 23
TCP3 TCP3 TCP2 M3 t2TCP2 31 TCP2 32 TCP1 23 M2
M1 t3 TCP2M2
M1 t TCP2
M2 TCP1
M1 t
M2
M2 t
M3
M2 t TCP3
M3 TCP2
M2 t
M3
x
d
d d d
x 0D E 0
x 0E E E D 0
x tt 0 0
t0 t 0 E D
0 0 t
t 0 0
0 t 0 E D
0 0 t
TCP1
TCP2
TCP3
t
Identification Measurement to TCP Frame III
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.38 10.04.2015
Sensor Calibration of the extern Pose
for Multi Camera, Point, Line and
Pattern Sensors
Hand Calibration for Gripper, Tools
and so on
Laser Tracker Measure Frame
Calibration
Identify Base Transforms for Multi
Robot Systems (used for cooperating
movements)
Applications
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.39 10.04.2015
Pose
Measurement
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.40 10.04.2015
Boeing
Application I
Pose measurement
of parts
Parts guidance from retracting to assembly pose
Magnetic surface Magnetic insert
Shank length
S h a n k
Offset
Reflector type
D H
S HL D RO
D H L
B n
B r B;R
r
B E
S R
Laser- Tracker
see robotic I
BB B
M RO B
ii i i
i
D n
r rn
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.41 10.04.2015
Application II
The first point defines the origin of a helper frame (HF)
The first and second point defines the x – axis of the helper
frame
First, second, third point defines the x/y – plane of the
helper frame (preferably nearly orthogonal, not on a straight line)
Boeing
Helper Frame
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.42 10.04.2015
Pose Measurement I
Origin of the Helper-FR at the
Reference-FR is R
1p
x-Axis of the Helper-FR in direction of
the line from Rp1 to Rp2
x/y-Plane of the Helper-FR through the
Points Rp1, Rp2
and Rp3
R R R
1 2 3, ,p p p := Coordinates in Reference-FR B B B
1 2 3, ,p p p := Coordinates in Body-FR
xR
yR
zR
TH
R
TB
R
TH
B
xH
yH
zH
B;Re
H
y
B;Re
H
x
B;Re
H
z
xB
yB
zB
P1
P2
P3
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.43 10.04.2015
R R R R
2 1 3 1R R H
R R R R
2 1 3 1
z
p p p pa e
p p p p
R R H R H R H
y z x o e e e
R RR R H 2 1
R R
2 1
x
p pn e
p p
Pose Measurement II
xR
yR
zR
TH
R
xH
yH
zH
Re
H
y
Re
H
x
Re
H
z
P1
P2
P3
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.44 10.04.2015
R H R H R H R
1H
R
1
x y z
e e e pT
0
R R H
1
tR H R H R H R R H
R 1H
R R H
1
1
x
x y z y
z
p e
e e e p eT
p e
0
Pose Measurement III
xR
yR
zR
TH
R
xH
yH
zH
Re
H
y
Re
H
x
Re
H
z
P1
P2
P3
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.45 10.04.2015
r r r rx y z
2 2 23 ,
x
y
z
r
r
r
r
c a b
e e e
x y z
x y z
x y z
a a a
b b b
a b a b a b a b a b a by z z y x z x x z y x y y x zc h b g c he e e
and
F
HGGG
I
KJJJ
a b a b
a b a b
a b a b
y z z y
z x x z
x y y x
Pose Measurement IV
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.46 10.04.2015
Boeing
S R
Laser- Tracker
xR
yR
zR
TH
R
TB
R
TH
B
xH
yH
zH
B;Re
H
y
B;Re
H
x
B;Re
H
z
xB
yB
zB
P1
P2
P3
CAD-Measurement
Laser-Tracker-
Measurement
Application Example I
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.47 10.04.2015
R;B R;B R;B
1 2 3, ,p p p := Coordinates in the body and reference
frame (Superscript Index B and R)
1
B H H
R R B , with
T T T
R H R H R H R
1H
R ,1
x y z
e e e pT
0
B B H
1
tB H B H B H B B K
1H 1B
B B K
1
1
x
x y z y
z
p e
e e e p eT
p e
0
Application Example II
xR
yR
zR
TH
R
TB
R
TH
B
xH
yH
zH
B;Re
H
y
B;Re
H
x
B;Re
H
z
xB
yB
zB
P1
P2
P3
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.48 10.04.2015
R;B R;B R;B R;B
2 1 3 1R;B H
R;B R;B R;B R;B
2 1 3 1
andz
p p p pe
p p p p
R;B H R;B H R;B H
y z x e e e
R;B R;BR;B H 2 1
R;B R;B
2 1
,x
p pe
p p
Application Example III
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.49 10.04.2015
Object-oriented
Program
Design
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.50 10.04.2015
Vektor<double> MessPointsIst(iDEF_DIMHomogeneKoodinaten),
XYZ1Pos(iDEF_DIMHomogeneKoodinaten);
HMatrix<double> HT_RA;
::::::::::::::::
::::::::::::::::
HT_RA.RPY(m_XYZAktuator.GetPoseRA());
PosErrorA = XYZ1Pos - HT_RA * MessPointsIst;
Object-oriented Program Design
MS Visual C++
see robotic I
Prof. Dr.-Ing. habil. Hermann Lödding
Prof. Dr.-Ing. Wolfgang Hintze
©
PD Dr.-Ing. habil. Jörg Wollnack
SGR.51 10.04.2015
END