TUHH im nächsten Jahrtausend · PDF filesee robotic I. Prof. Dr.-Ing. habil. Hermann...

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)



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SGR.2 10.04.2015

Sensor Guided

Robots / Machines



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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



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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



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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



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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 !!!!!



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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



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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



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SGR.9 10.04.2015

Spatial Eyesight and Measurement

A spatial eyesight

needs at least two

or more eyes



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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SGR.32 10.04.2015

Analytical

closed

Identification

Measure to TCP-Frame (Eye-Hand Calibration with analytical closed solution)



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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



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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



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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)



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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



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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

TUHH im nächsten Jahrtausend · PDF filesee robotic I. Prof. Dr.-Ing. habil. Hermann...

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Transcript of TUHH im nächsten Jahrtausend · PDF filesee robotic I. Prof. Dr.-Ing. habil. Hermann...