Lecture Topics MMC Prof. Dr.-Ing. habil. Hermann Lödding Prof. Dr.-Ing. Wolfgang Hintze. PD Dr.-Ing. habil.
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1 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) MMC
2 Motivation Model Calibration MMC
3 Video der Firma Volvo MMC
4 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 Z e n tra ls tra h l Ahlers Kuka Robot-, Hand-Eye- Relation und Work Piece Frame B ild p la tte MMC Measuring Techniques, Robotic and Medicine SHW Tool Machine Work Piece Frame
5 Accuracy Behavior of the Robot before and after the Model Calibration / 100 µm Calibrated Model RMS x / m y / m / 1 mm Non calibrated Model x / m y / m MMC
6 [m] 1 3 Accuracy behavior of the Sensor and Robot Model Calibration in x/y Direction ,00E-04 4,00E-04 3,00E-04 2,00E-04 1,00E-04 y Positionsfehler Error 0,00E+00-1,00E-04-2,00E-04-3,00E-04-4,00E-04-5,00E-04 Pose-Nr. MMC
7 Research Center CFK-Nord (Stade) MMC
8 Time Variance of the System Properties Boeing Operating point change Load change Kuka MMC Aging and Attrition as well as Changed Environmental Condition
9 Adaptive Production Technology Accuracy (0,1mm auf 10 to 20 m -> 5µm/m) Pose and Shape Error Linear Axis at TCP (5 20 mm) Pose Error Assembly (5 10 mm) Process Pose Error at TCP (0,5 1 mm) Process Force influenced Pose Error (0,5 1 mm) Pose Error Robot (1 5 mm) MMC
10 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) MMC
11 Assembly Shape and Pose Correction II Multi-Frames with separate and cooperating Movements (Adaptive hierarchical control process) MMC
12 Experimental Field for Wide Body Shape and Pose Automatic Control Loop Fotos: Roman Jupitz Preiswerte Inexpensive Greifer, Standard-Industrie Industrie- gripper, roboter und preis- robots werte Hallen- and fundamente hall foundations Absolute Absolute Positionier- fehler der Groß- bauteile 0,05 0,05 bis 0,1 0,1 mm mm (after typically 2-4 iterations) positioning errors (nach typisch 2-4 Iterationen) MMC
13 Wide Body handling with Cooperating Robots Inexpensive gripper, Preiswerte Greifer, Standard- robots and Industrieroboter und preiswerte hall Hallenfundamente foundations Fotos: Roman Jupitz Symposium 2004 Absolute positioning Absolute Positionierfehler der Großbauteile errors 0,1 0,2 mm 0,1 bis 0,2 mm (after typically 2-4 iterations) (nach typisch 2-4 Iterationen) MMC
14 Laser Scanner Remote Welding Laser-Scanner TRUMPF Laser-Scanner Mirror Movements are to be derived from Constructional Data (No Teaching!) MMC
15 Sensor guided Remote Laser Welding MMC Emmelmann
16 Fixateur Extern, Robotic und Picture Processing K u g e lg e le n k S te llsc h ra u b e Video Metric to Measure Pose of x-ray Source and Picture Plane R ö n tg e n g e rä t D istr a k to r Ilis a ro w -R in g R ö n tg e n q u e lle sc h e m a tisc h S tra h le n k e g e l Z e n tra ls tra h l B ild p la tte Fixateur Extern / Robotic MMC a b Medicinal 3D Picture Processing 3D x-ray Technology
17 Machine Off Line Programming Separation from plant enterprise and programming B lu m e Absolute pose errors require time consuming teaching MMC
18 System Approach in Mechanical Engineering Computer Aided Design Computer Aided Manufacturing Off-Line- Programmig Machines y z x w Tool Gripper Option Sensor Palette System with Index MMC Sensor-TCP Calibration Body
19 Examples System Identification MMC
20 System Identification at the Ohm's Resistance i Structure Identification? u R i Input Values w e rte S te u e r- x p Parameter P a m e r Output A u s g a n g s - Values w e rte y = f(x,p ) y u Parameter Identification? concentrated Element R u i Measure Voltage u and Current i, than Calculate Parameter R! MMC
21 System Identification of Linear Vector Maps Input S te u e r- Values w e rte x p Parameter P a m e r Output A u s g a n g s - Values w e rte y = f(x,p ) y y A p B x, i {1,, I} i i y y y A p B x x x 1 i I 1 i I Y A p B X A p Y B X 1, R an k D im p A Y B X A p MMC
22 System Identification with Linearization I Vector Map y f ( p, x ), i {1,, I} i i Measured Data x y, i {1,, I} i i Linearization y J ( p, x ) p R 0, R 0 i p 0 0i with y y y, y f ( p, x ), p p p i i 0 i 0 i 0 i 0 y A p, i {1,, I} i i MMC
23 System Identification with Linearization II 1 p A y ', R an k A D im p, with J ( p, x ) p 0 1 Α J ( p, x p 0 i ) J ( p, x p 0 I ) and t t t ' 1 i I y y y y t MMC
24 System Identification I The system identification appears to be very simple. Kuka y z What do you mean, are this is in principle like that? w x Why not? MMC
25 System Identification II 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 Input and output values must be measurable. Therefore principle sensors are needed. MMC
26 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) MMC
27 Analysis Analysis Linear approximation in one and multidimensional case Base for Iterative Optimization Procedures (Regula falsi Newton Method) Base for Iterative Identification Algorithms Base for Computation of the inverse Mapping Base for Error Propagation Analyses MMC
28 Learning by Use and Repetition MMC
29 Hand Eye Coordination MMC
30 Lerning and Remembering Modeling M o d e llb ild u n g Scheduling P la n u n g A k tio n Action Perception W a h rn e h m u n g MMC Long Time Memory and neuronal Catenations needs Repetitions M o to r is c h e Neuromuscular S te u e r u n g Movement
31 Memory Quota Hearing H ö r e n Seeing S e h e n Hearing and seeing H ö r e n u n d S e h e n Hearing, seeing and discuss H ö r e n, S e h e n u n d D is k u tie r e n Hearing, seeing, discuss and doing H ö r e n, S e h e n, D is k u tie r e n u n d Tu n 2 0 % 3 0 % 5 0 % 7 0 % 9 0 % MMC H a n d b u c h H o c h s c h u lle h re
32 Matlab-Class-Room-License to Practicing MMC
33 Hand Eye Calibration Movement Measure Iterative Model Calibration MMC
34 System Analysis and Calibration MMC
35 Methodology Systems Analysis Theoretische Theoretical Analysis Analyse see robotic I Annahmen Assumption zur Vereinfachung Simplification Aufstellen Set up the der Gleichungen Equations Theoretisches Theoretical Modell Model - Struktur - Parameter Structure/Param. Vereinfachung Simplification Vereinfachtes Simplified theo Theoretical retisches Modell Experimentelle Experimental Analyse Analysis A-priori-Kenntnis A über Knowledge das System Experiment nt Identifikation Identification Experim. Experiment Modell Model Struktur Structure unbebekannt known / unknown kannt parametrisch nicht parametrisch parametrisch nicht parametrisch Vergleich compare Q := Quality Ende yes ja Qualität Q nein no MMC
36 Model Quality and Process Knowledge Attainable Model Quality Theoretical Model Design Knowledge of Internal Processes Identification ME := Mechanical Electrical Systems ET := Energy-Technical Systems VT := Process Engineering systems MMC Isermann M := Model Quality K := Process Knowledge see robotic I
37 Model Quality and Investment Attainable Model Quality Expenditure (Costs) Expenditure (Costs) Isermann MMC see robotic I
38 Problem Definition Robot I Absolute Positioning Aaccuracy 2-10 mm Repetition Accuracy µm 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 => problem: zero errors of the sensors and arc errors between world and robot frame Decrease of the manufacturing tolerances of the construction components technically and economically limited. MMC see robotic I
39 0,5 m Problem Definition Robot II (Path Error) see robotic I z x Without extended regulation o h n e e r w e ite r te R e g e lu n g Weber Extended regulation e rw e ite rte r R e g le r z 0,5 m Destination S o llb a h n Path Is tb a h n Actual Path 0,5 m /s z t/s 0,1 0,8 0,9 MMC x x
40 Robot Model Pose Error MMC
41 Kinematics Transformation II S 0 i-th Joint i-te s G e le n k S R W K S S i T i T C P Robot- FR World-FR KS R o b o te r- S i+1 p := Parameter Vector x := Ideal Machine Coordinates S G i-th i-te s GJoint e le n k z i y i x i z i+1 t i y i+1 x i+1 (i+1)-th ( i+ 1 )-te s G e le n k Joint see robotic I Coordinates Transformation (classical) 3 x r R r t, w ith R, t, r i 1 i 1 i i 1 i 1 i 1 i r D D R R R R r t t t t t t, I 6 0 I 5 I 5 I 4 I 3 I 2 I 1 i I 1 I 2 I 3 I 4 I 5 I 5 MMC
42 Kinematics Transformation IV Advantages of Homogeneous Coordinates Transformation T with an open Kinematics Chain T T ( p, x ) f ( p, x ) j j j j Products of the homogeneous Matrices T j MMC see robotic I
43 Kinematics Transformation V p x x S := constant joint parameter of the cinematic model := ideal variable drive coordinates also ideal machine coordinates called := variable sensor coordinates of the internal position measuring systems and/or real variable machine coordinates MMC see robotic I
44 Internal Sensor Measured Machine Coordinates x f ( x ) A S S A MMC see robotic I
45 Kinematics Transformation with Sensor Coordinates Sensor zero position errors and sensor gradient errors can be interpreted as parameters of the model. T e d ' i d ' i S k 0 S k S k f p, x m x j ' ' ' ' ' f ( m, x, p, x ) f ( p, x ) S S 0 S S F I f ' ( p ', x ), p ' H d t t ' ' t m i d x i p S S k S k 0 K t MMC see robotic I
46 Parallel Kinematic I Analytic Inverse Kinematic Transform d d d D D i i 0i i A T C P T C P d r T ( p ) r i B i A T i E T C P r T i S T C P d i ( p T C P ) A S A T T C P A Wikipedia MMC A r B i i {1,..., 6} see robotic I
47 Parallel Kinematic II p T C P A 0 := N u ll P o se d D i := i-th D riv e D ista n c e d i := i-th C a rd a n Jo in t D ista n c e d 0 i := i-th O ffse t in N u ll P o se (S e n so r O ffse t) D i := i-th D ista n c e P a rt MMC see robotic I
48 Causes for Absolute Positioning Errors 1. Kinematics Parameters: (zero position, alignment and length) FR := Frame = coordinate system 10. Controller: (rounding and numeric procedural errors) 9. Friction Kuka 2. Relation from Machine FR to World FR 3. Variations Temperature 8. Position Sensor y z x w 4. Joint Elasticity MMC Bearing Backlash 6. Transmission Error (Linearity, Backlash Error) 5. Element Elasticity see robotic I
49 External 3D Position Sensors Theodolites T h e o d o lite n - Videometric V id e o m e tris c h e V e r fa h re n M e ß v e rfa 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 CCD/CMOS C C D -S e n s o r- 3D s ysensor s te m TCP Flange T C P - F la n s c h L E D - P a n e l J u d d 8 7, B e rg 9 0, M e y e r 9 1, T ra d t 9 1 Measuring Head (TCP-Sensor) M e ß k o p f-v e rfa h re n P o s e - u n d P o s itio n s - s e n s o re n Calibration K a rie rk ö rp body e r In te r fe ro m e tr is c h e Laser-Tracking L a s e r-t ra c k in g -V e r fa h re n 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 MMC Inductively, tactile: in d u k tiv, ta s te n d : G o s s e l 9 6 Ultrasonic: u s c h a ll: Videometric: v id e o m e tris c h : W a rn e c k e 8 6, S c h ie le 8 7, S to n e 8 6, B e rg 9 0 R o o s 9 6, W o lln a c k 9 6 D a in is 8 5, Z h u a n g 9 6, see robotic I
50 Homogeneous Error Transformation I Measured Messwerte Values Modellwerte Values S M T S T M T 1 M Δ T T T MMC see robotic I
51 Homogeneous Error Transformation II 2 t p E p p E E M in = M in, with E M 1 T T ( p ) T ( p ) T ( p ) I p p M p E 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. These approach is very important for pose calibration. MMC see robotic I
52 END MMC
Lecture Topics VMF Prof. Dr.-Ing. habil. Hermann Lödding Prof. Dr.-Ing. Wolfgang Hintze. PD Dr.-Ing. habil.
Lecture Topics. Introduction. Sensor Guides Robots / Machines 3. Motivation Model Calibration 4. 3D Video Metric (Geometrical Camera Model) 5. Grey Level Picture Processing for Position Measurement 6.
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