Multilateration Laser Tracker Systems

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Multilateration Laser Tracker Systems
Speaker Pieter Greeff e-mail pgreeff_at_nmisa.org
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Contents

1. Introduction
2. The Project
3. Multilateration
4. Conclusion

http//www.metronics.com/
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Standards Calibration Chain
Reproducible standard as prescribe in Metrology
Laser Radiation (Iodine 127)
SI unit for length (metre definition)
National Standard for length as in Government
Gazette Laser Interferometer (CSIR 4)
Laser Interferometer
Length Bar System
End Standards CMM Standard (R10 000)
Lower Accuracy CMM
Standard CMM (R 15 000)
Step Gauge
Squares
NMISA activities inside border
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Standards Calibration Chain
Reproducible standard as prescribe in Metrology
Laser Radiation (Iodine 127)
SI unit for length (metre definition)
National Standard for length as in Government
Gazette Laser Interferometer (CSIR 4)
Laser Interferometer
Length Bar System
End Standards CMM Standard (R10 000)
Lower Accuracy CMM
Standard CMM (R 15 000)
Step Gauge
Squares
CMM Measurements (R 120 000)
NMISA activities inside border
CMM Calibrations (350 CMMs/year R3 ,5mil)
CMM Measurements (R 50 mil estimation)
Automotive Exports (R 65 bill estimation)
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IntroductionApplication and Technology

• Applications of three dimensional metrology
• measure parts and assemblies ship building,
  aeroplane construction, rotor blades, satellite
  dish antennas, turbines, cars
• Instruments for three dimensional metrology
• photogrammetry systems, bridge type CMM
  (Coordinate Measuring System), portable
  measurement arms, total stations, GPS, indoor GPS
  systems, laser trackers

http//www.gom.com/
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IntroductionLaser Tracker Selection Motivation

• Accuracy
• A laser tracker is the most accurate type of
  device, for its measurement volume, on the market
• Volume restriction
• not have the size restriction of the bridge type
  CMM or portable measuring arm.
• Traceability
• A multilateration system is directly traceable to
  the metre, reducing uncertainties caused by
  intermediate calibration steps.
• The level of the required accuracy of dimensional
  metrology in manufacturing industries are
  increasing

http//www.leica-geosystems.com/
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Laser Tracker
Laser Tracker
Laser Interferometer
Laser
Retroreflective Target
Home Position
http//www.fieldcmm.com/Laser_Tracker.htm
CMM Measurements
CMM Calibrations
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Laser Tracker
(X,Y,Z)
Laser Tracker
Relative Distance Lr
?
(0,0,0)
a
Target
(L,?,a) ? (X,Y,Z) L Li Lr
Initial Distance Li
http//www.fieldcmm.com/Laser_Tracker.htm
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The Laser TrackerWorking Principle Tracking
Movement of Retroreflective Target
Beam Steering Mechanism
Beam Splitter
Measurement Beam
Optical Tracking Sensor
Beam Offset dy
Control System
Beam Offset dx
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The Project
http//www.primemachine.com/files/inspsvc.html

• What is it about?
• Traceability
• Resource Development
• Technical Development
• What did we obtain?
• Better System Understanding
• Multilateration Algorithm
• Multilateration Simulations

http//www.faro.com/
http//www.metronics.com/
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Understand System BetterMain Kinematic Error
Source
Target
Deadpath
Change in Target Position
Interferometer
Beam Steering Mechanism
Deadpath Error
Deadpath
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Understand System Better Kinematic
ModellingModel based on 10, described gimbal
type mirror with 10 parameters
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Understand System Better Kinematic Modelling
Mirror Centre
Covariance Ellipsoid
Z
Y
X
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Understand System Better Build a Laser Tracker
PrototypeDesign Scope

• Design scope
• select type of beam steering mechanism, design
  and build it
• sensor signal conditioning
• control of the system

CAD model of manufactured prototype tracker
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Understand System Better Laser Tracker
PrototypeComponent Integration
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Multilateration Solve target point coordinates,
with only the distance between the target points
and the station points precisely known
Z
Y

• Similar to triangulation or trilateration
• At least 4 tracker Stations Points (SP)
• At least 10 Target Points (TP)

X
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Multilateration Concept
Cost Function minimise residual

• Optimisation algorithm seeks local minimum for E
• Receives
• initial TP ((xyz)i) and SP ((XYZ)j)
• and initial length (lj)
• Measured Distances (Lij)

Residual (eij) (ith target point, jth station
position)
Initial distances

Measured distances
Assumed TP location
Assumed SP location
TP Target Point SP Station Point
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Multilateration Test Sequential Multilateration
Test Setup
TP6
Z
TP1
(200)
(700)
Y
TP5
X
(416)
TP2
TP4
(450)
(700)

• 20 target points
• Use only one tracker
• Sequentially at 6 different positions

TP3
(Distances in mm)
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Multilateration Test Result Sequential
Multilateration Optimisation History
Cost Function, E (mm)
Iteration Number
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Multilateration Test Result Sequential
Multilateration Tests Results 3D Distances 200
mm (-1,5 µm lt Error lt 2,0 µm)
mm
Distance Number
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Multilateration Test Result Sequential
Multilateration Tests Results 3D Distances 450
mm (140 µm lt Error lt 160 µm)
mm
Distance Number
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Multilateration and Uncertainty Estimation

• TP1

• TP2

5,4 µm

• Worst Case Error
• CMM
• (2,4 3L) µm, Max 1 m/ axis
• Maximum TP (CMM) 5,4 µm

• SP1

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SMR Repeatability (Spherically Mounted
Retroreflector)
10,67
15,33
18,33
10,67
Average of Differences (µm)
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Multilateration and Uncertainty
CMM 5,4 µm
SMR 10,67 µm
SMR and Tracker Repeatability From table 10,67
µm
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Multilateration and Uncertainty
CMM 5,4 µm
SMR 10,67 µm
TRACKER 7,55 µm
Laser Tracker (L in metres) Radial accuracy (1
1L) µm, (Max radial distance 4 m) Transverse
accuracy (3 1L) µm. (Max transverse
displacement 1 m) Worst case maximum Sqrt(52
422) 7,55 µm
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Multilateration and Uncertainty
5,4 µm
16,07 µm
10,67 µm
14,14 µm
7,55 µm
Combined worst case TP uncertainty Sqrt(5,42
10,672 7,552) 14,2 µm Worst case 3D
distance uncertainty 14,14x 2 28,28 µm
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Multilateration and Uncertainty Tracker
Measurement Result
Tracker Average Error per 3D Distance (Rounded to 5 µm) Tracker Average Error per 3D Distance (Rounded to 5 µm) Tracker Average Error per 3D Distance (Rounded to 5 µm) Tracker Average Error per 3D Distance (Rounded to 5 µm)
Axes Distance Min (µm) Max (µm)
Z 450 -5 10
X,Z 492 -5 10
Y,Z 832 0 25
X,Y 728 0 30
X,Y,Z 855 5 25
Y 700 5 30
X,Y,Z 461 -20 30
Y,Z 416 -20 30
X 400 -5 5
X 200 -5 5
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Multilateration and Uncertainty Fit Measurement
Result
Total 10 µm Variable 140 nm Max and Min for 3D Distances (With Initial Length Suppressed, Rounded to 5 µm) Max and Min for 3D Distances (With Initial Length Suppressed, Rounded to 5 µm) Max and Min for 3D Distances (With Initial Length Suppressed, Rounded to 5 µm)
Components Distance (mm) Min (µm) Max (µm)
Z 450 135 160
X,Z 492 120 150
Y,Z 832 5 35
X,Y 728 -80 -55
X,Y,Z 855 5 35
Y 700 -85 -60
X,Y,Z 461 -15 25
Y,Z 416 -5 30
X 400 -15 15
X 200 0 5
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Multilateration and Uncertainty
SP3
Assumed SP Position (cm precision)
FIT SP Position (µm precision)
TP Repeatability 14 µm
Distance (1 1L) µm
Distance (1 1L) µm
SP1
SP2
Residual Error

1. If TP, SP1 or SP2 moves relative to each other in
   the X-axis, it will have a 1 to 1 effect on
   residual.
2. However, if SP3 moves in X-axis, it will only
   have a cosine effect on residual.
3. Since there are more SP in the X-axis, over the
   full range of it, more information is available
   to solve it, while for the Y axis less data is
   available.

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Multilateration Effect of SP Positions Setup 1
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Multilateration Effect of SP Positions Setup 2
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Multilateration Effect of SP Positions Setup 3
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Result Summary of SP Effect Analysis For a 100
iterations for each setup
Max at 450 and 492
Min at 200 and 400
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Result Summary of SP Effect Analysis For a 100
iterations for each setup
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Reduction in Measurement Error with
MultilaterationFor a 100 iterations for each
setup
Simulated Measurement with Trackers
Average Error 600nm Max Deviation 1100 nm
Average Error -300 nm Max Deviation 800 nm
Measurement with Fit (Setup 3)
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Conclusion

• Laser Tracker
• A laser tracker is a highly accurate measuring
  instrument, with many applications in the
  coordinate measurement field.
• Multilateration
• The concept of multilateration should be able to
  even further improve the obtainable accuracy, due
  to direct traceability.
• However constraints are the beam steering
  mechanisms dead path error contribution and the
  fit algorithms dependence on SP coordinates.
• Future Work
• Investigate
• the absolute accuracy of the fit and effect of
  the kinematic errors
• Further development of the beam steering
  mechanism

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Acknowledgements

• OA Kruger and the NMISA for their sponsorship for
  this project
• Mechatronic Engineering Department of the
  University of Stellenbosch
• Prof. K Schreve, for supervising this project.

Photo of prototype tracker
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References
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Thank You!

• Any questions?

Covariance Ellipsoid Plot, for system kinematic
parameters