© nmisa 2010 multilateration laser tracker systems speaker : pieter greeff e-mail:...
TRANSCRIPT
© NMISA 2010
Contents
1. Introduction
2. The Project
3. Multilateration
4. Conclusion
http://www.metronics.com/
© NMISA 2010
Lower Accuracy CMMLower Accuracy CMM
Reproducible standard as prescribe in Metrology: Laser Radiation (Iodine 127)
SI unit for length
(metre definition)
Step GaugeStep
GaugeNMISA
activities inside border
National Standard for length as in Government Gazette: Laser Interferometer
(CSIR 4)
National Standard for length as in Government Gazette: Laser Interferometer
(CSIR 4)
End Standards: CMM Standard(R10 000)
End Standards: CMM Standard(R10 000)
Length Bar SystemLength Bar System
Standard CMM (R 15 000)
Standard CMM (R 15 000)
SquaresSquares
Laser InterferometerLaser Interferometer
© NMISA 2010
CMM Measurements (R 50 mil estimation)CMM Measurements (R 50 mil estimation)
Lower Accuracy CMMLower Accuracy CMM
Reproducible standard as prescribe in Metrology: Laser Radiation (Iodine 127)
SI unit for length
(metre definition)
Step GaugeStep
Gauge
CMM Calibrations(350 CMMs/year: R3 ,5mil)
CMM Calibrations(350 CMMs/year: R3 ,5mil)
CMM Measurements(R 120 000)
CMM Measurements(R 120 000)
Automotive Exports(R 65 bill estimation)Automotive Exports(R 65 bill estimation)
NMISA activities
inside border
National Standard for length as in Government Gazette: Laser Interferometer
(CSIR 4)
National Standard for length as in Government Gazette: Laser Interferometer
(CSIR 4)
End Standards: CMM Standard(R10 000)
End Standards: CMM Standard(R10 000)
Length Bar SystemLength Bar System
Standard CMM (R 15 000)
Standard CMM (R 15 000)
SquaresSquares
Laser InterferometerLaser Interferometer
© NMISA 2010
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/
© NMISA 2010
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/
© NMISA 2010
Laser Tracker
http://www.fieldcmm.com/Laser_Tracker.htm
Laser InterferometerLaser Interferometer
CMM MeasurementsCMM MeasurementsCMM CalibrationsCMM Calibrations
Laser
Laser Tracker
Home Position
Retroreflective Target
© NMISA 2010
Laser Tracker
http://www.fieldcmm.com/Laser_Tracker.htm
Laser Tracker
Target
Relative
Distance
L r
θ
α
(L,θ,α) (X,Y,Z)L = Li + Lr
(X,Y,Z)
(0,0,0)
Initial Distance
Li
© NMISA 2010Beam Offset δx
Measurement Beam
Beam Steering Mechanism
Optical Tracking Sensor
Beam Splitter
Control System
Beam Offset δy
Movement of Retroreflective Target
The Laser TrackerWorking Principle: Tracking
© NMISA 2010
The Project
http://www.metronics.com/
1. What is it about?
a) Traceability
b) Resource Development
c) Technical Development
2. What did we obtain?
a) Better System Understanding
b) Multilateration Algorithm
c) Multilateration Simulations
http://www.faro.com/
http://www.primemachine.com/files/inspsvc.html
© NMISA 2010
Understand System BetterMain Kinematic Error Source
Deadpath
Beam Steering Mechanism
Interferometer
Deadpath Error
Target
Deadpath
Change in Target Position
© NMISA 2010
Understand System Better Kinematic ModellingModel based on [10], described gimbal type mirror with 10 parameters
Source Beam
bi
Mirror Front Surface
bo
bc
Target Position
P
I
Om
Gimbal Axis 2
xb, x1
zm
θ2, z1
θ1
Gimbal Axis 1
Ob O1
xm
zb
bi
bo
bc
Om
zm
xm
ym
cx
cy
I
Mirror Frame
© NMISA 2010
Z
X
Y
Mirror Centre
Covariance Ellipsoid
Understand System Better Kinematic Modelling
© NMISA 2010
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
© NMISA 2010
Understand System Better Laser Tracker PrototypeComponent Integration
© NMISA 2010
Multilateration: Solve target point coordinates, with only the distance between the target points and the station points precisely known
•Similar to triangulation or trilateration
•At least 4 tracker Stations Points (SP)
•At least 10 Target Points (TP)
Z
X
Y
© NMISA 2010
𝑒𝑖𝑗 = ට൫𝑥𝑖 −𝑋𝑗൯2 +൫𝑦𝑖 − 𝑌𝑗൯2 +൫𝑧𝑖 − 𝑍𝑗൯2 −൫𝑙𝑖𝑗 − 𝐿𝑗൯
Multilateration Concept
Cost Function: minimise residual
Residual (eij); (ith target point, jth station position):
Initial distances
Measured distancesAssumed TP location Assumed SP location
TP: Target PointSP: Station Point
Optimisation algorithm seeks local minimum for E:
Receives: •initial TP ((xyz)i) and SP ((XYZ)j)•and initial length (lj)•Measured Distances (Lij)
𝐸= 𝑒𝑖𝑗2𝑛𝑖=0
4𝑗=0
© NMISA 2010
Multilateration Test Sequential Multilateration Test Setup
•20 target points
•Use only one tracker
•Sequentially at 6 different positions
Z
X
Y
TP1
TP3
TP4
TP5
TP6
(700)
(450)
(700)
(416)
(Distances in mm)
TP2
(200)
© NMISA 2010
Multilateration Test Result Sequential Multilateration: Optimisation History
Cos
t F
unct
ion,
E (
mm
)
Iteration Number
𝑒𝑖𝑗 = ට൫𝑥𝑖 −𝑋𝑗൯2 +൫𝑦𝑖 − 𝑌𝑗൯2 +൫𝑧𝑖 − 𝑍𝑗൯2 −൫𝑙𝑖𝑗 − 𝐿𝑗൯
𝐸= 𝑒𝑖𝑗2𝑛𝑖=0
4𝑗=0
© NMISA 2010
Multilateration Test Result Sequential Multilateration Tests Results: 3D Distances: 200 mm: (-1,5 μm < Error < 2,0 μm)
mm
Distance Number
© NMISA 2010
Multilateration Test Result Sequential Multilateration Tests Results: 3D Distances: 450 mm: (140 μm < Error < 160 μm)
mm
Distance Number
© NMISA 2010
Multilateration and Uncertainty Estimation
Worst Case Error
CMM
(2,4 + 3L) µm, Max 1 m/ axis
Maximum TP (CMM): 5,4 µm
TP1 TP25,4 µm
SP1
© NMISA 2010
SMR Repeatability (Spherically Mounted Retroreflector)
10,67 15,33 18,33 10,67Average of Differences (µm)
© NMISA 2010
Multilateration and Uncertainty
SMR and Tracker Repeatability
From table = 10,67 µm
CMM: 5,4 µm
SMR: 10,67 µm
© NMISA 2010
Multilateration and Uncertainty
CMM: 5,4 µm
SMR: 10,67 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(5^2 + 4^2*2) = 7,55 µm
TRACKER: 7,55 µm
© NMISA 2010
Multilateration and Uncertainty
5,4 µm
10,67 µm
7,55 µm
Combined worst case TP uncertainty:
Sqrt(5,4^2 + 10,67^2 + 7,55^2) = 14,2 µm
Worst case 3D distance uncertainty:
14,14x 2 = 28,28 µm
16,07 µm
14,14 µm
© NMISA 2010
Multilateration and Uncertainty: Tracker Measurement Result
Tracker Average Error per 3D Distance (Rounded to 5 μm)
Axes Distance Min
(μm) Max(μm)
Z 450 -5 10X,Z 492 -5 10Y,Z 832 0 25
X,Y 728 0 30X,Y,Z 855 5 25
Y 700 5 30X,Y,Z 461 -20 30Y,Z 416 -20 30X 400 -5 5X 200 -5 5
© NMISA 2010
Multilateration and Uncertainty: Fit Measurement Result
Total: 10 μmVariable: 140 nm
Max and Min for 3D Distances(With Initial Length Suppressed,
Rounded to 5 μm)
Components Distance
(mm)Min
(μm) Max(μm)
Z 450 135 160X,Z 492 120 150Y,Z 832 5 35X,Y 728 -80 -55
X,Y,Z 855 5 35Y 700 -85 -60
X,Y,Z 461 -15 25Y,Z 416 -5 30X 400 -15 15X 200 0 5
© NMISA 2010
Multilateration and UncertaintyAssumed SP Position
(cm precision)
Distance
(1 + 1L) µ
m
Distance (1 + 1L) µm
FIT SP Position (µm precision)
TP Repeatability 14 µm
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.
SP1
SP2
SP3
© NMISA 2010
Multilateration: Effect of SP Positions: Setup 1
TPSP
© NMISA 2010
Multilateration: Effect of SP Positions : Setup 2
TPSP
© NMISA 2010
Multilateration: Effect of SP Positions : Setup 3
TPSP
© NMISA 2010
Result Summary of SP Effect Analysis For a 100 iterations for each setup
Max at 450 and 492
Min at 200 and 400
© NMISA 2010
Result Summary of SP Effect Analysis For a 100 iterations for each setup
Max at 450 and 492
Min at 200 and 400
Setup 1
Setup 2
Setup 3 Measured with Trackers
© NMISA 2010
Reduction in Measurement Error with MultilaterationFor a 100 iterations for each setup
Measurement with Fit (Setup 3)
Simulated Measurement with Trackers
Average Error: -300 nm Max Deviation: 800 nm
Average Error: 600nm Max Deviation: 1100 nm
© NMISA 2010
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 algorithm’s 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
© NMISA 2010
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
© NMISA 2010
References
[1] Benjamin B. Gallagher, "Optical shop applications for laser tracking metrology systems," Department of Optical Sciences, University of Arizona, 2003.
[2] W. Cuypers et al., "Optical measurement techniques for mobile and large-scale dimensional metrology," Optics and Lasers in Engineering, vol. 47, pp. 292-300, 2009, Optical Measurements.
[3] Kam C Lau and Robert J Hocken, "Three and five axis laser tracking systems," Patent 1987.
[4] T. Takatsuji, M. Goto, T. Kurosawa, and Y. Tanimura, "The first measurement of a three-dimensional coordinate by use of a laser tracking interferometer system based on trilateration," Measurement Science and Technology, vol. 9, pp. 38-41, 1998.
[5] P.D. Lin, C.H. Lu, and others, "Modeling and sensitivity analysis of laser tracking systems by skew-ray tracing method," Journal of Manufacturing Science and Engineering, vol. 127, p. 654, 2005.
[6] EB Hughes, A Wilson, and GN Peggs, "Design of a High-Accuracy CMM Based on Multi-Lateration Techniques," CIRP Annals - Manufacturing Technology, vol. 49, pp. 391-394, 2000.
[7] G.X. Zhang et al., "A Study on the Optimal Design of Laser-based Multi-lateration Systems," CIRP Annals - Manufacturing Technology, vol. 52, pp. 427-430, 2003.
[8] M. Vincze, JP Prenninger, and H. Gander, "A Laser Tracking System to Measure Position and Orientation of Robot End Effectors Under Motion," The International Journal of Robotics Research, vol. 13, p. 305, 1994.
[9] Y. Bai, H. Zhuang, and ZS Roth, "Fuzzy logic control to suppress noises and coupling effects in a laser tracking system," IEEE Transactions on Control Systems Technology, vol. 13, pp. 113-121, 2005.
[10] H. Zhuang and Z.S. Roth, "Modeling Gimbal Axis Misalignments and Mirror Center Offset in a Single-Beam Laser Tracking Measurement System," The International Journal of Robotics Research, vol. 14, p. 211, 1995.
[11] H. Zhuang, S.H. Motaghedi, Z.S. Roth, and Y. Bai, "Calibration of multi-beam laser tracking systems," Robotics and Computer-Integrated Manufacturing, vol. 19, p. 301, 2003.
[12] P.L. Teoh, B. Shirinzadeh, C.W. Foong, and G. Alici, "The measurement uncertainties in the laser interferometry-based sensing and tracking technique," Measurement, vol. 32, pp. 135-150, 2002.
[13] H. Schwenke, M. Franke, and J. Hannaford, "Error mapping of CMMs and machine tools by a single tracking interferometer," CIRP Annals - Manufacturing Technology, vol. 54, p. 475, 2005.
© NMISA 2010
Thank You!
Any questions?
Covariance Ellipsoid Plot, for system kinematic parameters