1. © NMISA 2010 Multilateration Laser Tracker Systems Speaker : Pieter Greeff e-mail: pgreeff@nmisa.org

2. © NMISA 2010 Contents 1.Introduction 2.The Project 3.Multilateration 4.Conclusion http://www.metronics.com/

3. © NMISA 2010 Standards Calibration Chain Lower Accuracy CMM Reproducible standard as prescribe in Metrology: Laser Radiation (Iodine 127) SI unit for length (metre definition) Step Gauge 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 System Standard CMM (R 15 000) Standard CMM (R 15 000) Squares Laser Interferometer

4. © NMISA 2010 Standards Calibration Chain CMM Measurements (R 50 mil estimation) CMM Measurements (R 50 mil estimation) Lower Accuracy CMM Reproducible standard as prescribe in Metrology: Laser Radiation (Iodine 127) SI unit for length (metre definition) Step 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 System Standard CMM (R 15 000) Standard CMM (R 15 000) Squares Laser Interferometer

5. © NMISA 2010 Introduction Application 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/

6. © NMISA 2010 Introduction Laser 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/

7. © NMISA 2010 Laser Tracker http://www.fieldcmm.com/Laser_Tracker.htm Laser Interferometer CMM Measurements CMM Calibrations Laser Laser Tracker Home Position Retroreflective Target

8. © NMISA 2010 Laser Tracker http://www.fieldcmm.com/L aser_Tracker.htm Laser Tracker Target Relative Distance L r θ α (L,θ,α)  (X,Y,Z) L = L i + L r (X,Y,Z) (0,0,0) Initial Distance L i

9. © NMISA 2010 Beam Offset δx Measurement Beam Beam Steering Mechanism Optical Tracking Sensor Beam Splitter Control System Beam Offset δy Movement of Retroreflective Target The Laser Tracker Working Principle: Tracking

10. © 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

11. © NMISA 2010 Understand System Better Main Kinematic Error Source Deadpath Beam Steering Mechanism Interferometer Deadpath Error Target Deadpath Change in Target Position

12. © NMISA 2010 Understand System Better Kinematic Modelling Model based on [10], described gimbal type mirror with 10 parameters Source Beam bibi Mirror Front Surface bobo bcbc Target Position P I OmOm Gimbal Axis 2 x b, x 1 zmzm θ 2, z 1 θ1θ1 Gimbal Axis 1 ObOb O1O1 xmxm zbzb bibi bobo bcbc OmOm zmzm xmxm ymym cxcx cycy I Mirror Frame

13. © NMISA 2010 Z X Y Mirror Centre Covariance Ellipsoid Understand System Better Kinematic Modelling

14. © NMISA 2010 Understand System Better Build a Laser Tracker Prototype Design 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

15. © NMISA 2010 Understand System Better Laser Tracker Prototype Component Integration

16. © 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

17. © NMISA 2010 Multilateration Concept Cost Function: minimise residual Residual (e ij ); (i th target point, j th station position): Initial distances Measured distances Assumed TP locationAssumed SP location TP: Target Point SP: Station Point Optimisation algorithm seeks local minimum for E: Receives: initial TP ((xyz) i ) and SP ((XYZ) j ) and initial length (l j ) Measured Distances (L ij )

18. © 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)

19. © NMISA 2010 Multilateration Test Result Sequential Multilateration: Optimisation History Cost Function, E (mm) Iteration Number

20. © NMISA 2010 Multilateration Test Result Sequential Multilateration Tests Results: 3D Distances: 200 mm: (-1,5 μm < Error < 2,0 μm) mm Distance Number

21. © NMISA 2010 Multilateration Test Result Sequential Multilateration Tests Results: 3D Distances: 450 mm: (140 μm < Error < 160 μm) mm Distance Number

22. © NMISA 2010 Multilateration and Uncertainty Estimation Worst Case Error CMM (2,4 + 3L) µm, Max 1 m/ axis Maximum TP (CMM): 5,4 µm TP1TP2 5,4 µm SP1

23. © NMISA 2010 SMR Repeatability (Spherically Mounted Retroreflector) 10,6715,3318,3310,67 Average of Differences (µm)

24. © NMISA 2010 Multilateration and Uncertainty SMR and Tracker Repeatability From table = 10,67 µm CMM: 5,4 µm SMR: 10,67 µm

25. © 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

26. © 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

27. © NMISA 2010 Multilateration and Uncertainty: Tracker Measurement Result Tracker Average Error per 3D Distance (Rounded to 5 μm) AxesDistance Min (μm) Max (μm) Z450-510 X,Z492-510 Y,Z832025 X,Y728030 X,Y,Z855525 Y700530 X,Y,Z461-2030 Y,Z416-2030 X400-55 X200-55

28. © NMISA 2010 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) Components Distance (mm) Min (μm) Max (μm) Z 450 135160 X,Z 492 120150 Y,Z 832 535 X,Y 728 -80-55 X,Y,Z 855 535 Y 700 -85-60 X,Y,Z 461 -1525 Y,Z 416 -530 X 400 -1515 X 200 05

29. © NMISA 2010 Multilateration and Uncertainty Assumed SP Position (cm precision) 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

30. © NMISA 2010 Multilateration: Effect of SP Positions: Setup 1 TP SP

31. © NMISA 2010 Multilateration: Effect of SP Positions : Setup 2 TP SP

32. © NMISA 2010 Multilateration: Effect of SP Positions : Setup 3 TP SP

33. © 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

34. © 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

35. © NMISA 2010 Reduction in Measurement Error with Multilateration For 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

36. © 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

37. © 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

38. © NMISA 2010 References

39. © NMISA 2010 Thank You! Any questions? Covariance Ellipsoid Plot, for system kinematic parameters