Precise Automated Kinematic
Calibration of RCM Robots
Checkpoint Presentation
Group6
About our Project
Precise Automated Kinematic Calibration of RCM
Robots
Main Goal: Quantify the error of Optical Tracker,
Robot Remote Center of Motion
Important Steps:
• Calibrating the accuracy of Polaris Optical
Tracking System
• Quantify the error of RCM
• Update Kinematic Model
Status
• Done:
– Report on the accuracy and precision of Polaris tracker
(minimum)
– In Process: Submitting Paper to Engineering Urology
Society Conference 2012
• To-Do:
– Observe Revolving Needle Driver Robot (Expected)
– Identify errors in RCM motion (Expected)
– Update Kinematic Model (Maximum)
Background of Polaris
• From NDI Manual
3D RMS Volumetric Accuracy
3D RMS Repeatability acceptance
0.350 mm
0.200 mm
Background of Polaris
• From other papers
• Accuracy assessment and interpretation for optical tracking systems,
Andrew D Wile, 2004
- Good: RMS analysis, 3D pyramid shape, 1500 position readings
- Limit: Sample number
Weak Apparatus (small table mill)
No information about coordinate system registration
• Comparative Tracking Error Analysis of Five Different Optical Tracking
Systems , Rasool Khadem, 2000
- Good: Compare many trackers, use passive/active markers
- Limit : Only looked at precision
Did not align apparatus with tracker (plate with holes)
Only 100 samples
Polaris Error Quantification:
Objectives
• How many samples must we take?
• Where in the tracker volume should we read?
• What accuracy and precision can we get?
Polaris Error Quantification:
Coordinate Systems
• Directions which the observed Marker will
travel
Step 1: Machine Vibration
Conclusion: Do not take readings while spindle is turning
Testing Methods
• 1D, 2D tests
1D Precision Test:
How many samples?
• Carried out along Polaris Z
Conclusion: 500 samples is OK
2D Accuracy Test:
Point Cloud Registration
Tracker ^---^ Here
2D Accuracy Test:
What Subset for
Registration?
9 pts
16 pts
All
2D Test:
Point Cloud Registration
Closest Point: 32 micron precision,
152 micron accuracy
Furthest Point: 69 micron precision,
231 micron accuracy
2D Test:
Point Cloud Registration
• Results
X
Y
Z
Accuracy
Mean
0.0025
0.0125
0.1036
(mm)
Min
0.0001
0.0008
0.0116
Max
0.0078
0.0298
0.2315
Precision
Mean
0.0484
Euclidean
Distance
(mm)
Min
0.0314
Max
0.0705
Methods
• 3D test set up
3D Volume Test: Pyramid Slices
3D Volume Test: Pyramid Slices
Scaled Precision Radii and Accuracy Vectors show non-uniform error
3D Volume Test: Individual Points
Closest Point: 19 micron precision,
367 micron accuracy
Furthest Point: 23.7 micron precision,
276 micron accuracy
3D Volume Test: Middle Points
Middle Point: 25 micron precision,
31.5 micron accuracy
Conclusion: Accuracy not so great at extremes of point cloud
3D Volume Test: Numbers
• Results
X
Y
Z
Accuracy
Mean
0.0152
0.0349
0.1904
(mm)
Min
0.0006
0.0001
0.0017
Max
0.0375
0.0737
0.3868
Precision
Mean
0.0423
Euclidean
Distance
(mm)
Min
0.0024
Max
0.0737
Conclusions
• CNC more reliable, relatively accurate than
other calibration apparatus
• Can get more precise readings than previously
thought – take more samples
• Precision generally worse in Polaris Z
– Should measure in XY planes
• Accuracy is distorted over tracker volume
– Point cloud minimizes error at center
– Localize observation for better accuracy
Next Steps
• Continue pursuing Polaris accuracy &
precision
• Observe motion of the Revolving Needle
Driver (RND) End-Effector
– Gets isocenter(s) of RCM point, EEF motion
• Use these to update kinematic model
Questions?
– 2D
– 3D
Thank You!
X
Y
Z
Accuracy
Mean
0.0025
0.0125
0.1036
(mm)
Min
0.0001
0.0008
0.0116
Max
0.0078
0.0298
0.2315
Precision
Mean
0.0484
Euclidean
Distance
(mm)
Min
0.0314
Max
0.0705
X
Y
Z
Accuracy
Mean
0.0152
0.0349
0.1904
(mm)
Min
0.0006
0.0001
0.0017
Max
0.0375
0.0737
0.3868
Precision
Mean
0.0423
Euclidean
Distance
(mm)
Min
0.0024
Max
0.0737