View
216
Download
1
Embed Size (px)
Citation preview
Weighted Line Fitting Algorithms forMobile Robot Map Building and
Efficient Data RepresentationSam Pfister, Stergios Roumeliotis, Joel Burdick
Mechanical Engineering, California Institute of Technology
Overview:
• Motivation
• Problem Formulation
• Experimental Results
• Conclusion, Future Work
Motivation
Problem Formulation
- Improved data compression- Effective data correspondence- Increased robustness to outliers and noise
Raw PointData
Fit Line
Geometric Representation
Weighted Line Fitting
Correspondence and Merging
Goal : Efficient data representation
m1
b
(x1, y1)
(x2, y2)(x,y,)
Candidate Geometric Representations End points : [x1 y1 x2 y2] - 4D representation
Point + Orientation : [x y ] - 3D representation
Slope Intercept : [m b] y=mx+b - 2D representation
R
Polar Form : [R ] - 2D representation
Selected Geometric Representation
Polar line form • Minimal representation : L = [R,]
• Endpoints maintained as scalar value pairs : S1, S2
• Uncertainty maintained as 2x2 covariance matrix : PL =
R
R
R
R
S1
S2
RR bounds bounds Combined RR, bounds
Fit LineNoisy PointsTrue Line
Line Fit Simulation Single Run
Weighted Line Fitting : Motivation
Least Squares Fit vs. Weighted Fit
Fit LinesNoisy PointsTrue Line
Monte Carlo Simulation 100 Runs
Fit LinesNoisy PointsTrue Line
Monte Carlo Simulation100 Runs
Fit LineNoisy PointsTrue Line
Line Fit Simulation Single Run
Weighted Line Fitting : Formulation
Initial Point Grouping- Hough Transform (Duda & Hart [72])
Point Uncertainty Modelling- Zero mean gaussian assumption
- Laser rangefinder uncertainty parameters determined experimentally
dk
d
Robot Pose k
Qk
Laser RangeScan Data
Weighted Line Fitting : Formulation
Point Error Formulation : k
Point Error Formulation : Pk
Likelihood of obtaining errors {k} given line
Maximum Likelihood Estimation
•Position displacement estimate obtained in closed form
•Orientation estimate found using series expansion approximation
Non-linear Optimization Problem
Line Correspondence and Merging
Line Correspondence : 2 Test
Line Merge
Can merge non-overlapping line segments
Hallway Data
Results :
Kalman Filter Lab Run 1
KF Lab Run 2
Results :
Conclusions and Future Work
Developed general approach for working with line segments in a probabilistic framework
Showed that accurate error modelling can significantly improve line segment extraction accuracy and can enable robust line segment correlation.
Future Work:
Method can likely be extended for use in image processing applications as well as applications using other other range sensors (radar, ultrasound, etc.)
• requires specific sensor error models