Transcript Weighted Line Fitting Algorithms for Mobile Robot Map Building and

Weighted Line Fitting Algorithms for
Mobile Robot Map Building and
Efficient Data Representation
Sam Pfister, Stergios Roumeliotis, Joel Burdick
Mechanical Engineering, California Institute of Technology
Overview:
• Motivation
• Problem Formulation
• Experimental Results
• Conclusion, Future Work
Motivation
Goal : Efficient data representation
- Improved data compression
- Effective data correspondence
- Increased robustness to outliers and noise
Raw Point
Data
Fit Line
Problem Formulation
Geometric
Representation
Weighted
Line Fitting
Correspondence
and Merging
Candidate Geometric Representations
End points : [x1 y1 x2 y2]
- 4D representation
Point + Orientation : [x y ]
- 3D representation
(x1, y1)
(x,y,)
(x2, y2)
Slope Intercept : [m b] y=mx+b
- 2D representation
Polar Form : [R ]
- 2D representation
1
m
b
R

Selected Geometric Representation
Polar line form
S1
• Minimal representation : L = [R,]
• Endpoints maintained as scalar value
pairs : S1, S2
R
• Uncertainty maintained as
2x2 covariance matrix : PL =
R


Combined RR,  bounds
  bounds
RR bounds
R

S2
R

Weighted Line Fitting : Motivation
Least Squares Fit vs. Weighted Fit
Line Fit Simulation
Single Run
Line Fit Simulation
Single Run
Fit Line
Noisy Points
True Line
Monte Carlo Simulation
100 Runs
Fit Lines
Noisy Points
True Line
Fit Line
Noisy Points
True Line
Monte Carlo Simulation
100 Runs
Fit Lines
Noisy Points
True Line
Weighted Line Fitting : Formulation
Initial Point Grouping
Laser Range
Scan Data
- Hough Transform (Duda & Hart [72])
Qk
Point Uncertainty Modelling
- Zero mean gaussian assumption
- Laser rangefinder uncertainty
Robot
parameters determined experimentallyPose

dk
k
d
Weighted Line Fitting : Formulation
Point Error Formulation : k
Point Error Formulation : Pk
Maximum Likelihood Estimation
Likelihood of obtaining errors {k} given line
Non-linear Optimization Problem
•Position displacement estimate obtained in closed form
•Orientation estimate found using series expansion approximation
Line Correspondence and Merging
Line Correspondence : 2 Test
Line Merge
Can merge non-overlapping line segments
Hallway Data
Results :
Kalman Filter
Lab Run 1
Results :
KF Lab
Run 2
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