Transcript LECTURE 6 - International Institute of Information

LECTURE 6
Segment-based Localization
Position Measurement Systems

The problem of Mobile Robot Navigation:
Where am I?
Where am I going?
How should I get there?
Perhaps the most important result from surveying the vast body of
literature on mobile robot positioning is that to date there is no truly elegant
solution for the problem (Johann Borenstien, UMich Ann Arbor)
.
 The many partial solutions can roughly be categorized into two groups:
relative and absolute position measurements.
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Classification of Localization Methods
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Relative
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Odometry: Uses encoders to measure wheel rotation. Is self
contained and is ever ready to provide the vehicle with an estimate
of position. Position error grows out of bound
Inertial Navigation: Uses gyroscopes and accelerometers to
measure rates of rotation and acceleration. Self contained.
Unsuitable for accurate positioning over extended periods of time.
High manufacturing and equipment cost.
Classification of Localization Methods
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Absolute
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Active Beacons: Computes the absolute position of the robot by measuring the
direction of incidence of three or more actively transmitted beacons
Artificial Landmark Recognition: Distinctive landmarks placed in known locations.
Errors are bounded. Computationally intensive and raises questions for persistent
real-time position updates
Today’s Lecture
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Classification of Data Points: How do you classify the newly
obtained data point to the segments already present in the map
Weighted correction vector: Having classified the data points to
segments how to obtain the corrected position of the robot
Quality Measures: Performance evaluate the obtained corrected
position. i.e. how correct/probable is the corrected position
Orientation Correction: Having obtained the corrected position is
it possible to obtain the correct orientation of the robot
Classification of Data Points
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Under the assumption of small position error data points will not usually
be too far away from the objects they represent
The target line segment of each point is that segment to which the
point is closest in an Euclidean sense
The closest distance is computed by taking the minimum of the
distance of the point to the two end-points of the target segment and
the perpendicular distance if the perpendicular distance falls between
the two endpoints of the line
Weighted Correction of the Image Points to the
Target
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Let xi, yi be the displacement between the image point and the point
resulting from its perpendicular projection onto the infinite line passing
through the line segment
Then
n
 w(d i )xi
X  i 1n
 w(d i )
i 1


n
 w(d i )yi
Y  i 1n
 w(d i )
w(d )  1 
dm
d m  cm
i 1
di is the distance between the ith range data point and its target
segment computed in the manner specified in previous slide. The
sigmoid function introduces a soft non-linearity by ensuring that points
close to the target segments have a greater voting strength
c(t) = c(0)(1-t/T). In other words the value of c decreases as iterations
proceed and less and less points are brought into the correction vector
estimate
Weighted Correction of the
Image Points to the Target
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Then xc = xuc + X, yc = yuc + Y, where xc, xuc the corrected and
uncorrected x component of the robot’s position
If the target segments are parallel to one of the two axes of the
coordinate frame then the position correction can only be done along
the other orthogonal direction. This is called the hallway effect. In other
words if the target segment is parallel to x axis then position correction
can occur only along y and vice-versa
Quality Measures
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How correct are our corrections?
The mean-squared error measure: Emse = dist(pi,li)2/n, where pi is the
ith range data point and li is its corresponding target segment and dist is
the closest distance between the two
Global minimum of the function occurs at the true position of the robot.
Hence higher Emse lesser is the probability that the corrected position is
the true position.
Emse is susceptible to outliers
Quality Measures
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Classification Factor:
Ecf
1 n
dm
  (1  m
)
m
n i 1
d c
Here c is the neighborhood size, m = 2 is the steepness of the sigmoid,
d=dist(pi,li).
Higher the classification factor, higher is the probability that the corrected
position represents the true position of the robot.
Classification factor peaks at the
true position of the robot
Quality Measures
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Ecf is not a useful measure for comparing two robot’s positions which
are close to one another for their accuracy. Emse does not suffer from
this
Hence a combination of both of the form called comparative quantity is
used as:
Ecqm 
Ecfa
b
Emse
Reference: http://www.cim.mcgill.ca/~mrl/publications.html
“Precise positioning using model based maps”, 1994, IEEE ICRA