Segmentbased Localization

1
LECTURE 6

• Segment-based Localization

2
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.

3
Classification of Localization Methods

• Relative
• 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.

4
Classification of Localization Methods

• Absolute
• 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

5
Todays Lecture

• 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

6
Classification of Data Points

• 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

7
Weighted Correction of the Image Points to the
Target

• 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
• 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

8
Weighted Correction of the Image Points to the
Target

• Then xc xuc ?X, yc yuc ?Y, where xc, xuc
  the corrected and uncorrected x component of the
  robots 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

9
Quality Measures

• 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

10
Quality Measures

• Classification Factor
• Here c is the neighborhood size, m 2 is the
  steepness of the sigmoid, ddist(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
11
Quality Measures

• Ecf is not a useful measure for comparing two
  robots 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

Reference http//www.cim.mcgill.ca/mrl/publicati
ons.html Precise positioning using model based
maps, 1994, IEEE ICRA