McKerrow Method: A Sonar Refinement Technique

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McKerrow Method A Sonar Refinement Technique

• Nicole Takahashi
• Ryosuke Sakai

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McKerrow Method Overview

• Obstacle is tangent to closest sonar arc
• Use previous sonar sensor data
• Obstacle is tangent to both arcs
• Create outline segments
• Combine segments Outlined obstacle

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Assumptions

• Two dimensions
• Discrete motion
• Straight lines applicable to curves

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Terminology

• Arc Center point equidistant to all points on
  the arc
• Beam Angle angle from the beam axis to the
  outside of the cone
• Beam Width function of beam angle and distance
  to object
• Range Vector passes through
• arc center and tangent point

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Reference Frames
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Single Sonar Reading
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Two Sonar Readings
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Mapping Algorithm

• Orient left side to surface on left, scan
• Repeat
• Move robot parallel to surface by half the beam
  width, scan
• Calculate and display outline segments
• Terminating conditions
• Too close to another object
• Traveled a specified distance

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Outline Segment Algorithm (1)

• Calculations in sensor coordinates
• Final points are transformed into world
  coordinates
• Apply at each sensing position except the first
• Apply to each sensor except the front and rear
  sensors
• Current and previous readings for one sonar

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Outline Segment Algorithm (2)

• Calculate distance (d) robot has moved
• For each sensor
• Determine if common tangent exists between
  current and previous readings
• If so
• Calculate intersection points
• Transform points

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Common Tangent Condition

• d distance between
• arc centers
• r radius of arc
• b beam angle
• a angle of beam
• axis to x-axis
• -d cos (a - b) lt rc rp lt -d cos (a b)

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Common Tangent Condition

• d distance between
• arc centers
• r radius of arc
• b beam angle
• a angle of beam
• axis to x-axis
• -d cos (a - b) lt rc rp lt -d cos (a b)

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Common Tangent Condition

• d distance between
• arc centers
• r radius of arc
• b beam angle
• a angle of beam
• axis to x-axis
• -d cos (a - b) lt rc rp lt -d cos (a b)

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Calculate Intersection Points

• Tangent to arc Perpendicular
• to Range Vector
• Common tangent will have slope m
• Range vector will have slope 1/m
• Knowing arc centers and slope, equations
  describing range vectors can be found
• Using range vector equations and radii, points of
  intersection can be found

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Example World
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Example Cluttered
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Example Clearer Picture
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ATM Comparison

• Similarities
• Compares history of sonar readings
• Differences
• Only compare sonar readings with their own
  history
• Uses tangents, not intersections
• Finds segments, not points
• No transversal criterion

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Works Cited

• McKerrow, P.J. 1993. Echolocation From Range
  to Outline Segments, Special Issue Best Papers
  from IAS-3, Robitics and Autonomous Systems,
  Elsevier, Vol 11, No 4, pp 205-211.