Referring to Figure 2, prove in accordance with our development in class that, provided the region o

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HW2, problem 1a.

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

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• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

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Let xcxcoDxcycycoDyc

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

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Let xcxcoDxcycycoDyc

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

5

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

6

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

7

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

8

• Referring to Figure 2, prove in accordance with
  our development in class that, provided the
  region of the image within which the cue appears
  is small, a horizontal scan through camera space
  that passes through the center of the cue will
  result in a 111 ratio of black to white to
  black length segments in pixels.

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For our scan, Dyc 0
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For our scan, Dyc 0
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Dxc
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So a sweep through the center produces the 111
ratio, regardless of a, b or B.
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Note that this is also true for vertical and
diagonal sweeps since, due to radial symmetry of
the lens, the xc direction can be defined to be
in any direction.
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Lecture 7
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Since these are actual (unknown) kinematics,the
coordinates are exact.
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Increments
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Increments
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Consider a thought experiment entailing an
incremental rotation of the last DOF, q6.
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Let this be our Pose A.
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Then this is Pose A with an added Dq6 of ten
degrees.
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Compare predictions from this q6 rotation between
the nominal vs. actual kinematics.
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Compare predictions from this q6 rotation between
the nominal vs. actual kinematics.
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Compare predictions from this q6 rotation between
the nominal vs. actual kinematics.
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Compare predictions from this q6 rotation between
the nominal vs. actual kinematics.
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Suppose that the robot kinematics are perfect
with the exception of this one link lets say
its off by 2-degree twist.
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Nominal x y z
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Actual x y z
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Thus
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Substitute Dx Dy Dz into
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Substitute Dx Dy Dz into
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Estimation model
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where
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As we will see, a similar argument can be made
for the other five DOF.
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We seek locally valid estimates in each camera
space of C1 C2 C3 C4 C5 C6
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Example
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Example
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Example
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Nominal kinematics of P
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Nominal kinematics of P
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Predictive ability of estimates
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