Laserspot centers

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Lecture 5What is the best way to use
camera-detected features on the target and
manipulator bodies in order to exploit the
asymptotic-limit region?
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Laser-spot centers in a differenced image.
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How should we locate them?
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And is their camera-space center location
influenced by color?
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Although our camera registers only grayscale
intensity, refraction is still impacted by the
extreme position of the red color within the
visible spectrum.
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Although our camera registers only grayscale
intensity, refraction is still impacted by the
extreme position of the red color within the
visible spectrum.
Can we exploit our asymptotic-limit region with
cues that on average are incident onto the
lenses at different frequencies?
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Although our camera registers only grayscale
intensity, refraction is still
impacted by the extreme position of the red color
within the visible spectrum.
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Will the blue light fall on the same place as red?
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Same place as red?
Not with this lens.
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Same place as red?
With this one, yes.
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n (index of refraction) for various materials.
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How good of a job does the compound lens do in
placing this feature onto the image plane
consistently with the end-member cue feature?
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How good of a job does the compound lens do in
placing this feature onto the image plane
consistently with the end-member cue feature?
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Note that the cues are black and white,
reflecting roughly equally the entire visible
spectrum ...
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... whereas the laser spots are red.
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Sam Chen recently completed a number of
experiments to investigate this matter, using
laser spots combined with the cue-bearing plate
below.
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Before reporting his results, lets return to the
question of the algorithm to locate a laser-spot
center in camera space.
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One possibility The brightest
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One possibility The brightest
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Another possibility A weighted average of (say)
the ten brightest.
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In such a case, we need to be careful of
extraneous, non-spot pixels.
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Due to distances involved, these can drag the
assessed center far from the actual.
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Note that there is no particular right
definition of the feature-center coordinates.
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There are, however, a couple of ideal attributes
of these coordinates as identified in software.
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Recall our two-camera criterion for positioning a
dot onto the surface.
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Image of the spot in camera 1.
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Image of the spot in camera 2.
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The assessed spot center ideally locates the same
physical juncture in the actual mappings of
physical space into each of the participant
camera spaces.
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Or, at least on average, over several accumulated
spots, there is no bias in this regard.
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It is interesting to note that real cameras
have their own pixel-brightness manufacturing
quirks.
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It is interesting to note that real cameras
have their own pixel-brightness manufacturing
quirks.
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These flaws are used in forensics to
fingerprint images from individual, as-built
cameras.
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Our spot-center-detection method ideally produces
results that are robust to such variations.
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Also, as discussed previously, there should be no
relative bias due to frequency-dependent
refraction in the compound lens vis-à-vis the
paper cues.
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For Sam Chens experiments, the following mask
was applied to identify each spot center.
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Mask
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Mask
Remaining elements are zero.
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Mask overlay onto differenced image.
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Differenced image raw pixel data.
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Image conditioned with mask overlay.
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Possibility for subpixel identification of spot
center.
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Here is a plot of densely packed laser spots
accumulated over a 100mmx100mm flat region.
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Even with the smoothed, subpixel
pixel-center-location strategy, the data are
rough.
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Based on CSM (discussed later), the raw nominal
physical coordinates are mapped here.
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Although the plate on which they fall is flat,
random variation causes more than a mm of avg.
deviation from a common flat plane.
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Averaging about 50 individual-spot-center results
per 20mmx20mm region into 25 separate regions
reveals the flatness of the actual plate.
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So redundancy is our friend.
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This is one advantage that machines have. We can
accumulate and match among participant cameras
as many laser spots as desired in advance of the
introduction of the manipulator.
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This ability is due to the pan/tilt-ability
(re-directability) of the laser-pointing base
together with the ability to acquire multiple
differenced images in a very short period of time.
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A similar averaging effect though for
different reasons is applied to the positioning
or CSM side.
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S.C.s tests of precision of the whole occurred
over the
indicated, large region of physical space.
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The target plate was located throughout the
region,
and its orientation was varied.
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The mean error normal to the
plate surface (the only component that could be
assessed precisely) was 0.0mm.
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The std. dev. of the error
was about 0.1 mm, and, importantly, the range was
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-0.3mm 56
-0.3mmAbout 1/10 pixel.
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Return to the discussion of the asymptotic-limit
region of c.s. mapping that makes this level of
precision possible.
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Return to the discussion of the asymptotic-limit
region of c.s. mapping that makes this level of
precision possible.
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Any point x, y, z that is in focus and in view of
our camera will have a mapping, an actual
position or pair of coordinates in camera space.
The actual relationship here depends upon the
lens and electronics, and is complex, almost
impossible to determine globally.
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xcfx(x,y,z) ycfy(x,y,z)
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As a cue enters the cameras field of view its
x,y,z coordinates move as a function of the
robots internal joint angles.
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Consider any physical-space point xo yo zo that
happens to lie along the cameras focal axis
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Consider any physical-space point xo yo zo that
happens to lie along the cameras focal axis
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Consider any physical-space point xo yo zo that
happens to lie along the cameras focal axis
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xcfx(xo yo zo )0 ycfy(xo yo zo)0
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xcfx(xo yo zo )0 ycfy(xo yo zo)0
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xcfx(xo yo zo )0 ycfy(xo yo zo)0
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consider x xo Dxy yo Dy z zo
Dz
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consider x xo Dxy yo Dy z zo
Dz
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consider x xo Dxy yo Dy z zo
Dz
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consider x xo Dxy yo Dy z zo
Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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The constraints are due to radial symmetry of the
lenses.
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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for sufficiently small Dx Dy Dz, xc A11 Dx
A12 Dy A13 Dz yc A21 Dx A22 Dy A23 Dz
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Rigid body
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Nominal kinematics
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Actual kinematics
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EP
AP
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Nominal kinematics
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Nominal kinematics
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Nominal kinematics
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Nominal kinematics
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Nominal kinematics
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Nominal kinematics
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Example of development of a homogeneous transfor
mation
matrix for a 3-axis robot.
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Example of development of a homogeneous transfor
mation
matrix for a 3-axis robot.
Note that the first axis of rotation is vertic
al.
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Example of development of a homogeneous transfor
mation
matrix for a 3-axis robot.
Stationary, base frame.
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Example of development of a homogeneous transfor
mation
matrix for a 3-axis robot.
Moving end- member frame
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Example of development of a homogeneous transfor
mation
matrix for a 3-axis robot.
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This is the diplacement vector to point P with
respect to and referred to the stationary O
frame.
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This is the diplacement vector to point P with
respect to and referred to the stationary O
frame.
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This is the diplacement vector to point P with
respect to and referred to the end-most 3
frame.
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This is the diplacement vector to point P with
respect to and referred to the end-most 3
frame.
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