#
Elan Microelectronics Corporation v. Apple, Inc.

### Filing
293

Declaration of Jennifer Liu in Support of Plaintiff Elan Microelectronics Corporation's Reply to Apple, Inc.'s Opposition to Elan's Motion for Partial Summary Judgment of Infringement filed byElan Microelectronics Corporation. (Attachments: # 1 Exhibit A, # 2 Exhibit B, # 3 Exhibit C, # 4 Exhibit D, # 5 Exhibit E, # 6 Exhibit F, # 7 Exhibit G, # 8 Exhibit H, # 9 Exhibit N, # 10 Exhibit O)(Liu, Jennifer) (Filed on 6/16/2011)

EXHIBIT H
The nternationtf
Journal
of
tnt
of
robot
SE
Cur
ic reerch
Shel
UNIVERSITV
SN DIEGO
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1982-
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OF
on
no
CALIFORNIA
LI8RRIES
Q627-9Q
Cprinq
Editor
The
Michael
Brady Oxford
Paul University of Pennsylvania
Richard
Number
Volume
Editorial
ISSN 0278-3649
Research
review
June
April
December
and
August October
bimonthly
is
published February
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Editor
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International
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post
postage
offices
Manager
Department
Cambridge
MA
02142
253-2866
APE L0007542
Fearing
of Electrical
Department
Tactile Sensing
and Computer
Engineering
Mechanisms
Science
of California
University
California 94720
Berkeley
Abstract
from
orientation
Cameron
in
This
tactile
sensor
and
has been
depth
made between
been
dimensional
and
sensor
with
implemented
Jbr
are
sensitivity
contact
and
has
simple
one
The
1985
has an
contact
have
sensors
been
element
tactile
of
for
dextrous
trol for
dextrous
mine contact
with
Some
point
it
nice to
to
sensors to
finger
the finger
at
1984
It
is
necessary to
contact
on the
finger
for
know
accurate
This article addresses tactile finger
transduction
mechanism
tact
and magnitude using
location
niques
paper
Fearing
987b
iffTnverse
force
of the
linear
of
to
con
tech
based
on
curvature
and
hemispherical
ing elements
and
International
Vol
1990
No
June
Journal of Robotics
Research
1990
Massachusetts
Institute
of Technology
12
for
total
133-element
and
The
is
is
rubber
in
is
finger
Figure
on
the
cy
the
underneath
12
sens
capacitive
on cylinder
connected
externally
to
now
work
adequate
cylindrical
in
Fearing
for local
finger
the
in
sensor density has been
Other
256-element
roll
tactile
tactels
of
device described
main goal
shown
for
better
subset
The
and
gauges
but an
manipulation
are
elements
from previously reported
determination
1985
1988
as
elements
Only an
aliasing
for
molded
hand
tactile
gives
Strain
of force
shapes
in
and
electronics
reduce
tact
tip
point
Fearing 1986
under the tip
creased
to
The
12
portion
contacts
describing surfaces
fingers
are
the object
if
sensor that
single
Round
the Stanford/JPL
and
single
multiple
quantities
for
hands
about
ing objects
interface
recover surface
better
fool
sensors are not very useful
dextrous
lindrical
discusses
filtering
is
Object
other as well as the object
at
measuring
objects
measure
using
type
addition
and can
mea
difficult
is
It
contact
each
force
There
the
filtering
1988
with
In
touch
tip for
application
and determination
for
surface
explore
single
one
to
simultaneous
the object
sensor array was packaged
design issues
Fearing and Binford
nor
con
Fearing
the location
good
flat
to
parameters
example
are
array sensor
tips
surface
common
only the resultant
deter
to
and type of
curvature
see for
are quite
con
fingers
with
with the fingers
have
determine
where the
impor
force
shown the need
of the most useful
plane
line
is
multifingered
angle and magnitude of force
are
mals location of contact
tact
open-loop
hand have
types and location
Fearing 1986
recover
with
manipulation
Experiments
for
advantage
However
sensors
must remain grasped
hands
al
et
measurement
equivalent
while being manipulated
time consuming
fingers
be
sensor can
over the whole finger
ment
tant
Hillis
Siegel
single
measurements
tactile
surement at each
from the
from
shape
In one sense
and
force
Introduction
information
1987 and
transducers
1984 Chun and Wise
motion makes
contact
structure
and Dario
Bicchi
of deflection
location
gives
gauge
Preliminary
total
move
Local
strain
in
contact
obtaining
array sensor approach
1985
discussed
are also
sensor that
using
uses arrays
Boie
two-
to
finger-tip
force
Brock and Chiu 1985
that
measurements
and Speeter1987
approaches
are
resultant
1981
contact
line
formation
and
of strain
set
1988
et
different
determining
analyzed
normal deflection
only
of
of skin thickness
effects
location
infor
localization
comparison
sensor
model The
basic
of appropriate
analysis
accurate
the cylindrical
on
force
An
allow
Two
cylindrical
planar linear elas
spatial aliasing
methods for determining
tangential
to
of
for determining
contact
stress-strain
depth
using
analysis
used
and reduced
contacts
design
analysis
signal
mation about the applied
sensor
themes
mechanical
models
ticity
main
has three
paper
static
and inversion methods
Transduction
987a
con
tips are
Allen and Bajczy
fiber-optic
device Begej
the use of this finger
as
an
ex
APE
Fearing
LJOO7543
Tactile
Fig
sensing
Fig
finger
hand
Stanford/JPL
for
sensor
Capacitive
block
Drive
diagram
100
Ki-Ix
ultiplexor
Multiplexer
Output
Detector
device
perimental
The
search
and
It
in
is
not intended
not robust
probably
however
is
sensory and manipulation
for
is
finger
rather
as
enough
final
re
prototype
and reasonably
sensitive
use
for industrial
durable
laboratory use
output
improve
Hz
to
been
speed
were
tip
good
so that
many
designing
and low
sensitivity
designs could
be
quickly
and the success
with
Siegel
arrays
Bole and Miller
from capacitors
oped here
of other workers
al 1985
Boie
1984
devel
the sensor analysis
the most part
mechanism
transduction
evaluated
us to build tactile arrays
led
However
for
is
1985
et
described
as
and ease of fabrica
These considerations
capacitor
the tactile finger
aliasing
1985
and Hollerbach
by Fearing
tion
in
used
of the
independent
by having the
was not
intersection
As
in
tance
in
but
it
was
This
since
only
forces
the
has
not
was an issue thus the
remotely
shielded
cables
driving
from the sensor
distance
at
built
of about
into
30
the finger
of installing
cost
The
are
large
is
tip
it
enough
inter
thus lost in
of this
capacitance
Two
cable capacitance
significant
cm
electronics
of the signal
fraction
required to reduce
at
improved
significantly
the sensor design was stable
one
coupling
the array and one for sensing the array
output Improvements
used
the rate
constraints
could
be
in
sensitivity
and reduced
accomplished
embedded
in
by
wir
custom
the core of the finger
Design
Figure
of rows
the method
at
for static
capacitance
sensor allows
for
but
be increased
electronics
significant
the shielding
2.2
As shown
hand
that
felt
hybrid circuit
Electrical
done
the considerable
nally
ing
2.1
could
While performance would be
for
Hz
15
to
potential
The
improved noise performance
are mounted
the base of the
criteria
at
Simplicity of construction
Criteria
ground
to
cross-talk
limitation
electronics
primary
scanned
for
has been
analysis
The
and reduce
array was originally
reduced
Construction/Design
row and column Unused
selected
shielding
low scanning
Finger
for
voltage
and columns are switched
rows
junction
capacitors
are
formed
at
and columns of conductive
used
is
by
Siegel
measured
1986
by
the
the
strips
capaci
amplitude
Measurement
the
of the
Using an amplifier with input impedance
voltage
output
of the tactile sensor
is
RL
given
the
by
APE L0007544
The International
Journal
of Robotics
Research
in
Capacitor
Fig
elastic
model
strip
of width
mm and
2.5
0.5
tric
constant
From
00
surface
mm The
of
separation
pF
about
is
the dielec
for
of about
in
the arguments given
1985
bach
mm and
5.1
capacitance
normal
the
an important
beneath
strain
measuring the subsurface
the surface
is
To approximate
we use
measure
to
quantity
and Holler-
Fearing
strain
Ad
where Ad
is
capacitor
CSRLo
CSRLW
CL2
of the top
is
small and Ad
d0
d0
the bottom
since
VI
displacement
long
very
has no effect
the percent
WRLCL
C5
jVdI
C50
VSVCL__CL_1
_M
d0
d0
V5
where
Vd
the drive
is
tances between
for
and columns
CL
and columns
rows
thus the cable capacitance
dominate
The
will
significantly
CL C5
larger
and
shows
Figure
eq
large
is
simple
model
capacitor
plate
the sensor capacitance
plates
that
can
be assumed
are
the fractional
cell
at
the
same
twisting
for thin
well-behaved
each
and given
RL
and CL parameters
independent
of these
to
is
The
fractional
force
deflection
depends
elasticity for that
depth Percent
strain
to
directly
for
if
cell
will
all
be
par
cells are
used
throughout
the normal
con
order only
first
to
deflection
to
approximation
and compared
paper
for
measured with the same wiring and
deflection
parameters
first-order
valid
capacitance
is
V5 and
that
amplifier and the same
ticular
as
undeflected
measurements
cell
it
particular
stant
to the
without
compression
as
this
strain
is
C5K00
where K0
ty
Since
on the modulus of
The
for
to
valid
sumes capacitor
formula
made
capacitance
frequency
the nominal
function
with
than the sensor capacitance
sufficiently
in
approximation
capacitances
from the sensor
the amplifier and the amplifier input
is
This ratio of voltage
change
be
C0
where
cable
are
should
With the cable capacitance
d0Ad
CL
ca
sensor
of stray capaci
effects
rows
the load capacitance
into
the unselected
pressure
to
unselected
the
is
and amplifier input capacitance
capacitance
lumped
The
one junction
at
pacitance
and C5
voltage
deflec
by
obtained
is
signal
is
plate
of the
plate
Ignoring tilting of
of the plates
parallel translation
plates
tion
the
of free
separation
is
the dielectric
space
and
is
2.3 Mechanical Design
d0Ad
constant
the plate
Ad is
the plate
actual
capacitance
fields
because
pared
to the separation
may
the plate
is
The
d0
is
the permittivi
nominal
as
not
result
very
plate
The
displacement
be larger
area
is
area
of fringing
large
com
sensor has conductors
The
finger
Curved
size
surfaces
and shape
are
the fingers Fearing
can occur
anywhere
palmar surface
finger
is
Fearing
1986
chosen
are
needed
on the finger not
The
good grasping
objects
In these operations
thus complete
necessary
for
for rolling
finger
just
tip
made
of
contact
on the
sensor coverage
is
about
of the
cylin
APE L007545
Fig
Finger
construc
tip
dielectric
Outer
Electrodes
Inner
Electrode
JSA
of molded
Structure
Fig
tion
layer
STRIP
ON CORE
RUBBER
drical
mm long
25
section
with
hemisphere
with
coverage
For improved
design
versions
use 3.3
free
should
design parameter
be
twice
But
response
overall
finger
mm width
as
compliant
copper
rings
DPR
In the
is
inversely
sen
ap
ring
for
measured
is
incompressible
to
very
sensory
mm
covering
as
Poissons
on
10
force
is
the
rigid
coverage
strips
by
which
transmis
molded
modulus which
Nm2 The rubber
ratio
0.5 was veri
reduced
obtain
tric
section
spatial
The
im
without
sensitivity
for
as
case
sensor
of the wider
discussion
of
soft
the
and
the dielectric
to
struc
foam
the skin layer
give
Fig
of the
with
solid
layer
had only
of the molded
Siegel
1986
This
some
it
mm thickness
0.7
some
Thus
test finger
the sensitivity
1985
to
spaces
foam
of about
al
et
hollow
as
dielectric
in
as
in
cells
of some
strength and homogeneity
one-fourth
tabs
molding
during
was changed from
includes
Siegel
rubber
from the same rubber
sensitivity
using
because
the sensitivity
decreasing
increased
about
entire
improved
See
foam absorbed
structure
rubber
be
move
to
issues
molded
same
softer
In the limiting
wide as the
to
increasing aliasing
places
initially
The
foundation the
elastic
as
is
be
can
for
rubber This rub
separate sample
response
pulse response
The
Nm2 modulus
deforming
on an
plate
skin depth
layer
was
the harder rubber
for
without
layer
ture
disc
i0
at
dielectric
rubber
helps to widen the sensor response
also
the dielectric
of
thickness
For
low tensile
2.5
design
from the
Hardman Inc
its
be about
experimentally
0.5
the finger
4280-LV
chosen
give
layer
Figure
mm and
3.3
separated
of about
in
rings
outer
whole
of
the surrounding
of the tendency
aliasing
diameter pro
in
dielectric
foam
sensitivity
than
measured
impulse
is
was chosen
newest
at
to
open-cell rubber
is
fled
strain
shown
is
mm
17.7
spaced
are
sion and protection
ber was
structure
the seven
are
dielectric
molded
that
compromise between
core
integrity
the eighth
the tip The
with
strain
The
needed
tip
lDelrin
electrodes
connected
is
subsurface
equal to the sensor spacing
lightweight
at
alias
ratio
softer
cause
for negligible
and aliasing the sensor depth
vides structural
2.5
From
the sensor depth
signal-to-noise
also
is
For increased
much
used
the sensor depth
is
1985
depth As
to
proximately
driven
along
of the continuous
good
sensitivity
proportional
The
and 180
the length
the sensor spacing
ing from sampling
sitivity
and
initial
the latest
performance
spatial
mm spacing
and Hollerbach
Fearing
good
the
around the circumference
spacing
The
for
UPPER
RING
to
along the length
spacing
spacing around the circumference
450
diameter
of complete
goal
array on the cylinder led
mm center-to-center
3.8
mm in
and 25.4
end The
the
at
dielec
describe
increase compress
to
ibility
Unwrapped
the linear
around the circumference
mm which
would cause
separation
for
450
lot
of the elements
spacing
of aliasing
is
about
Since
AP
The International
Journal
of Robotics
Research
the
L0007546
Percent
Fig
load
applied
vs
deflection
to
one
celL
50-gm load
LLneorlty
Fearing
in
sured strain
C20
contact
pressure
area can
mate method
15
for
to
for
is
almost
reduce
the force
in
40
20
80
100
80
gnoms
toad
is
3.2-mm
does
orders of magnitude
is
copper
not stretch
beam
like
the sensor
but can
This
much
beam-like
better
might he obtained
rings
the length
around
localization
tion Fearing
the
tactcl
straight
load
0.5-N
rubber
relation
is
The
resolution
along
important
circumference
for
than
manipula
1986
of the
in
true
of
spond
sample
is
important
tion
cell
AID
The
for
for
of each
in
cells
diameter
element
tactile
the finger
units
gives
seven
7.8-mm2
voltage
pressure
sensitivity
meaning
because
figure
of about
The
0.5
real
gm
is
of
of 0.06
the response
for
cell
1t change
pressure distribution
sensitivity
output
of signal
of this
6%
sensor
6%
table
relation
medium
but
capacitor
the parallel
can
estimate
an
this
wasnt
would be sensed
linear The
truly
function
vernier and found to
in
for
force-deflection
make
to
the
for
very large even
force-strain
as
than
less
the strain
of load was
have
similar
the sensor appears
of
plate
capacitor
raw
sensitivity
if
deflec
to
re
eq
area probe
is
6% deflection
0.06
A/D
gm
mm2
unit
function
also
of merit
AID
units
Calibration
is
for
More
important
The
little
of the
force
than
measurement
capabilities
is
how
of the sensor that is
performance
of 2000
gm mm2 has
figure
100
l/
3.1
deflec
50-gram load on
voltage
bits
pressure sensitivity
sensed
is
the strain that
of rubber
with
counterbal
is
The
tactel
array give
hemisphere
with an undeflected
tactile
evaluating
50-gram weight on
for
3.2-mm
is
one
at
between
Evaluation
parameter
the sensitivity
least sensitive
as
the
in
to
friction
instrument
placed
nonlinear
medium were
the sensor and
relation The
An
look-up
strain
needed here This
tion
This
expected
used
measured
Performance
and thus
is
by
of the pivot point
through
origin
of 10%
strain
material
easily be
more
from the
This
trials
halfway
There
side
1-N load
to
response
line
than
conductor
improved
is
aliasing
degree
greater
of the finger which
The
caused
probe
it
of the rings gives
and reduces
compliant
for
the rubber
approximately
property
to
with
on the outside
are
bend
overlap
around the circumference
than
stiffer
only
cell
output
of seven
with weights
diameter
on the opposite
weight
tactel
application
and the weight
the pivot point
ance
beam
balance
the
force
of one
deflections
be
may
that
The
device
simply
end and
The
of the large
small variations
larger
approxi
in section
from the average
was generated
plot
of
from the capacitor
eq
using
in spite
An
response
as determined
output
linear
applied
described
is
to
the load from the strain
determining
sizes
mea
the
frequencies
peak strain
larger
increasing weight
sensor voltage
-o
force
shows the monotonic
Figure
10
give
contact
varying
of the spatial
The same
As
probe
1985
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-I-
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Sensor
25
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APE L0007547
Fearing
Fig
Responses along
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Fig
moving
length for
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Sensitivity
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time
APEL000754S
The International
Journal
of Robotics
Research
Fig
Superposition
loads
two
of
10 Sensor
Fig
on finger
for repeat
Superposition
25
--probe
Loads
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1985 The creep strain causes prob
can make the sensor output appear
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lems because
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sensor shows the effects
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100
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APE L0007549
Fearing
11 Probe
Fig
noise histo
Fig
gram
12
Viscoelastic
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13 Response
Fig
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450
1989
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Tip Behavior
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35
30
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20
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15
time
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The
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tends slightly into the tip area to improve sensitivity
and
to
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and the cylinder
the junction
From the
top
between
the
of the
APE L0007550
I9
The international
Journal
of Robotics
Research
14 Responses
Fig
normal
probe
ing
mov
for
to
15
Fig
plane
tip
geometry for
Finger
assumption
stress
Pressure
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Of
Half Plane
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two-dimensional
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Phillips
Hollerbach
strain
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finger
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and
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and Johnson
1985
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fractional
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der Consider
with the applied
1981
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plane Figure
15
reasonable
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Goodier
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medium
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linear
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Timoshenko and
1951
the
for stresses
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sensor at the top
vc5
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to
the responses of Figure
definitely
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inclusion
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Elastic
way
1985 used
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to
sumption
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and Hollerbach
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of the finger
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surface
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The
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sensors on
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14
be
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Figure
beneath
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It
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mm
10
force
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of analyzing
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sphere
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would be used
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about
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APEL0007551
Fearing
11
Fig
16 Plane
and
experimental
stress
model
data
lv
1.2
2Pz1v
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0.8
the relation
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1980
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11
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ure 16 The
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line
approximates
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increments
elastic
1985
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Fearing and Hollerbach
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33
Response Along Length
edge
Youngs
is
10
2.5
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about
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has
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dielectric
more giv
APE L0007552
12
The International
Journal
of Robotics
Research
ing an effective
greater
The
square
of
mean
root
scale which
full
of 0.5
made
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An
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18
19
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APEL07553
where
is
the
For an
Fourier transform
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W3
W2
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1980
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2w
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29
signal
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In the second
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Figure
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34
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ux
1980
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23
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Because
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33
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Bs
the
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1980
Gladweil
choose
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ap
stress
v/
strip of thickness
elastic
functions
tential
vt
substitution
stresses
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For the plane
shear stress
the
proximation
to
slightly
not go
the
reduced
gets larger so there
is
with
the capacitor
and the
plate
bottom
separation
d0
plate
is
is
fixed
at
at
APE L0007554
14
The International
Journal
of Robotics
Research
17 Gain
Fig
vs
and
separation
Fig
capacitor
thick
strip
half
18 Impulse response
plane and strip
for
ness
Coin
For
E2.5x105
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20
F20
N/m2
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ZJ////11//d/.//fJJ//J//t
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-15
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mm The
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soft
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It
above
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foundation
10%
about
predicts
3.8
mm
the capacitor
approach
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Because
gain changes
thickness
plane strip
half
in
is
agrees
quite similar
in
more
closely
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layer
to
The
soft
backing
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loss
model does not
The
than
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of
along the length
analysis
for
layer
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can
be
to
much
rigid
important
for
and
prob
The
simpler
The
for
pressure from
sis
for
is
the length
is
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cylindrical
much
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better
good position
get
of peak deflection
is
also
on the
estimating load magnitudes
describes
to
of the coarse
to
to
important
recovery
section
recovering
an interpolation
method
location and magnitude of the center
discrete
restricted
measurements
contact
type
is
in
better
Fearing
of
analy
and Bin-
1989
Assume
concluded
plate
spacing
it
signal Because
of the finger localization
finger This
data
measurements
strain
continuous
information
ford
of sensitivity
yield
the
here
it
Reconstruction
spacing of sensors along
the tactel
response
elastic
recover
section
the skin above
multiple
discrete
portion
half plane
the bottom capacitor
fabrication
From
simpler
for
response
the impulse
can be attached
significant
makes
for
much
of the previous
the plane strip analysis
not required
dation
experimental
Strain Signal
Fig
with increasing
with experimental
softer
lem has not been considered
with
plane
the half plane assumption
value As the
use the
and width
shape
cause this effect
From
to
little
18 the impulse
Figure
plane
dielectric
that
half plane
Nm1
200
the model
thicker
so
half plane analysis
stress
As shown
may
to
re
impulse
stress
the finger
half plane of the previous
seems reasonable
it
Ft
and
gets
section
The
that
for
adequate
enough
similar
assumption
the
the
for
calibration
with the experimental
should
model
have
is
sponse
but the calculated
response
obtain
to
deflection
used in the finger
as
well
agrees
layer beneath
the
increase
substantially
not necessary to
compliant
mm
0.5
plane
the capacitor
so
seen from the plot
be
not
the impulse
of the
15
err
tion
p051
sensitivity
same parameters
which
As can
thickness
model
This
increases
capacitor
backing
the sensor gain
capacitor
plotted as the thickness
is
10
-5
mm
thi ok ness
ond
depth
-10
discrete
sensors at spacing
then
seven
sensors of one row along the cylinder give
is
foundation
rigid
The
foun
hx
plane
closed form expression
nb
rect
37
for
APE L0007555
Fearing
is
Fig
Hs
As
19 Frequency response
and aliased response
maximum
The
assume
I.8
that
the low-pass
is
energy
The
but
continuous
1/b03
0.4
is
the normal
eq
strain
impulse
we
filtering
Ers
version
filtered
low-pass
recovered
Ers
and the
for
length
is
38
vx2
xEr4
defined
now
have
42
2bs
rect
has both
As
.tAs
As
and
the desired
2bs
rect
43
39
The
relative
from the
38
neglecting
spectrum
higher
by
leads
error
Hs
sinc
is
caused
by aliasing
an
Assuming
ideal
obtained
signal
low-pass
error
E0
filter
the
by
given
40
6xbs
is
44
of energy in the reconstruction
the energy in the original
to
1978
Pratt
to
error
ratio
ER
E0
domain eq
aliased
AsH4sHsQ
ifIxI
In the frequency
the
is
order terms given
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rectxl ifx
rII2b
Hs2ds
IHsI2ds
ijim
with
spatial
frequency
Fourier transform
is
which
is
frequency
in
of
periodic in frequency
widened
Because
of
Ess
of sampling
and the frequency
of having
response
and
cycles/mm
by the convolution
result
ex
finite
components
from
response
2z
function
Ess
by low-
by
hx
rect
aliasing
be
principle
limited by aliasing
is
Es
where
The
in
Ignoring the finite finger
0.5
The
defined
The
in practice
filtering of the periodic spectrum
of
the aliased
hx
may improve
slightly
cyctes/mm
fncquency
where
we
along the
occurs
reduced
can
signal
with ideal low-pass
0.2
is
If
pressure distributions
but this process
0.1
Hs
Figure
mm
3.8
sensor width
finite
significant
by low-pass
tent
of deflection
properties of
pass contact
a.1
the
1/3md
ford
response
integration
plate
capacitor
cC
occurs at
response
shows the frequency
19
with
only seven
hx eq
the plane stress assumption
the sinc
is
39
given
at
Ers
response
is
6irbs term
samples The
depth
with
This
cluded
are
by
the effects
e211
we
41
for localization
lated
function
eq
45
The
will
effects
errors
caused
Hs Not
low-pass
and amplitude
Fs
is
an upper bound
of aliasing
on
in the
sufficiently
and
3.8to
20%
interpo
bandlimited
on the expected
localization
in
filtering
0.20 which implies up
If
be
of
the sensor depth
for
get
error
2ird
reconstruction
of nonideal
numerically
mm spacing
3xdsI
includes
expression
by the cutoff of the high frequencies
Evaluated
Hs2irdIsllv
45
the
error
and amplitude
APE L0007556
16
The International
Journal
of Robotics
Research
20
Fig
Reconstruction
Fig 21 Interpolated
error
caused by aliasing
3.8
lion
mm
nterpototion
30
Error
continuous
ci
terpoo
in
25
ted
somptes
20
tocotizotion
15
1-
error
offiptitude
ci
-t-
dejiec
surface
10
ci
toctel
postion
in
force
estimation
now
will
be shown
row on the finger The
along
windowed
using
sinc
the seven
for
strain
sensors
estimate
response
angle of force
strain
be
principle
when
there
1985
no
is
and the applied pressure
hx0
function
nh
__________
46
This
to
is
find
with
window Oppenheim
the Hanning
1975 which
is
makes
the
ringing
the total
amplitude
point force
to
the
20
error
in
filter
of samples The
finite
extent
in
flection
function
N-IN-I
and
when compared
Here
are
response
tion
forces
accurately
for
Small
location
can
certain
finger
errors
example
lead to
configurations
location to
force
Localization
accurate
be
but can
tool
processing
the tactels
all
zj
where
The
is
11
the
de
interpolated
is
srnirxisrnnyj
48
wx zwyj
are
in tactel
21
shows
with
spacing units where
plot
of the deflection
soft object
large
useful
apply
contours
contours
distances
by dividing by the sensor spacing
normalized
tool
The
of height
than
is
surface
another
plot
conditions
plot
onto
for
of equal percent
for
where
finger
unwrapped
the surface
for
plane
analyz
deflec
equal deflection
are
1986
Fearing
large
maximum
single
by interpolation
strain
of element
ing the sensor output
the contact
ap
the surface
fl
more
know
at
array formed from the simul
of
the cylinder and the tip are
to
an even
real-time
10
Localization
important
force
to
contact
is
in
fxy
window
Figure
It
from the
used mainly for sensor evalua
be an
deflection
and reduces
the interpolated response
strain
47
forjnIN2l
the plane stress model
continuous
11
response
percent
shows the peak displacement
for
41
is
relatively
is
than as
rather
taneous
number
low-pass
Figure
tion
Let
is
wn4
and
and Schafer
is
and
loca
for
more general
tangential
the peak
scheme
simple
time consuming
force
sensors as was proposed
and Hollerbach
Fearing
done by solving
and magnitude of
at three
equations
proach
is
interpolation
could
tion
of
errors
in
xy
line
x_
APE L0007557
Fearing
17
22
Fig
Fig 23 Measured
contours
Deflection
on
probe
location
array
Contours
Strain
interpolated
for
IS
iN
degrees
III
Probe
interpoLated
Location
6.5---ideaL
-I-
6-
position
esensed
Cs
Experiment
position
--5.5-
-0
1CA
ID35
-0
around
tactel
The
of constant
direction
on the
height
4.5
3.5
circumference
surface
given
is
The
5.5
toctot
position
probe
maximum
conditions for
of
are
surface
by
4tan1f
.feee0
Ox
50
The
contours
found
are
from
iteratively
slopes
are
Oy
search
Using Newton-Raphson
where the
zero we
Ax\
\AJ
Thomas 1968
where Ar
is
the step size The
locationfx
Ax
and
to
locations
is
for
contact
sor
spacing
The
the deflection
with
finger
low-pass
surface
is
profile decreases
spacing
45
has
out at about
tion on the cylinder
rings
This
to
45
is
behaved
zero
at just
90
may
Fig
by 3.8-mm
sen
one
as
spacing
loca
by the cop
caused
of the
as
find
the
maximum deflection
an unknown pressure
iterative
and
its
techniques
location
spaced
are
are
needed
Fig
steps
location and
of the
portion
50-gm load
will
strips
is
be
the
The
higher
is
probe
if
moved
along the strip the tactile ele
mm along
the
row
the figures are given in tactile element
The
abscissas
tactel spac
ing units
The
ripple
on amplitude
caused
for
error
between the copper
3.8
three
of probe
effects
The
strip
by
aliasing
plitude
as well
rubber
To
in
is
from the max
two or
along the central
boundary
250-jim increments
ments
unit
Note how the cyl
by the incompressibility
probe
above
starting
recovery
deflection
avoid
cylinder to
at
the
tactel
0y2
in typically
and 24 show
centered
ensures that
45
32f
to 0.01 tactel
observed
is
peak percent
from the contact
be
tactel
the finger
The
Ox
OxOy
32f
Convergence
ures 23
not sufficient
around the circumference
inder bulges
per
to
new
tracking algo
characteristic
well
the
adjust
on the contour
rod at
around the circumference
strain
to
find
new
the
at
error
of this contour
where the
cylinder axis
used
ensure staying
ure 22 shows the output
rithm
height
Ox2
OyOx
51
\ArsinJ
to
have
a2ff
02
arcos4\
52
and
Ox
are
sensed
ing error
These
of
results
0.5
and peak location
The position of the probe
12% of
within
mm along
imply that
ideal
the length
aliasing
is
less
is
mainly
and
for
am
position
of the finger
severe than
APE L0007558
18
..The.Jmernational
JQzirjial
of Robotics Research
24 Measured
Fig
25
Fig
peak
around
amplitude
Poa
Interpolated
Localization
errors
circumference
Strain
30
4.5
ideaL
position
sensed
25
position
circumFerence
around
Q20
ci
15
a2
10
.5
1.5
3.5
probe
is
that
the
error
aliasing
above
directly
polation
tactel
when
zero
is
because
the
is
the nonuniform
10
probe
line
An
60
100
60
120
degrees
positior
HstHOdE
the
sinc
the sample points
passes through
source of errors
tional
plane stress model with
by the simple
load Note
20
6.5
toictet
position
probe
predicted
5.5
inter
addi
Then
normal force
for
of
positioning
the sensor rings from manufacture
Localization
of the finger
ing the probe
is
tested
in
the same
25
10 Fig
manner
The
increments
at
larger about
mm error
This
need good
of
line
contact
localization
along
on the
by apply
localization
determine
Fearing l987a The
the circumference
was too large so improved
built
with
180
we
and
and around
the length
the circumference
were
HOF Fsdx
the
cylinder
finger
around
error
fingers
where
Force
is
is
the total force
recovered
the interpolated
different
It
is
useful
sensor
to
This
estimate
know
section
this
the total normal
uses
simple
force For contacts
three times the sensor depth
proximated
Fs
will
as
tend
constant
to
be
56
HOF1Psdx
spacing
Total
Estimating
55
error
2.3-
about
is
To
along the circumference
orientation
L. FHsFsdx
performance around the circumference
was
force
aproximation
longer
Hs can
because
bandlimited
on the
than
be
to
two or
crudely
the surface
finger
ap
pressure
The
contact
integrals
disagreement
Aliasing can
ing
987b
method
simple
fractional
the normal direction
lengths
contribute
errors
do not show
filter
in
Fear
the integrals
more accurate
but
contact
large
approximation
description of
fast for large
three
for
SO-gram load
deflection
to
and
shows
26
profile
with
in spite of the crude
has
Figure
deflection
each
of fractional
using an inverse
and
in
by interpolation
the method
here
is
areas
APE L0007559
Fearing
19
Fig 26 Contacts
and
total
load
contact
Strain
Interpol.oted
car
Bar
normal
Loads
Smith and
there
stress
40
aS
run
fc2dx
A1
21
30
mnff
rnmJcdx
dx
123
132
115
zOpx
crx
where
Now
tan
/3
sensor at constant
fx
1-
for
the
px
we
fx
where
px
is
of an
lution
Thus
components
Force Angle
would be
useful
to
get
result
normal pressure information
as well
as
sensor
From eq
with
be
the plane
both
stress
contribute
and
for
contacts
where the contact
1985
method
is
function
an even
pressure
is
contacts
with
type
here for the
proposed
edges
vertices
it
The
the
convolution
angle of force
planes
normal
stress
and the
function
odd function
as
tangential
can
be
stress
The
measured and interpolated
and odd
us even
gives
fx
fx
fx
corresponds
to
eq
an
57
vx2
cos
skew index
sin
which
Note
gives
is
defined
Similarly
are
and odd impulse
even
responses
The
assumption
at
the surface
can
at
be
made
any point
that
is
the tangential
proportional
to
best
be
63
maxJ
index
In general
function
plicated
might
heven
stress
as
maxf
an indication
the skew
that
indentation
there
62
into
2F
vx2
fx
strain
Ejj
2F
function
deflection
by
parts
skew
Cy
61
for
and odd components
even
60
ddx0
pxx0h0x0ddx0
and cyl
spheres
seen by breaking
an
stress
in
x0hx0
symmetric
an even
to
corresponds
in
xc
fx
inders
The
results
tangential
and
have
known
priori
case when the contact
for example
and the convo
function
normal and
by the
of two even
can
Fearing and Hollerbach
is
by convolution
caused
respectively
./
stresses
strain Methods
the
strain
load
line
pressure
tactile
normal
surface
tangential
recovering
cylindrical
from
for
for
assumption
the normal
to
been proposed
line
the expression
normal and
seen that
information
force
tangential
the
at
even
58
hoxo ddx0
px
It
have
and an odd function
even
odd function
Recovering
strain
by an
the strain at
functions results in an even
Length
normal
xoEhcvenXo
pressure on the surface
aLong
is
Jx fdx
Jx0
toctel
that
z0Jipx
caused
depth
px
distribution
020
cAx
and
1953
Liu
of the relative
wili
the
be
force
skew index
will
as
com
be
of the pressure distribution
used
angle
zero for pure normal
and
means of tracking
force
angle
be simply evaluated
for
line
changes
the
The
skew index can
APE L0007560
20
The International
Journal
of Robotics
Research
27 Even
Fig
and odd
Fig 28 Measured
strain
odd percent
model
components from
300
and
even
deflection
for
contact
Knife
40-
Experiment
Edge
at30
CF
degrees
oeven
port
odd
0.9
30
port
--interpoLated
0.6
--3
-3-
020
0.4
4-
0.2
-D
-0.2
mm
position
toctot
indentor
tion
force
0.5
angles
The
this
the plane
for
Unfortunately
with
is
stress
low-fidelity
maximum
even
signal
strain
assumpfor
Knife
Edge
at
Experiment
t30
degrees
40
small
occurs at
Oandisgivenby
30
2Pcosa
max
64
020
The
maximum
odd
strain
occurs at
010
_____________
65
and the
maximum
odd
strain
ratio
0.5
2F0.2441
maxec
The
for
of odd to even
strain
is
given
by
toctet
sin
66
is
strain
even
max
max
Figure
knife
and Figure
edge
driven
from normal with
recovered
by
along the edge
0.2441
67
tan
67
analytic
result
28 gives
experimental
into
the surface
100-gm force The
interpolation
for
line force
at
strain
from the seven
of the cylinder
Since
the
at
results
response
tactels
maximum
esis
offer
is
0.1
for
however
and
aliasing
300
the
maximum
and odd functions
with this point as the origin The
of about
zcvee
27 shows the
30
for
E0
to
corresponds
sponse the even
the skew
10%
also
improved
signal
well
agrees
can
be
problem
force
Strain
result
with
obscured
errors
gauge
angle recovery
re
strain
determined
experimental
errors Amplitude
calibration
are
ratio
are
eq
by hyster
caused
methods
by
may
Brock and Chiu
1985
For
more general even
the line load the force
Fearing
than
pressure distribution
angle can
also
be
obtained
by
APEL907561
inverse
using
the
Taking Fourier transforms of
filtering
and odd impulse
even
we
responses
allows partial
68
neous
real
is
the normal
function the
frequency
of surface
component
and
stress
is
which
for
sponse
The
an
is
strain
Fs
frequency
component
of surface
inclusions
not an isotropic
medium
from the
theoretical
existence
Fs
of the inverse
by
filter
Es
71
thanks
ration
be
in
Rise and
sensor design and
ment and
comments
for
to
This work
tried
of inverse
limitations
and Binford
Ess
Tm
filtering
1989
72
by
Stanford
at
DARPA
provided
K-0002
and F336l5-82K-5
and
nition
Conclusion
elastic
Simple
tactile
it
for the
is
for
many
0.2
Perhaps
to
results
tactile
finger
is
forces
is
ade
and
Intrinsic
is
to
Robotics
Boie
for the
within
to
im
Stanford
improvements required
and the delayed
elastic
are
re
IEEE
sen
tactile
optical
Automat
Robot
31
Boie
eds
Roth
Research
1984
Proc
Atlanta
artificial
of the 4th
Capacitive
and
1985
Miller
Chiu
ASME
Winter Annual
Daniel
robot
hand
Meeting
and
mt Symp
Bolles
on
Press
readout
and
on Robotics
Conformable
4526043
1985
Miami
Califor
In
impedance
IEEE mt Conf
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