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MAS836Sensor Technologies for Interactive Environments
Lecture 8Inertial Sensors
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Inertial Sensing
Measures the inertial properties of a bodyi.e. thosehaving to do with dynamics (time derivatives ofcoordinates) Exploit only the properties of objects moving in space
> Black-Box devices require no external field or reference (ideally). But they do respond also to gravity (more later)
> Where does inertial come from (Machs Principle, Higgs field, etc.)?
Sensors include accelerometer, gyroscopes, velocity sensors,tilt switches, compasses and more.
Note that multiple measurements from a locationsensing technology can also be used to infer inertialmeasurements (e.g., obtain the time derivatives) Magnetic, acoustic, radiolocation, GPS, etc.
But this is generally backwards from what people want to do> Plus measurements can be noisy (more later)
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Inertial Sensors:Accelerometers
One of the two main inertial sensors, accelerometers
measure the translational acceleration exerted on a body
relative to some reference frame
Key uses: Airbag triggers
Simple biomedical sensing
Human computer interfaces Borehole and missle/aircraft/spacecraft navigation (high end!)
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Inertial Sensors:Gyroscopes
The other main inertial sensor, gyroscopes
measure the rotational rate of a body about a
fixed axis
Key uses:
Video camera stabilization
Automotive roll-over detection
Human-computer interfaces
Again, navigation (once more, high end)
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Inertial Sensors:Miscellaneous
There are number of other sensors which couldfit under the rubric of inertial sensors. Two keyones are:
Tilt switches for translational acceleration> Used for very low frequency, low resolution systems, we
will comment on a few later on
Compasses for rotational position> Useful for navigation in areas ofconsistentmagnetic field.
>Not inertialexploit an outside magnetic field.
> Covered in the previous lecture.
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Why measure inertialparameters?
Infrastructure free Simplifies task Only body of interest is instrumented
Vastly increases areas of use Cannot provide infrastructure for the whole world
> Well, actually, you can (aircraft navigation (LORAN),
GPS) but it is extraordinarily expensive
Self-contained
Cannot be jammed or fooled
> Unless you have a huge mass laying around!
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Why measure inertialparameters?
The problem with derivates (1) It is certainly possible to derive acceleration,velocity, rotational rate, tilt, etc from
conventional positioning system
Both from large scale systems such as GPS and
small scale systems such as the Flock of Birds
The design problem with this is that you are
measuring one quantity and then processing it tocalculate another quantity, which could have
been measured directly in the first place.
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Why measure inertialparameters?
The problem with derivates (2) There are also two key mathematical problems Time lag
> The more accurate your derivative (ie, the more points
back in time you look), the greater the delay.> Now consider that acceleration is the second derivative
Frequency noise
> A pure differentiator provides a linearly increasing gain
with frequency. This amplifies high-frequency noisewhich can swamp out the signal.
> Often have to low-pass before and/or after high-passing(see above).
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Why measure inertialparameters?
More direct measurement Most importantly, inertial parameters are oftenthe ones of fundamental interest.
Simple example with airbag
> I dont care where the car is, just if it stopped suddenly
More complex example with human muscle motion
> Unconstrained motion minimizes jerk
> Acceleration signal provides motion parameters trivially
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Inertial Measurement Units:Basics
An inertial measurement unit (IMU) is a sensor package
containing three orthogonal axes of rate sensors (gyros)
and three orthogonal axes of acceleration sensors
(accelerometers) Often supplemented with additional sensors for
calibration (i.e., magnetometers provide a rudimentary
degree of orientation reference)
Historically used for inertial navigation or tracking
out of price range for HCI
Typically on the order of $1000 and 10 cm3
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Inertial Measurement Units:Brief Survey
Made by: Xsens Motion Technologies http://www.xsens.com
MicroStrain http://www.microstrain.com
Cloud Cap Technology http://www.cloudcaptech.com
Intersense http://www.isense.com
Crossbow http://www.xbow.com
Us: http://www.media.mit.edu/resenv/Stack
and:
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http://www.xsens.com/http://www.microstrain.com/http://www.cloudcaptech.com/http://www.isense.com/http://www.xbow.com/http://www.media.mit.edu/resenv/Stackhttp://www.media.mit.edu/resenv/Stackhttp://www.xbow.com/http://www.isense.com/http://www.cloudcaptech.com/http://www.microstrain.com/http://www.xsens.com/7/29/2019 Class8 Inertial v2 Ayb
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Inertial Measurement Units:Gimballed
Most early IMUs were placed on a platform which stayedfixed relative to the inertial or earth frame
Still used for very accurate systems
Allows for gyros to measure a much smaller range, since
they only detect the small deviations (more linear, moreaccurate)
Simplifies transforms
Platform is servoed
> Zero rate
However
Very expensive
Suffer from gimbal lock
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Inertial Measurement Units:Gimbal Lock
Given a fixed set of movements, it is possible toalign all three axes on the gimballed platform,
causing it to lock up and topple
Can be fixed by adding a fourth gimbal (expensive)
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Inertial Measurement Units:Strapdown
Far easier than gimballing, wecan simply fix the IMU in theframe of the device.
Mechanically much simpler andstronger, but increases thecomplexity of the math if worldframe position/orientation isneeded
Most useful if body frame itself
has meaning Makes choice of alignment key
Virtually all IMUs for HCI arestrapdown
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Position Calculations
X = ax d2t
q = w dt
Lots of ways to integrate (Polynomial, Simpsons Rule, etc.)
Note that gravity complicates thingsrotation measurements must
compensate for the change in the gravitational vector, which needs to besubtracted from the accelerationalso note that this is done in the body frame
usually should be transfored to inertial coordinates.
But, theres more..
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Inertial Measurement Units:Fundamental Error Source
Bias drift
Changes over time in the baseline (zero input) outputof the part
Scale factor drift Changes over time in the slope of the input-output
curve
Drift results in an additive noise which causes anerror proportional to t in angle and t2 in position
These noises/errors are separate from theadditive white noise seen on all sensors
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Inertial Measurement Units:Tracking (1)
IMUs are traditionally used for navigation or
dead-reckoning.
Given a known starting position and orientation, data
is integrated forward to get current position and
orientation
The most common algorithm for doing this is a
Kalman filter, which combines knowledge about theerror in the measurements and the error in a model of
the system propagation to give a (linearly) optimal
results (minimizes mean-squared error)
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Inertial Measurement Units:Tracking (2)
However, IMUs made from low-cost parts quickly
diverge from reality because of both poor drift and
random walk noise
When noisy data is summed, the is increased by afactor of t
For example, in a gyro, this creates an error in the orientation
estimate
That error then couples into the position estimate (dx = rdq)
The only solution is to use external information to reset
the orientation or position at regular intervals
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A Brief Interlude:Expressive Footwear
http://www.media.mit.edu/resenv/danceshoe.html
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Principle of Acceleration
Acceleration (a) is the second derivate of position withrespect to time (x)
Newtons 1st Law: An object in motion remains in
motion unless acted upon by outside forces Einsteins Principle of Equivalence: The acceleration
due to gravity is indistinguishable from otheraccelerations.
Gamow vs. Draper
> Gravity gradient (at least for a nonconstant g)
> Rotate the inertial platform as the earth curves away underneath
Schuler Tuning (add pendulum dynamics, with the mass @ earths core)
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Principles of Accelerometry
Newtons 2nd Law F=ma
Since force is a fundamental quantity, we derive theacceleration by determining the force on an object of
known mass (ie the proof mass) This proof mass is usually attached to a spring of
some style allowing us to use Hookes Law
F = -kx
As F = ma, a = -x(k/m)
Deflection can then be converted into accelerationusing knowledge of the mass and spring constant
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Accelerometers:Fluid Inclinometers
Not used as an accelerometer per se, but very useful for
determining the tilt of a slowly moving object
Inclinometers are most often built as a small bubblefilled with electrolytic fluids.
These devices have slow response and
tend to be sloshy. However, in steady state, differences of
0.5 or better can be detected
Check out Spectron Glass
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Accelerometers:Inclinometers (bubble
levels)
C1C2
- Bubble (white) in fluid (blue) changes capacitance when
it moves across plates
- (C1C2) / (C1 + C2) = relative bubble displacement
- Can also read bubble position optically
Level is accurate to 0.5 arc seconds (0.00003"/ft or .0025 mm/M)
- [Also available with 0.1 arc second accuracy]
Large measuring range of +/-1000 arc seconds (0.06/ft or 5 mm/M)
EL-905 ELECTRONIC BUBBLE LEVEL
(Hamar Laser, CH)
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Accelerometers:Tilt Switches
Effectively a threshold on a single angle (with respect
to gravity), tilt switch draw virtually no power and are
excellent for simple motion detection
Mercury tilt switch
Connection between two pins made or
broken by bubble of mercury
Pinball tilt switch
Cross between mercury tilt switch and
inclinometer
ALPS SPSF100100
SMT version of ball in cup 3-axis Ball in Cup
Mechanical tilt switches can also bespring-mounted for higher acceleration
thresholds
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Accelerometer switches and piezo cantilevers
Acceleration switch
e.g., proof-mass reed, ball in magnetic can (old airbagsensors!)
Made by many companies
Piezoelectric Cantilevers
Made by MSI
Spring Steel Proof Mass displaces under
acceleration
Closes switch above threshold
Proof Mass
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Giveaway Sensor Schematic
100 ms dead timer prevents multipulsing Ultra low powerbattery lasts up to shelf life
Extremely cheape.g., under $1.00 in large quantity
MSI
Minisense 100Gated single-transistor
300 MHz RF oscillatorCould be mechanicaltamper switch
Th Wi l J k S
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The Wireless Jerk Sensors
Very simple motion sensor
Cantilevered PVDF piezo strip with proof mass
Activates CMOS dual monostable when jerked Sends brief (50 ms) pulse of 300 MHz RF
Glued into a tube for simple handheld use
Front Back
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Demos
Early conductor mapping in Lab
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Accelerometers:Piezoelectric
Piezoelectric accelerometers use a cantilevered beam asa combination proof mass and spring
Beam is deflected by acceleration, creating a charge
related to its mass and flexibility This charge can be measured to find the acceleration.
ACH-04-08 from MSI (3 axis)
Range: 10g to 250g
Size: 0.3in x 0.3in x 0.2in
Bandwidth: 5 kHz
Noise: 250mg
Cost: $25
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Accelerometers:Piezoelectric - Circuitry
Also have digital versions
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Whats inside (complex folded beam)
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Piezoelectric accelerometers for rugged,sensitive vibration measurement
Lamerholm,EndevCo, Etc.
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Accelerometers:MEMS
Most MEMS accelerometers are based on a
system of interdigitated capacitors, as shown at
right.
Motion unbalances
the pair of capacitors
shown, unbalancing a
driven signal. The most common MEMS accelerometer is the
ADXL203 from Analog Devices, and is a staple
of low cost inertial sensing.
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Sidebar:What are MEMS?
Micro-Electro-Mechanical Systems (MEMS) is theintegration of mechanical elements, sensors, actuators,and electronics on a common silicon substrate.
This combination not only reduces costs, but the closeintegration of sensor and signal processing greatlyreduces system noise
MEMS have been used for everything for sensors to
microgenerators. Many companies make MEMS accelerometers now
Analog Devices, Motorola, Silicon Designs, STMicroelectronics
Some make 3-axis devices!
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Accelerometers:ADXL203
ADXL203 from Analog Devices (2 axis)
Range: 1.7g
Size: 5mm x 5 mm x 2 mm
Supply Current 0.7mA Max Bandwidth: 2.5 kHz
Noise: 0.8mg (@50Hz)
Cost: $12
Older model (ADXL202) includes duty-cycle output
for easy interfacing
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ADI single-chip 3-axis accelerometers:ADXL330
ADXL330 from Analog Devices Range: 3g
Size: 4mm x 4mm x 1.5mm
Supply Current: 0.2mA Max BW: 1.6 kHz (X,Y)
0.5 kHz (Z)
Noise: 2mg (@50Hz) (X,Y)
2.5mg (@50Hz) (Z)
Cost: $6
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Accelerometers:Thermal
A heated bubble of air can also act as aproof mass.
Its shifts with acceleration can be detectedby a quadrant of temperature sensors
giving a two-axis system. MXR7202GL from MEMSIC (2 axis)
Range: 2g
Size: 5mm x 5 mm x 2 mm
Bandwidth: 20 Hz
Noise: 1.3mg (@20Hz)
Cost: $3
Pin for pin same as ADXL203
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Accelerometers:Interferometric
Enormously small accelerationscan be detected based on
interfermetry.
In the device at right, deflectionof the proof mass changes the
intensity of the 0th order output
Resolution of 2g achieved See Cooper et alApplied Physics
Letters v.76 n.22 for more details
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Accelerometers Particle Trap
PhD Thesis of Rehmi Post
Electrostatically suspended multiple charged particles
in a tiny homemade electrostatic trap
Used a video imager to observe orientations andpositions
Ideally particles stay inertially stable, and platform
rotates around them Particles deflect (crystal deforms) under acceleration
Very preliminary workmany loose ends
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Rehmis Particle-trap Accelerometer
Actual image of oscillating particle clusters in trap
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Rotational Hough Analysis
Hough Xform looks at angles of linear structurespeak indicates orientation
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Accelerometry Based Applications:Pedometry and Body Position
Analog Devices App. Note 602
Real-Time Motion Classification for
Wearable Computing Applications
http://www.media.mit.edu/~rich
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Accelerometry Based Applications:Human-Computer Interfaces
Microsoft Sidewinder Joystick
http://www.microsoft.com/hardware/sidewinder/
Itsy Pocket Computer
http://research.compaq.com/wrl/projects/itsy/
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Gyro from Displaced Accelerometers
Sum is gravitydifference is acceleration. Need large lever arm for accuracy
Must subtract out gravity, etc.
a1 a2
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Principles of Angular Velocity
Angular velocity (w) is the first derivate of anglewith respect to time (q)
Note the relationship between angular velocityand translational velocity (instantaneous) v = w x r
Angular momentum, like translational
momentum, is conserved Figure skater (change in moment of inertial)
Toy gyroscope (would have to change w to fall)
Processional Torque is t = w x HAngular Momentum
Body Rotation
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Principles of Gyroscopes
The Coriolis force is a fictitiousforce exerted on a body when itmoves in a rotating reference
frame. ac = -2v x w
The Sagnac effect is the change in
path length experienced by lighttraveling in a rotating referenceframe.
)/8( cAN
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Gyroscopes:SDFG
The simplest mechanical gyroscopes, the single
degree of freedom gyroscope consists of a
rotating wheel attached to torsion bars
Rotation
perpendicular to the
axis of the wheel will
cause a deflection dueto the conservation of
angular momentum
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MEMS Implementation
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Gyroscopes:Tuning Fork
The tuning fork gyroscope was designed to be amuch simpler mechanical structure than SDFG.
Consists of two masses, connected to a common
base, oscillating out of phase with each other.Note that there is therefore no net motion.
Output is proportional to tine velocity and input
rotational rate, and is usually measured as a twistat a stiff base
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Gyroscopes:Vibrating Reed
This technique is quite similar to the tuning forkgyroscope, and uses piezoelectrics both as input
and output
A central vibrating reed drives two others,creating equal piezoelectric output.
A rotation deflects the velocity, driving one reed
more than the other, creating a differential output
w
Stationary Case Driven Case
drive
output 1output 2
drive
output 1output 2
coriolis
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Gyroscopes:Murata ENC03J
ENC03J from Murata (1 axis) Range: 300/sec
Size: 0.6in x 0.3in x 0.2in
Bandwidth: 50 Hz
Noise: 0.5/sec (@50 Hz)
Cost: $40
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Gyroscopes Wineglass(or hemispherical resonator)
Standing wave modal pattern of vibrations in ashell is perturbed by rotation
Wave propagation velocities around shell are
unequal in the presence of rotation Coriolis force effect
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Gyroscopes:Interferometric
Interferometric gyroscopes rely on the Sagnac
effect in light traveling in very long loops
(usually a small package with many turns).
Rotation causes a phase difference, which can be
converted to a magnitude by mixing the signals
Suffer from reflection
and limited by shot
noise
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Gyroscopes:Fizoptika VG941-3AS
VG941-3AS from Fizoptika (1 axis)
Range: 600/sec
Size: 50mm x 24mm dia
Bandwidth: 1 kHz
Noise: 0.01/sec (@50 Hz)
Cost: $1300
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Gyroscopes:Ring Laser
Ring laser gyros achieve far better results than IFOGsin a smaller volume by creating a loop within a lasing
resonator.
Finite number of wavelengths must fit in cavity, hence lasing
frequency must change with rotation Suffer from lock-in due to scatter and coupling
These gyros achieve tactical
performance levels
Military, aviation,
spacecraft
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Gyroscopes:
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Gyroscopes:MEMS
Several companies now make MEMS gyros
Analog Devices, Delphi, ST Microelectronics, Silicon Sensing Systems,
Applied MEMS inc.
Analog Devices now makes a MEMS gyroscope very similar in
principle to their MEMS accelerometer
An oscillating mass with capacitive fingers is driven relative to
fixed finger on the substrate
Perpendicular rotation will create an imbalance
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Gyroscopes:
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Gyroscopes:Analog Devices ADXRS300
ADXRS300 from Analog Devices (1 axis)
Range: 300/sec
Size: 7mm x 7mm x3mm
Bandwidth: 40 Hz
Noise: 0.6/sec (@40 Hz)
Cost: $33
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Gyroscopes:
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Gyroscopes:Extending the range of the ADXRS300
Human motion easily exceeds 300 deg/sec Reduce internal amplifier gain with external
resistor
Works up to ~ 4x increase in range (45kmin)
Reduce sensitivity of internal drive circuitryby overriding internal 12V regulator withexternal reference voltage
Can be accomplished easily with external
Zener diode
7.5V Zener gives ~ 10x increase in range
Together, a 7.5V Zener and a 120 k externalresistor can be used to extend the range to
roughly 10,000 deg/sec !
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IMU Based Applications:
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IMU Based Applications:Medical Data Collection
Gait Shoe
http://www.media.mit.edu/resenv/GaitShoe/
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Position Calculations
X = ax d2t
q = w dt
Lots of ways to integrate (Polynomial, Simpsons Rule, etc.)
Note that gravity complicates thingsrotation measurements must
compensate for the change in the gravitational vector, which needs to besubtracted from the accelerationalso note that this is done in the body frame
usually should be transfored to inertial coordinates.
But, theres more..
R t t d F t Pit h
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Reconstructed Foot Pitch
Z-gyroscope
integrated once
with respect to
time, over a
single leg swing.
maximum pitch minimum pitch
-3 -2 -1 0 1 2 3 4-400
-200
0
200
400
600
Calibrated Gyro-Z Output
AngularVelocity[deg
rees/sec]
Time [sec]
Calibrated Gyro-Z DataIntegration Bounds
-3 -2 -1 0 1 2 3 4
-40
-20
0
20
40
60
Final Results of Gyro-Z Integration
Angle[degrees]
Time [sec]
Linearly Integrated DataSpline-Fit of Integrated DataBML Foot Pitch
Integrated Data [zero offset adjusted,
iteratively, per integration].
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F t Pit h R lt
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Foot Pitch Results
-20 -15 -10 -5 0 5 10 15 20 25 300
50
100
150
[count]
Magnitude Difference, Max Pitch
[degrees]
-20 -15 -10 -5 0 5 10 15 20 250
50
100
150
[count]
Magnitude Difference, Min Pitch
[degrees]
Recommendation: Consider replacing Murata Gyroscopes with Analog Devices Gyroscopes
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Stride Length: Accelerometers
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Stride Length: Accelerometers
Accelerometers measure dynamicand static acceleration;pitch used
to subtract static component of
gravitational acceleration.
X- and Y- accelerometer
outputs can be combined
to determine acceleration
in room coordinates (also
requirespitch).
Axdynamic
Ax
Axstatic
Xroom
gsin=Ax
static
g
y
Ay-shoedynamic
Xroom
Ax-roomdynamic
Ay-roomdynamic
Yroom
Ax-roomdynamic
Ay-roomdynamic
Afoot
x
Ax-roomdynamic
Ay-roomdynamic
Ax-shoedyny
Ax-shoedynx
Xshoe
Yshoe
Ax-shoedynamic
Ay-shoe
dyn
x
Ay-shoe
dyn
y
cosx sin
x
cosy sin
y
Ax-shoedynamic
Ay-roomdynamic
Ax-roomdynamic
Ay-shoedynamic=
=
Ay-roomdynamic
Ax-roomdynamic
+
+
AYB4/06
Stride Length
7/29/2019 Class8 Inertial v2 Ayb
64/67
64
Stride Length
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5-30
-20
-10
0
10
20
30
[m
/s2]
Acceleration Lower integration boundUpper integration boundA
x-room
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.50
1
2
3
4
5
[m/s]
Velocity
Vx-room
-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.50
1
2
3
4
5
6
[sec]
[m]
Displacement
Displacementx-room
BML reference displacement
Dynamic component along room x-axis integrated twice with
respect to time, over a single leg swing.
AYB4/06
Stride Length Results
7/29/2019 Class8 Inertial v2 Ayb
65/67
65
Stride Length Results
-60 -40 -20 0 20 40 600
10
20
30
40
50
60
70
[count]
Magnitude Difference, Stride Length using AX-room
[cm]
Recommendation: Improve pitch, incorporate all IMU outputs, Kalman filter
AYB4/06
7/29/2019 Class8 Inertial v2 Ayb
66/67
66
What if Money is no Object? (1)
The state of the art in IMU design is the system used inthe MX missile, known as the Advanced Inertial
Reference System (AIRS).
Uses the best accelerometers and gyroscopes available
(strangely, from 1986)
The two part spherical structure is gimballed by floating
the outer sphere in fluorocarbon fluid and maintaining
the orientation of the inner sphere via hydraulic thrustvalves.
Circular error probable (CEP) of 100m
Will fall within that range 50% of the time.
AYB4/06
7/29/2019 Class8 Inertial v2 Ayb
67/67
What if Money is no Object? (2)
Ask Joe what he did as a UROP!
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