Inertial Measurement Units
(IMUs) – Theory and Practice
H.J. Sommer III, Ph.D.
The Pennsylvania State University
University Park, PA 16802
hjs1@psu.edu
www.mne.psu.edu/sommer
IMU Tutorial 10.05.12
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Inertial Measurement Unit ?

Kinematic measurements using inertial
references




Attitude and magnetic heading
Angular velocity
Acceleration
Fuse data to provide more reliable results
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Inertial Measurement Unit ?
14x28 mm
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Inertial Measurement Unit ?
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Inertial Measurement Unit ?
qOP
m, JP
qOP
qP
h
rP
qOP+ qP
rP
r
s
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

q  qO  q  
2
5
Inertial Measurement Unit ?
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Inertial Measurement Unit ?
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Traditional Kinematic
Measurements

Photogrammetry


Goniometry


Absolute location of point markers
Relative angles across body segments
Electromagnetic digitizers

6DOF of discrete sensors
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Photogrammetry
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Photogrammetry Quiz
(for Oldtimers)

Vanguard or RightGuard?

DLT or BLT?

Lo-Cam or Hi-Cam?
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Photogrammetry

Positive






Absolute location and attitude of body segments
Multiple IR cameras with ambient lighting
Automatic marker tracking
No cables to subject
> 100 Hz, high resolution
Markerless motion capture (MMC)
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Photogrammetry

Negative





Calibration relative to anatomy (joints and mass
centers)
Requires finite differences for velocity and
acceleration
Marker occlusion
Soft tissue artifact
Limited workspace in a gait lab
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Goniometry
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Goniometry

Positive



Direct measurement of joint motion
Easy to use
Negative


Does not measure absolute position/attitude
Physical attachment to subject
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Electromagnetic Digitizers
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Electromagnetic Digitizers

Positive


6 DOF for each body segment
Negative




Limited workspace
Cables (new wireless)
Physical attachment to subject
Accuracy degraded by speed
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IMUs
Integrated Kinematic Sensor (IKS) Wu and Ladin, 1993
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IMUs




Attitude relative to gravity vector
Magnetic heading
Rotational velocity
Translational acceleration
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IMUs

Positive





Absolute attitude of body segments
Direct measurement of angular velocity
Direct measurement of acceleration
No marker occlusion
Large work space in unstructured environment
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IMUs

Negative





Does not provide absolute location, translational
velocity or rotational acceleration
Calibration relative to anatomy
Soft tissue artifact
Data communication
< 100 Hz, medium resolution
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History of IMUs

Vehicle navigation



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Intercontinental ballistic missiles (ICBM)
Nuclear submarines
Cruise missiles
MicroElectroMechanical Systems (MEMS)


Automotive
Consumer products
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MEMS IMUs - Automotive

Automotive


Accelerometers to deploy airbags
Vehicle roll handling
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MEMS IMUs – Consumer Products




Games (WiiMote)
PDA (iPhone)
Camera stabilization
Hard disks
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MEMS Fabrication
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MEMS Comb Sensor/Drive
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MEMS accelerometer
(proof mass)
gravity
acceleration
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MEMS accelerometer
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MEMS gyro (tuning fork)
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MEMS magnetometer
(magnetoresistive)
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MEMS IMU Outputs

Signal




Analog voltage (0 to 3V)
Fixed frequency, variable duty cycle
Digital (internal A/D converter)
Bandwidth

< 150 Hz
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Two-Dimensional (2D) IMU


Biaxial accelerometer
Uniaxial gyro
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Three-Dimensional (3D) IMU



Triaxial accelerometer
Triaxial gyro
Triaxial magnetometer

Required to determine spin about gravity vector
az
ay
ax
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MEMS 9DOF IMU

Triaxial accelerometer


Triaxial gyro


±300 deg/sec (dps), 3.3mV/dps, 140 Hz
Triaxial magnetometer


±3g, 300 mV/g, 550 Hz
50 Hz
On-board CPU, serial I/O
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Break Time
Stand up
Stretch
Say hello to your neighbor
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Data Fusion


Sensor uncertainty
Geometric



Rigid body
Articulated model
State space

Kalman filter
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Sensor Uncertainty





s = measured signal
b = zero drift or bias (function of temp)
f = scale factor (function of temp)
w = Gaussian white noise
s2 = variance
q  b  f sGYRO  s w
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LSY530 gyro ±300 degps




Nonlinearity ±1%
b = 1.23 V, 0.05 degps/C°
f = 300 degps/V, 0.05 %/C°
s = 0.035 degps/sqrt(Hz) pink noise
q  b  f sGYRO  s w
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Rigid Body Fusion

ayC
axC

C
r

Multiple IMUs per body
Parallel axes
Rejects gravity effects
q
ayD
axD
q  a  a  / r
xD
xC
D
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Articulated Model - Pendulum
simple pendulum
J  m P G2 q  m g P G sin q  0

P

G

q  m g P G sin q / J  m P G2
G
q
G
ayD

m PG PD 

a xD  g sin q1 
2 
 JG  m P G 
uniform rod a xD  0 for P D  43 P G
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
axD
D
a xD  PD q  g sin q
q  a  g sin q / PD
xD
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Multiple Segment Model
 REV q r 
  q 
DR
r

 REV q q  q r  REV 



 DR q q   qq   DR 
27 x 27
REV
18 x1
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27 x1
27 x1


















q G2 2 A G 2  G 2 s RHL 2 / G 2
 2
G3
G2
2
 q G 3 A G 3  s RAN 3 / G 3  q G 2 A G 2  s RAN 2 / G 2
 q G2 4 A G 4  G 4 s RKN 4 / G 4  q G2 3 A G 3  G 3 s RKN 3 / G 3
 2
G5
G4
2
 q G 5 A G 5  s RHP 5 / G 5  q G 4 A G 4  s RHP 4 / G 4

  q G2 6 A G 6  G 6 s RWA 6 / G 6  q G2 5 A G 5  G 5 s RWA5 / G 5
 q 2 A  G 7 s
 q G2 6 A G 6  G 6 s RSL 6 / G 6
G
7
G
7
RSL
7
/
G
7

 q G2 8 A G 8  G 8 s REL8 / G 8  q G2 7 A G 7  G 7 s REL7 / G 7
 2
G9
 2 A  G 8 s


q
A
s

q
G
9
G
9
RWR
9
/
G
9
G8
G8
RWR 8 / G 8

q G2 10 A G10  G10 s RNK 10 / G10  q G2 6 A G 6  G 6 s RNK 6 / G 6































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Kalman Filter

Uses state space model






Position
Velocity
Adaptive time domain filter
Combines states
Tracks variance-covariance
Rejects zero drift
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Kalman Filter - 2D IMU
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Kalman Filter - Simplified
Measure q t and q t at time t
Computeq t   q t  q t  t  / t
Compareq to q
t
t
Computeq t   q t  q t t
Compareq t  to q t
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Kalman Filter – Prediction
probability
q latitude
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Kalman Filter - Measurement
probability
q latitude
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Kalman Filter - Correction
probability
q latitude
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Kalman Filter - Prediction
probability
constant speed
fixed time
q latitude
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Kalman Filter – 2D IMU
probability
qPRED  qCORR  q t t
dynamicmodel
q angle
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Kalman Filter - Extended

State space


Nonlinear state relationships


Include acceleration
ax-ay-qdot versus qqdot
Include geometric multisegment model

Include states for multiple bodies
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Kalman Filter
estimatestatexk  Axk 1  wk 1
based on measurements zk  Hxk  vk
trackPk  var cov of xk
xk 1  prior est imat e
A   stat edynamicmat rix
wk 1  processnoise
H   sensor dynamicmat rix
vk  sensor noise
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Q  var cov of w
R   var cov of v
Kk  adaptivegain matrix
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Kalman Filter
prediction
x  Axk 1
P  APk AT

k
k
correction
K k  P H HP H  R 
xk  xk K k zk  Hxk 
Pk  I K k HP

k
T

T
1
k
k
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Applications





Stationary
Simple attitude
Simple motion
Coordinated movement
Inverse dynamics
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Stationary


Minimal change in sensor orientation
Hand/arm tremor



Extended arm, tracing spiral
Triaxial accelerometer, >150 Hz
Postural sway


Supracranial accelerometer
Lumbar accelerometer
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Simple Attitude

Body position during sleep




Treatment for sleep apnea
Triaxial accelerometer, very low sample rate
Not interested in spin about gravity vector
Restless Leg Syndrome (RLS)



Monitor sudden movement
High frequency sample rate
Interested in event itself, not characterization
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Simple Motion

Planar lifting or reaching



Simple articulated model
2D IMU provides position, velocity, acceleration
Passive manipulation or drop


Assess spasticity
Compute jerk from acceleration
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Coordinated Movement

Basic assessment



Triaxial accelerometer, >100 Hz
Number of strides, timing
Asymmetry of motion


Rehabilitation, prosthetic fitting
Full body motion


Thirteen 9DOF IMUs
Multiple segment model
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Inverse Dynamics

2D




Lower data throughput (3ch versus 9ch)
Require sagittal and frontal IMUs
Does not require magnetometers
3D


Lifting or reaching most promising
Difficulty in assessing absolute location of feet
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Practical Considerations

Motion variables


Number of IMUs


Consider alternate signals to describe motion
May require two per segment
Synchronization

In-shoe pressure transducers
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Data Transfer


Umbilical with local A/D
Belt-pack data logger


Belt-pack wireless


SD card
Bluetooth, longer battery life
Network wireless

Dropouts, battery life
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Commercial Systems

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Xsens MVN
Biosyn FAB
NexGen Ergonomics
Microstrain wireless
MEMSense
Sparkfun WiTilt
Nintendo WiiMote
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