Inertial Measurement Units (IMUs) – Theory and Practice

IMU Tutorial 10.05.12 1

H.J. Sommer III, Ph.D.The Pennsylvania State University

University Park, PA [email protected]

www.mne.psu.edu/sommer

Inertial Measurement Units(IMUs) – Theory and Practice


Kinematic measurements using inertial references

Attitude and magnetic heading Angular velocity Acceleration

Fuse data to provide more reliable results

Inertial Measurement Unit ?



14x28 mm





hr

s

OP

OP

P

P

P OP+P

m, JP

2O






Photogrammetry Absolute location of point markers

Goniometry Relative angles across body segments

Electromagnetic digitizers 6DOF of discrete sensors

Traditional KinematicMeasurements


Photogrammetry


Vanguard or RightGuard?

DLT or BLT?

Lo-Cam or Hi-Cam?

Photogrammetry Quiz(for Oldtimers)


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)

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

Photogrammetry


Goniometry


Positive Direct measurement of joint motion Easy to use

Negative Does not measure absolute

position/attitude Physical attachment to subject

Goniometry


Electromagnetic Digitizers


Positive 6 DOF for each body segment

Negative Limited workspace Cables (new wireless) Physical attachment to subject Accuracy degraded by speed

Electromagnetic Digitizers


IMUsIntegrated Kinematic Sensor (IKS) Wu and Ladin, 1993


Attitude relative to gravity vector Magnetic heading Rotational velocity Translational acceleration

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

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

IMUs


Vehicle navigation Intercontinental ballistic missiles (ICBM) Nuclear submarines Cruise missiles

MicroElectroMechanical Systems (MEMS) Automotive Consumer products

History of IMUs


Automotive Accelerometers to deploy airbags Vehicle roll handling

MEMS IMUs - Automotive


Games (WiiMote) PDA (iPhone) Camera stabilization Hard disks

MEMS IMUs – Consumer Products


MEMS Fabrication


MEMS Comb Sensor/Drive


acceleration

gravity

MEMS accelerometer(proof mass)


MEMS accelerometer


MEMS gyro (tuning fork)


MEMS magnetometer (magnetoresistive)


Signal Analog voltage (0 to 3V) Fixed frequency, variable duty cycle Digital (internal A/D converter)

Bandwidth < 150 Hz

MEMS IMU Outputs


Biaxial accelerometer Uniaxial gyro

Two-Dimensional (2D) IMU


Triaxial accelerometer Triaxial gyro Triaxial magnetometer

Required to determine spin about gravity vector

Three-Dimensional (3D) IMU

ax

ayaz


Triaxial accelerometer ±3g, 300 mV/g, 550 Hz

Triaxial gyro ±300 deg/sec (dps), 3.3mV/dps, 140 Hz

Triaxial magnetometer 50 Hz

On-board CPU, serial I/O

MEMS 9DOF IMU


Break Time

Stand upStretch

Say hello to your neighbor


Sensor uncertainty Geometric

Rigid body Articulated model

State space Kalman filter

Data Fusion


s = measured signal b = zero drift or bias (function of

temp) f = scale factor (function of temp) w = Gaussian white noise 2 = variance

Sensor Uncertainty

wsfb GYRO


Nonlinearity ±1% b = 1.23 V, 0.05 degps/C° f = 300 degps/V, 0.05 %/C° = 0.035 degps/sqrt(Hz) pink noise

LSY530 gyro ±300 degps

wsfb GYRO


Rigid Body Fusion

r/aa xCxD

axC

r

ayC

axD

ayD

C

D

Multiple IMUs per body Parallel axes Rejects gravity effects


Articulated Model - Pendulum

2G

2G

PGmJ/sinPGgm

0sinPGgmPGmJ

pendulumsimple

axD

ayD

P

D

G

PD/singa

singPDa

xD

xD

PGPDfor0aroduniform

PGmJ

PDPGm1singa

34

xD

2G

xD


Multiple Segment Model

1x27DR

REV

1x27

r

27x27DRrDR

REVrREV

q

q

qq

qq

6G/6RNK6G

6G26G10G/10RNK

10G10G

210G

8G/8RWR8G

8G28G9G/9RWR

9G9G

29G

7G/7REL7G

7G27G8G/8REL

8G8G

28G

6G/6RSL6G

6G26G7G/7RSL

7G7G

27G

5G/5RWA5G

5G25G6G/6RWA

6G6G

26G

4G/4RHP4G

4G24G5G/5RHP

5G5G

25G

3G/3RKN3G

3G23G4G/4RKN

4G4G

24G

2G/2RAN2G

2G22G3G/3RAN

3G3G

23G

2G/2RHL2G

2G22G

1x18REV

sAsA

sAsA

sAsA

sAsA

sAsA

sAsA

sAsA

sAsA

sA


Uses state space model Position Velocity

Adaptive time domain filter Combines states Tracks variance-covariance Rejects zero drift

Kalman Filter


Kalman Filter - 2D IMU


Kalman Filter - Simplified

tt

ttt

tt

tttt

tt

toCompare

tCompute

toCompare

t/Compute

ttimeatandMeasure


Kalman Filter – Prediction

latitude

probability


Kalman Filter - Measurement

latitude

probability


Kalman Filter - Correction

latitude

probability


Kalman Filter - Prediction

latitude

probability

constant speed

fixed time


Kalman Filter – 2D IMU

angle

probability

elmoddynamic

ttCORRPRED


State space Include acceleration

Nonlinear state relationships ax-ay-dot versus dot

Include geometric multisegment model

Include states for multiple bodies

Kalman Filter - Extended


Kalman Filter

kk

kkk

1k1kk

xofcovvarPtrack

vxHztsmeasuremenonbased

wxAxstateestimate

noisesensorv

matrixdynamicsensorH

noiseprocessw

matrixdynamicstateA

estimatepriorx

k

1k

1k

matrixgainadaptiveK

vofcovvarR

wofcovvarQ

k


Kalman Filter

k

kk

k

PHKIP

xHzKxx

RHPHHPK

correction

APAP

xAx

prediction

kk

kkkkk

1TTk

Tk

1kk


Stationary Simple attitude Simple motion Coordinated movement Inverse dynamics

Applications


Minimal change in sensor orientation Hand/arm tremor

Extended arm, tracing spiral Triaxial accelerometer, >150 Hz

Postural sway Supracranial accelerometer Lumbar accelerometer

Stationary


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

Simple Attitude


Planar lifting or reaching Simple articulated model 2D IMU provides position, velocity,

acceleration Passive manipulation or drop

Assess spasticity Compute jerk from acceleration

Simple Motion


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

Coordinated Movement


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

Inverse Dynamics


Motion variables Consider alternate signals to describe

motion Number of IMUs

May require two per segment Synchronization

In-shoe pressure transducers

Practical Considerations


Umbilical with local A/D Belt-pack data logger

SD card Belt-pack wireless

Bluetooth, longer battery life Network wireless

Dropouts, battery life

Data Transfer


Xsens MVN Biosyn FAB NexGen Ergonomics Microstrain wireless MEMSense Sparkfun WiTilt Nintendo WiiMote

Commercial Systems

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Inertial Measurement Units (IMUs) – Theory and Practice

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