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 16802hjs1@psu.edu

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

P OP+P

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

Positive Absolute attitude of body segments Direct measurement of angular velocity Direct measurement of acceleration No marker occlusion Large work space in unstructured

environment

Negative Does not provide absolute location,

translational velocity or rotational acceleration

Calibration relative to anatomy Soft tissue artifact Data communication < 100 Hz, medium resolution

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

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

Multiple IMUs per body Parallel axes Rejects gravity effects

Articulated Model - Pendulum

PGmJ/sinPGgm

0sinPGgmPGmJ

pendulumsimple

PD/singa

singPDa

PGPDfor0aroduniform

PDPGm1singa

Multiple Segment Model

1x27DR

27x27DRrDR

REVrREV

6G/6RNK6G

6G26G10G/10RNK

10G10G

8G/8RWR8G

8G28G9G/9RWR

7G/7REL7G

7G27G8G/8REL

6G/6RSL6G

6G26G7G/7RSL

5G/5RWA5G

5G25G6G/6RWA

4G/4RHP4G

4G24G5G/5RHP

3G/3RKN3G

3G23G4G/4RKN

2G/2RAN2G

2G22G3G/3RAN

2G/2RHL2G

1x18REV

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

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

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

xofcovvarPtrack

vxHztsmeasuremenonbased

wxAxstateestimate

noisesensorv

matrixdynamicsensorH

noiseprocessw

matrixdynamicstateA

estimatepriorx

matrixgainadaptiveK

vofcovvarR

wofcovvarQ

Kalman Filter

xHzKxx

RHPHHPK

correction

prediction

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

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

Inertial Measurement Units (IMUs) – Theory and Practice

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