Measurements and Signal

processing (part 1) MCE 493/593 & ECE 492/592 Prosthesis Design and Control

September 25, 2014

Antonie J. (Ton) van den Bogert

Mechanical Engineering Cleveland State University

1

Today

• Body-mounted measurement systems – for human movement field studies

• real-time or off-line data processing

– for prosthetic control systems • real-time data processing

• Next week – laboratory techniques for human motion studies

Kinematic measurement

• Potentiometer for joint rotation – “electrogoniometer” – simple, analog signal – must be aligned with joint or allow translation

• Or resistive “bend sensors”

from Winter book Cyberglove

flexible goniometer

Kinematic measurement

• Encoders on joints or motors – standard robotics technology – incremental encoders

• (requires “homing”) • not desirable in prosthetics

– absolute encoders

absolute encoder with 3 bit precision (optical)

10 bits $110

Electromagnetic receiver-transmitter

• Original application: virtual reality • Measures position and orientation

of receiver relative to transmitter – multiple receivers, one on each body

segment of interest • Can be body mounted for research

– e.g. skiing with transmitter in backpack • Not suitable for prosthesis

– transmitter is large – inaccurate near metal

Polhemus system

Application of joint angle sensing

• “Echo control” for powered prosthetic knee – Donald Grimes, MIT, PhD Thesis 1979 – joint angles measured on intact leg – “played back” on prosthetic leg, some time later

• Advantages – user has full control over cadence and amplitude

• Disadvantages – movement must always start with intact leg – only suitable for symmetrical movements – requires instrumentation on intact leg – mistakes get copied also

From Grimes 1979

transition from level walking to uphill ramp walking

Processing of position data

• For dynamic analysis (F = m a) we need acceleration • Position signals have noise

– from the sensor and electronics – from the analog-to digital conversion – these types of noise have high bandwidth

• Differentiation amplifies high frequencies – noise can become larger than the signal – solution: low pass filtering – this works because human motion has low bandwidth (<10 Hz)

Vertical position of the heel

heelY = mocap_077(4000:4400,112); % 4 seconds of data heelYd = diff(heelY)/0.01; % numerical derivative heelYdd = diff(heelYd)/0.01; subplot(3,1,1);plot(heelY);ylabel('position (m)'); subplot(3,1,2);plot(heelYd);ylabel('velocity (m/s) '); subplot(3,1,3);plot(heelYdd);ylabel('acceleration (m/s^2)'); xlabel('frame number');

Digital low pass filter

• Butterworth filter

– matlab functions: butter, filter, filtfilt – Winter’s book has a table with filter coefficients

• careful: a and b & signs are defined differently than in Matlab

– This can be done in real time also (Simulink, Labview, etc.)

• Consider Kalman filter – especially if something is known about dynamics of the process that

generated the signal

FILTER x(t) y(t)

231223121 −−−− −−++= iiiiii yayaxbxbxby

Matlab code for 10 Hz low pass filter a = [1 -1.01905 .25962]; % a coefficients from Winter book, for ratio % fs/fc = 100 Hz / 10 Hz = 10 b = [.06014 .12028 .06014]; % b coefficients from Winter book heelYdd_filtered = filter(b,a,heelYdd); >> plot(heelYdd); >> hold on; >> plot(heelYdd_filtered,'r','LineWidth',2);

real-time filtering always introduces a time lag (phase response of filter) lower cutoff frequency larger time lag

Force measurement

• Force transducer (load cell) – 1-axis, 3-axis, 6-axis (3D force and torque)

www.ichida.com For 1-axis, specifications will say how much off-axis load is allowed

Designing a load cell

• 1-axis: strain gauges on a piece of metal tube – four strain gauges for bridge circuit for temperature

compensation

• 6-axis: at least six strain gauges needed – when randomly placed: no temperature compensation – calibration with known forces and moments – linear model – C is a 6xN calibration matrix – s can be a raw voltage signal rather than strain

=

N

z

y

x

z

y

x

s

sC

MMMFFF

1

Calibration

• Apply known loads F,M, record the strains s – do this many times (T times) with different loads

• Or: apply random loads and record F,M (with already calibrated load cell) and record s

• Solve calibration matrix C from:

[ ] [ ]MF, loads knowndata =

NC

Cs

6

1

=

zT

yT

xT

zT

yT

xT

z

y

x

z

y

x

N

NTT

NTT

NTT

NTT

NTT

NTT

N

N

N

N

N

N

MMMFFF

MMMFFF

C

CC

ssss

ssss

ssss

ssss

ssss

ssss

1

1

1

1

1

1

6

12

11

1

1

1

1

1

1

111

111

111

111

111

111

000000000000000000000000000000000000000000000000000000000000

000000000000000000000000000000000000000000000000000000000000

161666 TxNxNTx bCA =Matlab solve: C = A\b (linear least squares) all six load variables are calibrated simultaneously

Using a bone as a 6-axis load cell

(and you can do this with aluminum tube also) – glue strain gauges on bone – post-mortem calibration required to get calibration matrix

Weinans & Blankevoort J Biomech 1995

Transformation of force/moment data

• Load cell is between ankle and knee • What are force and moment at ankle and knee?

– assume m*a between load cell and joint can be neglected

( )( )TzPyPxPP

TzPyPxPP

MMM

FFF

=

=

M

Fforce and moment measured at point P

is equivalent to another force and moment measured at point Q:

PPQ

PQ

FQPMMFF

×−+=

=

)(• derived from free body diagram and statics • distinguish action and reaction loads • (internal vs. external moment)

Example (instrumented prosthesis)

• 6-axis load cell between ankle and knee – distance to knee is 20 cm – assume load cell is outside the joint actuation system – measures load on the upper half of the lower leg – X = anterior, Y points towards knee (load cell coordinate system)

• P is load cell, Q is knee joint center

( )( ) m N

N T

P

TP

0,0,0

0,0,200

=

−=

M

F( )

m N

N

−=

−×

−+

=

−=

4000

00200

02.0

0

000

0,0,200

Q

TQ

M

F

This is a clockwise external moment acting at the knee. Assuming static equilibrium, the knee motor must have generated a 10 N counterclockwise moment that acts on the lower leg (extension moment).

Homework assignment (due Oct 2)

• We have the same load cell as in the example – same placement, same assumptions, same coordinate system – length of thigh is 60 cm, length of lower leg is 45 cm

• Measurements (in middle of stance phase) – from encoder: knee is 15 degrees flexed – from load cell:

– what are the joint moments (torques) at hip, knee, ankle? – which of the following hip muscles might be active?

• hamstrings, gluteals, iliacus, psoas, rectus femoris • explain your reasoning

( )( ) m N

N T

P

TP

50,0,0

0,800,50

−=

−=

M

F

Accelerometer

• Contains a small mass (test mass) sitting on a load cell – 1 axis, 2 axis or 3 axis – MEMS accelerometers are cheap (<$10)

• Accelerometer signal depends on – acceleration and gravitational force – in accelerometer XYZ reference frame:

– with a and g in world XYZ reference frame (Z=up)

from Winter book

gaFs

agF

−==

=+

m

mm

loadcellteraccelerome

loadcell

( )

−−=−=

81.900

aRgaRs TTteraccelerome

R: attitude matrix (orientation matrix, rotation matrix) of the accelerometer with respect to the world. Columns of R are the world XYZ coordinates of unit vectors along the accelerometer’s coordinate axes

measurement model:

Three examples • No acceleration, accelerometer XYZ aligned with world XYZ

– R = identity matrix, a = 0 – accelerometer signals are (0,0,g)

• Upward acceleration az, accelerometer XYZ still aligned with world XYZ – R = identity matrix, a = (0,0,az)T

– accelerometer signals are (0,0,g+az) • No acceleration (a = 0), accelerometer is rotated about (horizontal) X axis

−=

−=

θθθθ

θθθθ

cossin0sincos0

001

cossin0sincos0001

TR

Raccelerometer signals:

=

−−=

θθ

cos81.9sin81.90

81.900

T

z

y

x

sss

R

yworld

zworld

θ

Accelerometer

• Can not distinguish between acceleration and gravity – sometimes you can assume a<<g (tilt sensor) – or assume g<<a ( pure acceleration sensor) – or use additional sensors: IMU (inertial measurement unit)

• 3D magnetic field sensor • 3D MEMS gyro (angular velocity sensor)

– or do an analysis where they don’t need to be distinguished

• load estimation (two slides from here)

www.sparkfun.com, $49.95

www.xsens.com, $3290

Inertial Measurement Units

• Kalman filter or equivalent for state estimation and sensor fusion – state variables: 3D position, velocity,

orientation, angular velocity – nine measurements: 3D

accelerometer, magnetometer, gyro

• Can provide good 3D orientation • Unavoidable drift in 3D position

Accelerometers for force/moment measurement • Multiple accelerometers on a rigid body

– can provide information about angular velocity and angular acceleration

• Measurement model – 3-axis accelerometer mounted at position r

orientation

acceleration at body origin gravitational field

angular acceleration angular velocity

sensor mounting position

Rigid body dynamics

If we know motion of a rigid body (mass m, inertia I), the total force and moment acting on the body are:

Gravity and acceleration can’t be separated

−≡

αω

g)(aRsx

T0

But we don’t need to, for this purpose. Given enough accelerometers (12 channels is a good number), nine kinematic variables of the rigid body can be measured:

We have nonlinear measurement model: )( 91121 xhy =

Solve x by nonlinear least squares: find x for which is minimized (Numerical Recipes book, Chapter 15, Levenberg-Marquardt method) Kalman filtering would have been better

( )∑=

−=−12

1

22 )()(i

ii hy xxhy

van den Bogert, Read, & Nigg, J Biomech 1996

Clinical question

• Is skiing a safe activity after total hip replacement?

• Goals: 1. quantify forces in the hip joint during various skiing activities 2. compare skiing to walking and running 3. discussion of possible effects on prosthesis

Instrumentation

• analysis of upper body movement

• 4 triaxial accelerometers – 12 channels

• data logger

Alipne skiing, left hip joint upper body reference frame

lateral posterior superior

flexor abductor int.rotator

Estimation of joint contact force

muscles

contact

dM

FFFF

FFFd

F

+=+=

⇓

=−

=

muscles contact

musclescontact

musclesM

d

Summary of results

9 subjects

2 subjects

van den Bogert, Read, & Nigg, Med Sci Sports Exerc 1999

Foot switches

• To detect heelstrike and (sometimes) toe off • Mechanical switch • Force-sensitive resistor • Heelstrike impact detection

– Accelerometer – Cheap microphone

Electromyography

• Electrodes – surface electrodes – indwelling electrodes

• Dipole or quadrupole • Differential amplifiers

– to cancel the noise

16-channel wireless system (Delsys Trigno) $20,000

to iPad stereo microphone input

EMG amplifier with footswitch for $5

Winter book

EMG signal processing steps

1. Bandpass filter (30-600 Hz) to remove high frequency noise and movement artifacts

2. Full-wave rectification (take absolute value) to make the signal positive

3. Low-pass filter to obtain “EMG envelope”

arm muscles in gymnasts during giant swing

EMG during running recorded on iPad imported in Matlab with “wavread”, processed by software

0 2 4 6 8 10 12 14 16 18-0.5

0

0.5Raw EMG signal

0 2 4 6 8 10 12 14 16 18-0.5

0

0.5EMG after bandpass filter

0 2 4 6 8 10 12 14 16 18-0.5

0

0.5EMG envelope

0 2 4 6 8 10 12 14 16 18-0.5

0

0.5

1Motion sensor

Time (s)

Average of many strides

0 100 200 300 400 5000

0.02

0.04

0.06

0.08Mean and standard deviation (N=97)

0 100 200 300 400 5000

0.1

0.2

0.3

Mean and standard deviation (N=127)

Vastus Lateralis

Vastus Medialis

heelstrike

no evidence of a stretch reflex quadriceps is activated before impact feedforward control time (ms)

Application in prosthetics: myoelectric control

Kuiken et al., JAMA 2009

• Nerves from amputated arm (green) are surgically connected to the Pectoral muscles

• EMG electrodes placed on Pectoral muscles • User activates muscles in amputed arm, causes electrical

activity in Pectorals • EMG signals are decoded and used as command input for

robotic arm