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Active Tremor Compensation in Handheld Instrument for Microsurgery
Wei Tech AngSchool of Mechanical & Aerospace Engineering
Nanyang Technological UniversitySingapore
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Contributors
Cameron N. RiviereAssociate Research Professor
David Y. ChoiPh.D. Student
Si Yi KhooResearch Engineer
Medical Robotics Technology CenterThe Robotics InstituteCarnegie Mellon UniversityPittsburgh, PA, USA
Wei Tech AngAssistant Professor
Mounir KrichaneExchange Student (EPFL)
Robotics Research Centre &Sch. of Mechanical & Aerospace Eng.Nanyang Technological UniversitySingapore
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Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
Micron
VitreoretinalMicrosurgery
Estimation of erroneous motion
Tip manipulation for active error compensation
Task Definition
Problem Analysis
Engineering Solutions
Technical Details
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Vitreoretinal Microsurgery
Removal of membranes ≤ 20 µm thick from front or back of retina
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Vitreoretinal Microsurgery
Injection of anticoagulant using intraocular cannulation to treat retinal vein (~∅100 µm) occlusion
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Vitreoretinal MicrosurgeryTremor: under microscope
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Involuntary Hand Movement and Microsurgery
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Involuntary Hand Movement and Microsurgery
Complicate microsurgical procedures and makes certain delicate interventions impossibleImpact on microsurgeons
2 of 10 surgeons become microsurgeonsFactors affecting tremor
Fatigue – strenuous exercise etc.Caffeine/alcohol consumptionLack of practice – long vacation etc.Age – experience vs hand stability
Microsurgeons’ consensus:10 µm positioning accuracy
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Involuntary Hand Movement of Healthy Human
Physiological TremorRoughly sinusoidal motion, 8-12 Hz ≤ 50 µm rms in each principal axis
Non-tremulous ErrorsMyoclonic jerk, drift etc.Aperiodic, may be in the same frequency band as voluntary motionLarger amplitude: > 100 µm
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Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
Micron
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
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Robotic Error Compensation Approaches
Telerobotic systems: Zeus (Computer Motion) & Da Vinci (Intuitive Surgical)
Master-Slave manipulators
Erroneous motion filtered by motion scaling
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Robotic Error Compensation Approaches
‘Steady-hand’ robot:Russell Taylor et al., Johns Hopkins University
Surgeon and compliant robot hold tool simultaneouslyForce feedback‘Third hand’ operation
Erroneous motion damped by rigidity of robot
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Robotic Error Compensation Approaches
Active Handheld Instrument:Paolo Dario, Scuola SuperioreSant’Anna, Pisa, ItalySame concept
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Comparison of Robotic Solutions
Telerobotics‘Steady Hand’ robot Active Handheld Instrument
CheapUnobtrusiveSaferLimited workspaceNo motion scalingNo ‘third hand’
Obtrusive
Unobtrusive
< US$15K
> US$150K> US$1M
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Micron Current Prototype
Length: 180 mm long Diameter: Ø20(16) mmWeight <100 g9 DOF inertial and magnetic sensing system at the back end3 DOF piezoelectric driven parallel manipulator at front end with disposable surgical needle
180 mm (w/o needle)
Ø20 mm
Ø16 mm
Manipulator System
Sensing System
Disposable surgical needle
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System OverviewMotion of instrument
Magnetometer-aided all-
accelerometer IMU
ADCSensor fusion
Estimation of erroneous
motion
Erroneous tip displacement
WDtremor(3×1)
Inverse kinematics
Joint variables λ1, λ2, λ3
DAC
Power Amplifier
Piezoelectric-driven parallel
manipulator
V1, V 2, V 3
Motion of instrument tipWDvoluntary (3×1)
Host PC
Inverse feedforwardcontroller
BA(6×1), BM(3×1)
Forward kinematics
WDB(3×1), WΘB(3×1)
WDtip(3×1)
Sen
sing
Filtering
Man
ipulatio
n
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Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
Micron
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
• Resolution
• Accuracy
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Sensing System Design
Magnetometer-aided all-accelerometer inertial measurement unit (IMU):
3 dual-axis miniature MEMS accelerometers Analog Devices ADXL-203: 5mm x 5mm x 2mm, < 1gThree-axis magnetometerHoneywell HMC-2003: 26mm x 19mm x 12mm, <10g
Housed in 2 locations
Back Sensor Suite
Sensing direction
Front Sensor Suite
ZB
XB
YB
Dual-axis accelerometer
Dual-axis accelerometers
Tri-axial Magnetometer
Manipulator System
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Sensing Modality
Internally referenced sensors because:Less obtrusiveExternally referenced sensors require a line of sightResolution:Inertial sensor < 1 µmExternally referenced (e.g. Optotrak): ~ 0.1 mm
All accelerometers because:Low cost, miniature gyros too noisy→ Poor sensing resolutionNavigation/tactical grade gyros - too expensive and bulky
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Differential Sensing Kinematics
Body acceleration sensed by accelerometer at location i:
Differential Sensing
onsAccelerati inducedRotation−
×Ω+×Ω×Ω++= BiBiCGi PPgAA
Xw
P23
P13
P12
P3
P2P1
Yw
Zw
W
B 2
3
1
Y2
Z2
( )
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡••
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
•
•=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
••=
=×Ω+×Ω×Ω=−=
z
y
x
ijijij
aAaA
aA
jiPAAA
12
122323
13
13 ,,
3 2, 1,,,][]][[
Centripetal Acceleration
Tangential Acceleration
Measurement
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Differential Sensing Kinematics
3 unknowns:Ω = [ωx ωy ωz]T
3 differential acceleration measurements:AD = [a13x a23y a12z]T
Solve system of nonlinear equations by Gauss-Newton or Levenberg-Marquart methodNumerical instability
Assume Ω2 ≈ 0, solve for analytically
ΩXw
P23
P13
P12
P3
P2P1
Yw
Zw
W
B 2
3
1
Y2
Z2
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Sensing KinematicsUpdating quaternions:
Directional Cosines matrix
Gravity Removal: WAE = WCBBA – Wg
Tip Displacement:
⎥⎦
⎤⎢⎣
⎡Ω−
Ω×Ω=ΩΩ=
×
××
0][
21~ ),()(~)(
31
1333Ttqttq
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
+−−+−−−+−++−−−+
=23
22
21
2010322031
103223
22
21
203021
2031302123
22
21
20
)(2)(2)(2)(2)(2)(2
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
CBW
tipBB
BW
t
TtE
Wtip
Wtip
W PtCddATtPtP ])[()()()( ×Ω++−= ∫ ∫−
τττ
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Sensing Resolution (Error Variance) Analysis
Sensing resolution dependent on sensor noise floorAngular Sensing
Sensing equation:Aij = f(Ω)= ([Ω×] [Ω×] + [ ×])Pij
Covariance:C(Aij) = C(Ω) Pij
Pij↑, C(Ω)↓
Pij
σAx2
σAy2
σAy2
σAx2
σωx2 orσωy
2
Back sensor suite
Front sensor suite
Ω
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Proposed All-Accelerometer vs Conventional Inertial Measurement Unit
All-accelerometer IMUMaximized Pij, with physical constraint of a slender handheld instrument
Conventional IMU (3A-3G)Tokin CG-L43D rate gyros x 3
96.9% / 32x4.42 × 10-21.41ωz
99.3% / 130x1.08 × 10-21.41ωx & ωy
Noise reduction / resolution
improvement
6A Error std. dev.
(deg/s)
3G-3AError std. dev.
(deg/s)
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Angular Sensing Resolution Comparison
Small angular velocity & sensor noise floor
0 50 100 150 200 250 300 350 400 450 500-2
0
2
4
6
8
0 50 100 150 200 250 300 350 400 450 500-2
0
2
4
6
8
0 50 100 150 200 250 300 350 400 450 500-2
0
2
4
6
8
ωz
(deg
/s)
ωx, ω
y(d
eg/s
)
ωG
(deg
/s)
Time (ms)Time (ms)
Tokin Gyroscope
All-accelerometer IMU
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Sensing Resolution (Error Variance) Analysis
Translational Sensing2 accelerometers in each sensing direction:
Sensing resolution improves by a factor of 2½
Better orientation estimation → more complete removal of gravity → better translation estimation
2111222
AiA
AjAiA
σ=σ→
σ+
σ=
σ
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Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
Micron
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
• Resolution
• Accuracy
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Integration Drift of Inertial Sensors
Integration driftErroneous DC Offset
Ramp QuadraticError accumulates and grows unbounded over time
Poor sensing accuracy
∫∫0 0.2 0.4 0.6 0.8 1
-1
-0.5
0
0.5
1Acc
eler
atio
n (m
m/s
2 )
0 0.2 0.4 0.6 0.8 10
0.02
0.04
0.06
Vel
ocity
(mm
/s)
0 0.2 0.4 0.6 0.8 1
0
0.01
0.02
0.03
Time (s)D
ispl
acem
ent (
mm
)
Mean = 0.05 mm/s2
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Measurement Model
Measurement model allows error analysis and compensationMeasurement Model = Physical (Deterministic) Model + Stochastic Model
Measurement Error
Measurement Model• Physical
• Stochastic
Compensation
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Accelerometer Model
CalibrationRecord accelerometer outputs at orientation inline (V+g) and opposite (V-g) to gravity
Linear modelAcceleration, A = (Vo–B)/SF gScale factor, SF = ½(V+g−V-g) V/gBiasB = ½ (V+g+V-g) V
β = 0°
+90°
180°
90°
α = 180°
- 90°- 90°
β
α
y
x
g
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Experimental Observations
-1 -0.5 0 0.5 11.5
2
2.5
3
3.5
Acceleration (g)
Acc
eler
omet
er O
utpu
t (V
)
A
B+
+
−
−
CW: A+ → B-
CCW: B+ → A-
g
-1 -0.5 0 0.5 11.5
2
2.5
3
3.5
Acceleration (g)
Acc
eler
omet
er O
utpu
t (V
)
α±150
α±90
g
α = 90°, β = -180° to 180°
α±30
α = 30° & 150°, β = -180° to 180°
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Phenomenological ModelingBias, Bx(Vy, Vz) = Bx+gx(Vy)+hx(Vz)Scale Factor,SFx(Vz) = rx2Vz
2 + rx1Vz + rx0
Model
Ax = (Vx− Bx(Vy, Vz)) / SFx(Vz)
-1 -0.5 0 0.5 11.06
1.07
1.08
1.09
1.1
1.11
z-Acceleration (g)
Sca
le F
acto
r (V
/g)
1.5 2 2.5 3 3.5 4-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
y-Accelerometer Output, Vy (V)
Res
idue
Rxy (V
)-1 -0.5 0 0.5 1
-5
0
5
10
15x 10-3
z-Acceleration (g)R
esid
ue R
xz (V)
gx(Vy) = px2Vy2 + px1Vy + px0
hx(Vz) = qx2Vz2 + qx1Vz + qx0SFx(Vz) = rx2Vz
2 + rx1Vz + rx0
In plane cross- axis effect
Out of plane cross- axis effectScale Factor
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Sensing Experiment - Translation
Motion generator10 Hz, 50 µm p-p sinusoid
Displacement SensorInfrared interferometer (Philtec, Inc., Model D63)Sub-micrometer accuracy
Rotary Stages Accelerometer
Displacement Sensor
Motion Generator
Motion
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340 0.2 0.4 0.6 0.8 1-500
-400
-300
-200
-100
0
100
200
Time (s)
Acc
eler
atio
n (m
m/s
2 )Sensing Results - Translation
0 0.2 0.4 0.6 0.8 1-150
-100
-50
0
50
100
150
200
Time (s)
Acc
eler
atio
n (m
m/s
2 )
--89.7Error Reduction (%)
<1<531*Proposed Physical Model
6272300Linear Model
Scale Factor (mm/s2)Bias (mm/s2)Rmse (mm/s2)
Linear Model Proposed Physical Model
* ADXL-203 rated rms noise = 22.1 mm/s2
Interferometer
Accelerometer
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Stochastic Model
Random noise analysis by Allan Variance method Dominant accelerometer noise types:
Velocity random walkWhite noise in acceleration
Acceleration random walkWhite noise in jerk
Trend / Bias InstabilityTemperature drift
10-2 100 102 104100
101
102
Velocity random walk
Acceleration random walk
τ (s)
σ(τ)
(m/s
/s)
Trend / Bias Instability
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Temperature Drift
Time varying zero biasHeating up of internal circuitrySteady state: 2-12 hours
Solutions:ModelingWait for steady stateOvenization
Heat up sensor using power resistorChanges sensor behavior
0 2 4 6 8 10 122.64
2.645
2.65
Bia
s (V
)0 2 4 6 8 10 12
1.075
1.08
1.085
1.09
1.095
Time (hr)S
cale
Fac
tor (
V/g
)
Steady State
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Sensor Fusion via Cascaded Two-Stage Kalman Filtering
Motion
Bias
+
_Scale Factor
Local Gravity
Misalign-ment
Correction
Location & Orientation
Error
Magnetic North
Augmented State
Kalman Filtering
Acc. Trend
Acceleration Random
Walk1/s
Velocity Random Walk
+
+
Acc.
Mag.
White Noise 1/s
White Noise
+ +
Physical Model
+Norma-lization
Misalign-ment
Correction
Bias Orientation Error
Q-based Kalman Filtering
Kinematics
Tool tip displacement
_Numerical
Transform-ation Error
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380 2 4 6 8 10
-50
0
50
100
Augmented State Kalman Filtering
Time domain sensor fusionAugmented state dynamic equation:
[ ][ ][ ][ ][ ]
[ ][ ][ ][ ][ ] ( )
[ ][ ]
[ ]][
0
0
][
20000
][10000
1000001000010
00211
]1[
11111
221
2
kw
k
kk
kc
TkTcTc
kx
kbkbkakaku
A
T
T
TT
kx
kbkbkakaku
arw
vrw
a
u
a
u⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
+
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
++
+
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
+
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
+++++
β
ξξ Velocity Random
WalkAcceleration Random Walk
Quadratic Model of Bias Drift
⎪⎩
⎪⎨
⎧x
⎩⎨⎧
b
State Transition Matrix
Vel
ocity
(mm
/s2 )
Time (s)
KF
ASKF
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39
Orientation Fusion
Source 1: Differential sensing kinematicsΩA[k] from differential accelerationState transition matrix:
Dynamic state equation: qA[k + 1] = F[k]qA[k] + γ[k]Orientation defined by quaternion
+ : high resolution− : drift
)44()44( ][~2
][sin
][1
2][
cos][ ×× += kΘk
kΩI
kkF
θθ
TkTkk TA
AAA ⎥
⎦
⎤⎢⎣
⎡Ω−
Ω×Ω=ΘΩ=θ
×
××
0][
21][~ ;][][
31
1333
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40
Orientation Fusion
Source 2: TRIADGravity vector & Magnetic North vector are non-collinearTRIAD algorithm:
zB = –gB/||g||; yB = zB×NB/|| zB×NB ||; xB = yB×zB
WCB = [xB yB zB]
+ : non-drifting– : poor resolution
zw
yw
xw
Nw
gw
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41
Quaternion-based Kalman Filtering - Gravity Tracking
Source 1: ΩAHigh resolution, drifting
Source 2: NB + gBNoisy, non-drifting
Quaternion-based KF: Q-KFReduced noise, non-drifting
0 200 400 600 800 1000 12000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 200 400 600 800 1000 12000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
ΩA
0 200 400 600 800 1000 12000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Time(ms) Time(ms)
Nor
mal
ized
Gra
vity
Nor
mal
ized
Gra
vity
Nor
mal
ized
Gra
vity
NB + gB
Q-KF
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42
Sensing Experiment - Orientation
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43
Translational Sensing Accuracy
No non-drifting referencePoor translational sensing accuracy
Not important if tremor is separable from drift and intended motion
0 500 1000 1500 2000-20
-10
0
10
20
0 500 1000 1500 2000-10
0
10
20
30
40
0 500 1000 1500 2000-10
0
10
20
30
40
Tremor Filtering
-
+
Sensed motion
Intended+Drift
Tremor
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44
Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
MICRON
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
• Real-time
• Phase lag
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45
Frequency Selective Filters Phase Characteristics
Physiological tremor has a distinct frequency bands:8 – 12 Hz
Voluntary motion: ≤ 1 Hz; Electrical noise: >> 12 HzClassical frequency selective bandpass / band-stop (notch) filters
Phase lag ≡ Group (time) delayFiltered signal is a time delayed version of the actual sensed motionUnacceptable condition for real-time error canceling application: compensating action might worsen the error
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46
Zero Phase Filtering
Separation of tremor from the intended motion without introducing phase lag
Prediction/projection capabilityAdaptive
Non-linear phase response of IIR filter, i.e. phase characteristic changes with frequency
Two proposed algorithmsWeighted-frequency Fourier Linear Combiner (WFLC)Adaptive Phase Compensating Band-pass Filter
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47
Fourier Linear Combiner (FLC)
Truncated Fourier series to adaptively estimate amplitude and phase of periodic signal with known frequency (ω0)
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48
Weighted-frequency Fourier Linear Combiner (WFLC)
Extends FLC to also adaptively estimate the frequency using another LMS algorithmBand-pass filter to select the band of interest
Assumption: rate of change of the dominant input signal frequency is slow
Zero-phase notch (band-stop) filter effect
FLC
WFLC
Signal input
ω0
Tremor
BandpassFilter
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49
Weighted-frequency Fourier Linear Combiner (WFLC)
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50
Weighted-frequency Fourier Linear Combiner (WFLC) Experiment
1 DOF motion canceling experimentAve. rms tremor amplitude reduced 69%Stability problem
Double adaptive algorithm
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51
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Filter Phase Characteristics
Low-pass filters create phase lagHigh-pass filters create phase lead
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TimeInput Output
Low-pass Filter High-pass Filter
Time
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52
Adaptive Phase Compensating Band-pass Filter
The idea:To design a cascaded low-pass and high-pass filters such that phase lag of low-pass is compensated by phase lead of high-pass for a certain known input frequencyWFLC to estimate the instantaneous frequency
MotivationMost sensors come with built-in low pass filters
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53
Implementation
Design LP-HP filter pairs with equal and opposite phase characteristicsFilter design frequency band: 3 – 7 HzFilter type: Elliptical 2nd
order Roots of transfer function can be modeled by a linear function
LP HP
Roots of Filter Transfer Functions
× - Poles ο - Zeros
7 Hz
7 Hz
3 Hz3 Hz
5.67 Hz
5.67 Hz
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54
Adaptive Phase Compensating Band-pass Filter
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55
Motion Canceling Experiment
Motion generator oscillating at 2.0 HzCamcorder recording a rectangular target
25 frames per secondImage post processing to simulate real-time compensation
Motion generator
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56
Adaptive Phase Compensating Band-pass Filter
Rmse:Raw footage = 2.61 pixelsCompensated = 0.66 pixelsError reduction: 75%
Original Compensated
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57
Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
MICRON
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
•High precision tracking control
• Mechanism design
![Page 58: Active Tremor Compensation in Handheld … Active Tremor Compensation in Handheld Instrument for Microsurgery Wei Tech Ang School of Mechanical & Aerospace Engineering Nanyang Technological](https://reader031.vdocument.in/reader031/viewer/2022021423/5aa9aac97f8b9a7c188d25ea/html5/thumbnails/58.jpg)
58
Piezoelectric Actuator Hysteresis
+ : High bandwidthFast responseHigh output force
– : Hysteresis
~15% of max. displacement
0 20 40 60 80 1000
2
4
6
8
10
12
14
Voltage (V)
Dis
plac
emen
t (µm
)
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59
0 20 40 60 80 10010
20
30
40
50
60
70
80
90
0 0.2 0.4 0.6 0.8 1-20
0
20
40
60
80
100
Commercial Piezo-System with Feedback Controller
Piezo-driven 3 axis micro-positionerPolytec-PI, Germany, NanoCubeTM P-611>$ 10,000Feedback sensors: strain gagesTracking a 10 Hz, 100 µm p-p sinusiod
Hysteresis still presentLow-pass filtered behavior
Time (s)
Dis
plac
emen
t (µm
)
Measured Desired
Dis
plac
emen
t (µm
)
Voltage (V)
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60
Open-loop Feedforward Controller with Inverse Hysteresis Model
Develop a mathematical model that closely describes the hysteretic behavior of a piezoelectric actuatorExistence of an inverse hysteresis model
0 2 4 6 8 10 12 140
20
40
60
80
100
0 20 40 60 80 1000
2
4
6
8
10
12
14
0 2 4 6 8 10 12 140
2
4
6
8
10
12
14
Feedforward controller Piezoelectric
Desired Displacement (µm)
Actuator Response (µm)
Voltage(V)
Displacement (µm)
Dis
plac
emen
t (µm
)
Voltage (V)
Vol
tage
(V)
Actuator Response (µm)
Displacement (µm)
Dis
plac
emen
t (µm
)
Desired Displacement
(µm)
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61
Prandtl-Ishlinskii (PI) Operator
Rate independent backlash operator:Hr = maxx(t) – r, minx(t) + r, y0Linearly weighted superposition of backlash operators:
r1
-r1
y
x
wh1
ri
y
x
Whi = Σwhi
[ ] )(,)( 0 tyxHwty rTh=
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62
Modified PI Operator
Backlash operators are symmetric but real hysteresis is not
Modeling saturation by linearly weighted superposition of dead-zone operators:
)]([)(
0 ),(0 ,0,)(max
)]([
tySwtz
dtyddty
tyS
dTs
d
⋅=
⎩⎨⎧
=>−
=
PI modelReal
Hysteresis
di
z
yd0 d1
∑=
=i
jsjsi wW
0
z
yd >0
ws
d =0
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63
Modified PI Operator
( ) )]](,[[][)( 0 tyxHwSwtxtz rThd
Ts ⋅⋅=Γ=
x(t) y(t) z(t)
x(t) z(t)
time time
Backlash operators Saturation operators
Γ
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64
Inverse Modified PI Hysteresis Model
Hysteresis Model
Inverse Model
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65
Inverse Modified PI Operator
( ) )](],ˆ[[]ˆ[ ,,,10,, tyzSwHwtz
dT
srT
h ⋅⋅=Γ−
)(ˆ tz )(tx
1−Γtime time
)(ˆ tz )(tx
Inverse saturation operators
Inverse Backlash operators
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66
Piezoelectric Hysteresis is Rate Dependent
Basic assumption of Prandtl-Ishlinskii operator:
Hysteresis is rate independent
Our observation:Hysteresis is ratedependent
Tremor frequency is time varying and person specific
8-12 Hz
25 Hz
15 Hz
5 Hz
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67
Rate-dependent PI Operator
Assume saturation is rate independentSum of the backlash weights up to ri (slope of the hysteresis curve at interval i) is linearly dependent on actuation rate Whi = Σwhi; 0 200 400 600 800 1000 1200
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Whi
Actuation rate (µm/s)
( ) ( ) nitxcxWtxW ihihi ...0 ),()( 0 =+=
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68
Rate Dependent PI Hysteresis Model
Rate dependent model:
Also a PI type → Inverse existsRate dependent inverse model
)]](,[))(([)](,[)( 0 tyxHtxwSwtxxtz rT
hdT
s ⋅⋅=Γ=
( ) )](],ˆ[[))((]ˆ[ ,,))((
,10, tyzSwHtxwtz d
Tstxr
Th ′
− ⋅⋅=Γ
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69
Open-Loop Feedforward Controller with Inverse Rate-Dependent PI Hysteresis Model
Measured Desired
0 0.05 0.1 0.15 0.2-2
0
2
4
6
8
10
12
14
Dis
plac
emen
t (µm
)
Error
Rate-dependent
Time (s)
0 0.05 0.1 0.15 0.2-2
0
2
4
6
8
10
12
14
Error
Rate-independent
Time (s)
Dis
plac
emen
t (µm
)0 0.05 0.1 0.15 0.2
-2
0
2
4
6
8
10
12
14
Time (s)
Dis
plac
emen
t (µm
)
WithoutModel
Tracking single frequency stationary sinusoids
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70
0 0.05 0.1 0.15 0.2-2
0
2
4
6
8
10
12
14
Open-Loop Feedforward Controller with Inverse Rate-Dependent PI Hysteresis Model
Tracking multiple frequency non-stationary sinusoids
0 0.05 0.1 0.15 0.2-2
0
2
4
6
8
10
12
14
Time (s)D
ispl
acem
ent (µm
)
Error
Error
Measured Desired
Without model.
Rate- independent.
0 0.05 0.1 0.15 0.2-2
0
2
4
6
8
10
12
14
Dis
plac
emen
t (µm
)
Time (s)
Error
Dis
plac
emen
t (µm
)
Rate- dependent.
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71
Dynamic Motion Tracking Results
5.38.017.3
0.59 ± 0.060.89 ± 0.041.91 ± 0.08max error ± σ(µm)
1.42.89.2
0.15 ± 0.0030.31 ± 0.031.02 ± 0.07rmse ± σ (µm)
Rate-dependent
Rate-independent
Without model
(%)amplitude p-prmse
(%)amplitude p-p
errormax
rms noise of interferometer = 0.01 µm
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72
Tremor Tracking Results
Tracking recordings of real tremor using 1 piezoelectric stackRmse = 0.64% of max ampl.; Max error = 2.4% of max ampl.
0 0.2 0.4 0.6 0.8 2-2
0
2
4
6
8
10
12
14DesiredObtainedError
0 0.2 0.4 0.6 0.8 1-2
0
2
4
6
8
10
12
14DesiredObtainedError
Without Model Rate-Dependent Controller
Time (s) Time (s)
Dis
plac
emen
t (µm
)
Dis
plac
emen
t (µm
)
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73
Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
MICRON
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
•High precision tracking control
• Mechanism design
![Page 74: Active Tremor Compensation in Handheld … Active Tremor Compensation in Handheld Instrument for Microsurgery Wei Tech Ang School of Mechanical & Aerospace Engineering Nanyang Technological](https://reader031.vdocument.in/reader031/viewer/2022021423/5aa9aac97f8b9a7c188d25ea/html5/thumbnails/74.jpg)
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Design of Parallel Mechanism
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Manipulator Design
3 DOF piezoelectric-driven parallel manipulator1 actuator per axis, max effective stroke = 12.5 µmMotion amplification = 9.4x, total stroke > 100 µm
Tool tip approximated as a point, hence only 3 DOF manipulationParallel manipulator design because
Rigidity, compactness, and design simplicity
Located at the front end to balance the weight of the instrument
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Design of Parallel Mechanism - New
IEEE EMBS 2005 (Shanghai) Best Student Design Competition winner
David Choi et al.Monolith design using Stereolithography∅22 x 58 mm
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Manipulator Kinematics
Inverse kinematicsModeled as Lee & Shah RS-typeClosed-form solution
No internal singularity
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Workspace Analysis
Xmax, Ymax = 650 µmZmax = 100 µmTremor Space = ∅ 50 µm
Tremor SpaceManipulator Workspace
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Manipulator 3D Tracking Result
Tracking planar circle of ∅200 µmMean tracking rmse ~ 12.1 µm
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Microsurgery with Active Handheld Instrument
Visuomotor Control System
Noisy, Tremulous Motion
Motion Sensing
Visual Feedback
Micron
VitreoretinalMicrosurgery
Estimation of erroneous motion
Manipulation of tip for active error compensation
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Motion Canceling Experiment
Translation onlyGenerated motion: 9 Hz, 91 µm p-p
Ave compensated tip motion over 10 runs = 60 µm p-p34.3% reduction3D optical sensing system
< 1.0 µm rms accuracy
8.8 9 9.2 9.4 9.6 9.8 10
-40
-30
-20
-10
0
10
20
30
40
Tip Displacement in Z
time (seconds)
Dis
plac
emen
t (m
icro
ns)
0 5 10 15 20 250
5000
10000
15000
Frequency Response without Compensation
Mag
nitu
de
0 5 10 15 20 250
5000
10000
15000
Frequency Response with Compensation
Frequency (Hz)
Mag
nitu
de
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Motion Canceling Experiment
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Micron Canceling Hand Tremor
Total range: 52% reduction
RMS amplitude: 47% reduction
0 1 2 3
-60
-30
0
30
60
time (s)
disp
lace
men
t (µm
) compensated
uncompensated
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Other Applications
Surgery and DiagnosticsActive compensation of periodic human physiological and pathological motion
Beating heart, breathing, etc.Pathological tremor due to Parkinson’s diseases, multiple sclerosis, etc.
Military optical tracking devicesHandheld, vehicle & ship mounted
Consumer camera/camcorder
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Other Applications: Cell Manipulation / Dissection
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Questions & Comments
Wei Tech AngSchool of Mechanical & Aerospace Engineering
Nanyang Technological UniversitySingapore