Active Tremor Compensation in Handheld Instrument for Microsurgery - - PowerPoint PPT Presentation

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Active Tremor Compensation in Handheld Instrument for Microsurgery

Wei Tech Ang

School of Mechanical & Aerospace Engineering Nanyang Technological University Singapore wtang@ntu.edu.sg

2

Contributors

Cameron N. Riviere

Associate Research Professor

David Y. Choi

Ph.D. Student

Si Yi Khoo

Research Engineer Medical Robotics Technology Center The Robotics Institute Carnegie Mellon University Pittsburgh, PA, USA

Wei Tech Ang

Assistant Professor

Mounir Krichane

Exchange Student (EPFL) Robotics Research Centre &

• Sch. of Mechanical & Aerospace Eng.

Nanyang Technological University Singapore

3

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback Micron

Vitreoretinal Microsurgery Estimation of erroneous motion Tip manipulation for active error compensation Task Definition Problem Analysis Engineering Solutions Technical Details

4

Vitreoretinal Microsurgery

Removal of

membranes ≤ 20 µm thick from front or back

• f retina

5

Vitreoretinal Microsurgery

Injection of anticoagulant using intraocular

cannulation to treat retinal vein (~∅100 µm) occlusion

6

Vitreoretinal Microsurgery

Tremor: under microscope

7

Involuntary Hand Movement and Microsurgery

8

Involuntary Hand Movement and Microsurgery

Complicate microsurgical procedures and makes certain

delicate interventions impossible

Impact on microsurgeons

2 of 10 surgeons become microsurgeons

Factors affecting tremor

Fatigue – strenuous exercise etc. Caffeine/alcohol consumption Lack of practice – long vacation etc. Age – experience vs hand stability

Microsurgeons’ consensus:

10 µm positioning accuracy

9

Involuntary Hand Movement of Healthy Human

Physiological Tremor

Roughly sinusoidal motion,

8-12 Hz

≤ 50 µm rms in each

principal axis

Non-tremulous Errors

Myoclonic jerk, drift etc. Aperiodic, may be in the

same frequency band as voluntary motion

Larger amplitude: > 100

µm

10

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback Micron

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

11

Robotic Error Compensation Approaches

Telerobotic systems:

Zeus (Computer Motion) & Da Vinci (Intuitive Surgical)

Master-Slave

manipulators

Erroneous motion

filtered by motion scaling

12

Robotic Error Compensation Approaches

‘Steady-hand’ robot:

Russell Taylor et al., Johns Hopkins University

Surgeon and compliant

robot hold tool simultaneously

Force feedback ‘Third hand’ operation

Erroneous motion damped

by rigidity of robot

13

Robotic Error Compensation Approaches

Active Handheld

Instrument: Paolo Dario, Scuola Superiore Sant’Anna, Pisa, Italy

Same concept

14

Comparison of Robotic Solutions

Telerobotics ‘Steady Hand’ robot Active Handheld

Instrument

Cheap Unobtrusive Safer Limited workspace No motion scaling No ‘third hand’

Obtrusive Unobtrusive < US$15K > US$150K > US$1M

15

Micron Current Prototype

Length: 180 mm long Diameter: Ø20(16) mm Weight <100 g 9 DOF inertial and

magnetic sensing system at the back end

3 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

16

System Overview

Motion of instrument Magnetometer- aided all- accelerometer IMU ADC Sensor 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 tip

WDvoluntary (3×1)

Host PC Inverse feedforward controller

BA(6×1), BM(3×1)

Forward kinematics

WDB(3×1), WΘB(3×1) WDtip(3×1)

Sensing Filtering Manipulation

17

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback Micron

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

• Resolution
• Accuracy

18

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, < 1g

Three-axis magnetometer

Honeywell 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

19

Sensing Modality

Internally referenced sensors because:

Less obtrusive

Externally referenced sensors require a line of sight

Resolution:

Inertial sensor < 1 µm Externally referenced (e.g. Optotrak): ~ 0.1 mm

All accelerometers because:

Low cost, miniature gyros too noisy

→ Poor sensing resolution

Navigation/tactical grade gyros - too expensive and bulky

20

Differential Sensing Kinematics

Body acceleration sensed by

accelerometer at location {i}:

Differential Sensing

• ns

Accelerati induced Rotation −

× Ω + × Ω × Ω + + =

Bi Bi CG i

P P g A A

Xw P23 P13 P12 P3 P2 P1 Yw Zw {W} {B} {2} {3} {1} Y2 Z2

( )

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡

• =

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡

• =

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡

• =

= × Ω + × Ω × Ω = − =

z y x ij i j ij

a A a A a A j i P A A A

12 12 23 23 13 13

, , 3 2, 1, , , ] [ ] ][ [

• Centripetal

Acceleration Tangential Acceleration Measurement

21

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 method

Numerical instability

Assume Ω2 ≈ 0, solve for

analytically Ω

• Xw

P23 P13 P12 P3 P2 P1 Yw Zw {W} {B} {2} {3} {1} Y2 Z2

22

Sensing Kinematics

• Updating quaternions:
• Directional Cosines matrix
• Gravity Removal: WAE = WCB

BA – Wg

• Tip Displacement:

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Ω − Ω × Ω = Ω Ω =

× × ×

] [ 2 1 ~ ), ( ) ( ~ ) (

3 1 1 3 3 3 T

t q t t q

• ⎥

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ + − − + − − − + − + + − − − + =

2 3 2 2 2 1 2 1 3 2 2 3 1 1 3 2 2 3 2 2 2 1 2 3 2 1 2 3 1 3 2 1 2 3 2 2 2 1 2

) ( 2 ) ( 2 ) ( 2 ) ( 2 ) ( 2 ) ( 2 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q CB

W

tip B B B W t T t E W tip W tip W

P t C d d A T t P t P ] )[ ( ) ( ) ( ) ( × Ω + + − =

∫ ∫

−

τ τ τ

23

Sensing Resolution (Error Variance) Analysis

Sensing resolution dependent

• n sensor noise floor

Angular Sensing

Sensing equation:

Aij = f(Ω)= ([Ω×] [Ω×] + [ ×])Pij

Covariance:

C(Aij) = C(Ω) Pij

• Pij↑, C(Ω)↓

Pij σAx

2

σAy

2

σAy

2

σAx

2

σωx

2 or σωy 2

Back sensor suite Front sensor suite

Ω

24

Proposed All-Accelerometer vs Conventional Inertial Measurement Unit

All-accelerometer IMU

Maximized Pij, with physical constraint of a slender handheld

instrument

Conventional IMU (3A-3G)

Tokin CG-L43D rate gyros x 3

96.9% / 32x 4.42 × 10-2 1.41 ωz 99.3% / 130x 1.08 × 10-2 1.41 ωx & ωy

Noise reduction / resolution improvement

6A

Error std. dev. (deg/s)

3G-3A

Error std. dev. (deg/s)

25

Angular Sensing Resolution Comparison

Small angular velocity

& sensor noise floor

50 100 150 200 250 300 350 400 450 500

• 2

2 4 6 8 50 100 150 200 250 300 350 400 450 500

• 2

2 4 6 8 50 100 150 200 250 300 350 400 450 500

• 2

2 4 6 8

ωz (deg/s) ωx, ωy (deg/s) ωG (deg/s)

Time (ms) Time (ms)

Tokin Gyroscope All-accelerometer IMU

26

Sensing Resolution (Error Variance) Analysis

Translational Sensing

2 accelerometers in each sensing direction: Sensing resolution improves by a factor of 2½

Better orientation estimation → more complete

removal of gravity → better translation estimation

2 1 1 1

2 2 2 Ai A Aj Ai A

σ = σ → σ + σ = σ

27

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback Micron

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

• Resolution
• Accuracy

28

Integration Drift of Inertial Sensors

Integration drift

Erroneous DC Offset

Ramp Quadratic

Error accumulates and

grows unbounded over time

Poor sensing accuracy ∫ ∫

0.2 0.4 0.6 0.8 1

• 1
• 0.5

0.5 1 Acceleration (mm/s2) 0.2 0.4 0.6 0.8 1 0.02 0.04 0.06 Velocity (mm/s) 0.2 0.4 0.6 0.8 1 0.01 0.02 0.03 Time (s) Displacement (mm)

Mean = 0.05 mm/s2

29

Measurement Model

Measurement model allows error analysis and

compensation

Measurement Model = Physical (Deterministic)

Model + Stochastic Model

Measurement Error Measurement Model

• Physical
• Stochastic

Compensation

30

Accelerometer Model

Calibration

Record accelerometer outputs at

• rientation inline (V+g) and opposite (V-g)

to gravity

Linear model

Acceleration,

A = (Vo–B)/SF g

Scale factor,

SF = ½(V+g−V-g) V/g

Bias

B = ½ (V+g+V-g) V

β = 0° +90° 180° 90° α = 180°

• 9

0°

• 9

0°

β α y x

g

31

Experimental Observations

• 1
• 0.5

0.5 1 1.5 2 2.5 3 3.5 Acceleration (g) Accelerometer Output (V)

A B + + − − CW: A+ → B- CCW: B+ → A-

g

• 1
• 0.5

0.5 1 1.5 2 2.5 3 3.5 Acceleration (g) Accelerometer Output (V)

α±150 α±90

g

α = 90°, β = -180° to 180° α±30 α = 30° & 150°, β = -180° to 180°

32

Phenomenological Modeling

Bias, 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

0.5 1 1.06 1.07 1.08 1.09 1.1 1.11 z-Acceleration (g) Scale Factor (V/g) 1.5 2 2.5 3 3.5 4

• 0.03
• 0.02
• 0.01

0.01 0.02 0.03 0.04 y-Accelerometer Output, Vy (V) Residue Rxy (V)

• 1
• 0.5

0.5 1

• 5

5 10 15 x 10

• 3

z-Acceleration (g) Residue Rxz (V)

gx(Vy) = px2Vy

2 + px1Vy + px0

hx(Vz) = qx2Vz

2 + qx1Vz + qx0

SFx(Vz) = rx2Vz

2 + rx1Vz + rx0

In plane cross

• a

xis effect Out of plane cross

• a

xis effect Scale Factor

33

Sensing Experiment - Translation

Motion generator

10 Hz, 50 µm p-p sinusoid

Displacement Sensor

Infrared interferometer

(Philtec, Inc., Model D63)

Sub-micrometer accuracy

Rotary Stages Accelerometer Displacement Sensor Motion Generator Motion

34

0.2 0.4 0.6 0.8 1

• 500
• 400
• 300
• 200
• 100

100 200 Time (s) Acceleration (mm/s2)

Sensing Results - Translation

0.2 0.4 0.6 0.8 1

• 150
• 100
• 50

50 100 150 200 Time (s) Acceleration (mm/s2)

• 89.7

Error Reduction (%) <1 <5 31* Proposed Physical Model 6 272 300 Linear 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

35

Stochastic Model

Random noise analysis

by Allan Variance method

Dominant accelerometer

noise types:

Velocity random walk

• White noise in

acceleration

Acceleration random walk

• White noise in jerk

Trend / Bias Instability

• Temperature drift

10

• 2

10 10

2

10

4

10 10

1

10

2

Velocity random walk Acceleration random walk τ (s) σ(τ)(m/s/s) Trend / Bias Instability

36

Temperature Drift

Time varying zero bias

Heating up of internal

circuitry

Steady state: 2-12 hours

Solutions:

Modeling Wait for steady state Ovenization

• Heat up sensor using

power resistor

• Changes sensor behavior

2 4 6 8 10 12 2.64 2.645 2.65 B ias (V ) 2 4 6 8 10 12 1.075 1.08 1.085 1.09 1.095 Time (hr) S cale Factor (V/g)

Steady State

37

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 Walk 1/ 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

38 2 4 6 8 10

• 50

50 100

Augmented State Kalman Filtering

• Time domain sensor fusion
• Augmented state dynamic equation:

[ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]

( )

[ ] [ ] [ ]

• ]

[ ] [ 2 ] [ 1 1 1 1 2 1 1 ] 1 [ 1 1 1 1 1

2 2 1 2

k w k k k k c T kT c T c k x k b k b k a k a k u A T T T T k x k b k b k a k a k u

arw vrw a u a u

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = + ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + + + + β ξ ξ

Velocity Random Walk Acceleration Random Walk

Quadratic Model

• f Bias Drift

⎪ ⎩ ⎪ ⎨ ⎧ x ˆ ⎩ ⎨ ⎧ b ˆ

State Transition Matrix Velocity (mm/s2) Time (s)

KF ASKF

39

Orientation Fusion

Source 1: Differential sensing kinematics

ΩA[k] from differential acceleration State transition matrix: Dynamic state equation: qA[k + 1] = F[k]qA[k] + γ[k] Orientation defined by quaternion

+ : high resolution

− : drift

) 4 4 ( ) 4 4 (

] [ ~ 2 ] [ sin ] [ 1 2 ] [ cos ] [

× ×

+ = k Θ k k Ω I k k F θ θ

T k T k k

T A A A A

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Ω − Ω × Ω = Θ Ω = θ

× × ×

] [ 2 1 ] [ ~ ; ] [ ] [

3 1 1 3 3 3

40

Orientation Fusion

Source 2: TRIAD

Gravity vector & Magnetic North vector are non-

collinear

TRIAD 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

41

Quaternion-based Kalman Filtering

• Gravity Tracking

Source 1: ΩA

High resolution, drifting

Source 2: NB + gB

Noisy, non-drifting

Quaternion-based KF: Q-KF

Reduced noise, non-drifting

200 400 600 800 1000 1200 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 200 400 600 800 1000 1200 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

ΩA

200 400 600 800 1000 1200 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Time(ms) Time(ms) Normalized Gravity Normalized Gravity Normalized Gravity

NB + gB Q-KF

42

Sensing Experiment - Orientation

43

Translational Sensing Accuracy

No non-drifting reference

Poor translational sensing accuracy

Not important if tremor is separable from drift and intended

motion

500 1000 1500 2000

• 20
• 10

10 20 500 1000 1500 2000

• 10

10 20 30 40

500 1000 1500 2000

• 10

10 20 30 40

Tremor Filtering

• +

Sensed motion Intended+ Drift Tremor

44

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback MICRON

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

• Real-time
• Phase lag

45

Frequency Selective Filters Phase Characteristics

Physiological tremor has a distinct frequency

bands:8 – 12 Hz

Voluntary motion: ≤ 1 Hz; Electrical noise: >> 12 Hz

Classical frequency selective bandpass / band-stop

(notch) filters

Phase lag ≡ Group (time) delay Filtered signal is a time delayed version of the actual

sensed motion

Unacceptable condition for real-time error canceling

application: compensating action might worsen the error

46

Zero Phase Filtering

Separation of tremor from the intended

motion without introducing phase lag

Prediction/projection capability Adaptive

Non-linear phase response of IIR filter, i.e. phase

characteristic changes with frequency

Two proposed algorithms

Weighted-frequency Fourier Linear Combiner

(WFLC)

Adaptive Phase Compensating Band-pass Filter

47

Fourier Linear Combiner (FLC)

Truncated Fourier series to adaptively estimate amplitude

and phase of periodic signal with known frequency (ω0)

48

Weighted-frequency Fourier Linear Combiner (WFLC)

Extends FLC to also adaptively estimate the frequency

using another LMS algorithm

Band-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 Bandpass Filter

49

Weighted-frequency Fourier Linear Combiner (WFLC)

50

Weighted-frequency Fourier Linear Combiner (WFLC) Experiment

1 DOF motion

canceling experiment

• Ave. rms tremor

amplitude reduced 69%

Stability problem

Double adaptive

algorithm

51

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

0.2 0.4 0.6 0.8 1

Filter Phase Characteristics

Low-pass filters create phase lag High-pass filters create phase lead

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

0.2 0.4 0.6 0.8 1

Time

Input Output

Low-pass Filter High-pass Filter

Time

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 frequency

WFLC to estimate

the instantaneous frequency

Motivation

Most sensors come

with built-in low pass filters

53

Implementation

Design LP-HP filter pairs

with equal and opposite phase characteristics

Filter design frequency

band: 3 – 7 Hz

Filter type: Elliptical 2nd

• rder

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 Hz 3 Hz 5.67 Hz 5.67 Hz

54

Adaptive Phase Compensating Band-pass Filter

55

Motion Canceling Experiment

Motion generator

• scillating at 2.0 Hz

Camcorder recording a

rectangular target

25 frames per second

Image post processing

to simulate real-time compensation

Motion generator

56

Adaptive Phase Compensating Band-pass Filter

Rmse:

Raw footage = 2.61 pixels Compensated = 0.66 pixels

Error reduction:

75%

Original Compensated

57

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback MICRON

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

• High precision tracking control
• Mechanism design

58

Piezoelectric Actuator Hysteresis

+ :

High bandwidth Fast response High output force

– :

Hysteresis

~15% of max. displacement

20 40 60 80 100 2 4 6 8 10 12 14

Voltage (V) Displacement (µm)

59

20 40 60 80 100 10 20 30 40 50 60 70 80 90

0.2 0.4 0.6 0.8 1

• 20

20 40 60 80 100

Commercial Piezo-System with Feedback Controller

• Piezo-driven 3 axis micro-positioner
• Polytec-PI, Germany, NanoCubeTM P-611
• >$ 10,000
• Feedback sensors: strain gages
• Tracking a 10 Hz, 100 µm p-p sinusiod
• Hysteresis still present
• Low-pass filtered behavior

Time (s) Displacement (µm) Measured Desired Displacement (µm) Voltage (V)

60

Open-loop Feedforward Controller with Inverse Hysteresis Model

• Develop a mathematical model that closely describes the

hysteretic behavior of a piezoelectric actuator

• Existence of an inverse hysteresis model

2 4 6 8 10 12 14 20 40 60 80 100 20 40 60 80 100 2 4 6 8 10 12 14 2 4 6 8 10 12 14 2 4 6 8 10 12 14

Feedforward controller Piezoelectric

Desired Displacement (µm) Actuator Response (µm) Voltage (V)

Displacement (µm)

Displacement (µm)

Voltage (V)

Voltage (V)

Actuator Response (µm)

Displacement (µm)

Displacement (µm)

Desired Displacement (µm)

61

Prandtl-Ishlinskii (PI) Operator

Rate independent backlash operator:

Hr = max{x(t) – r, min{x(t) + r, y0}}

Linearly weighted superposition of backlash operators:

r1

• r1

y x wh1 ri y x Whi = Σwhi

[ ] )

( , ) (

0 t

y x H w t y

r T h

• =

62

Modified PI Operator

• Backlash operators are symmetric but real hysteresis is not
• Modeling saturation by linearly weighted superposition of dead-zone
• perators:

{ }

) ]( [ ) ( ), ( , , ) ( max ) ]( [ t y S w t z d t y d d t y t y S

d T s d

• ⋅

= ⎩ ⎨ ⎧ = > − =

PI model Real Hysteresis

di z y d0 d1

∑

=

=

i j sj si

w W

z y d >0 ws d =0

63

Modified PI Operator

( )

) ]]( , [ [ ] [ ) ( t y x H w S w t x t z

r T h d T s

• ⋅

⋅ = Γ =

x(t) y(t) z(t)

x(t) z(t)

time time Backlash operators Saturation operators

Γ

64

Inverse Modified PI Hysteresis Model

Hysteresis Model Inverse Model

65

Inverse Modified PI Operator

( )

) ]( ], ˆ [ [ ] ˆ [

, , , 1

, ,

t y z S w H w t z

d T s r T h

• ⋅

⋅ = Γ−

) ( ˆ t z

) (t x

1 −

Γ

time time

) ( ˆ t z ) (t x

Inverse saturation

• perators

Inverse Backlash

• perators

66

Piezoelectric Hysteresis is Rate Dependent

Basic assumption of

Prandtl-Ishlinskii operator:

Hysteresis is rate

independent

Our observation:

Hysteresis is rate

dependent

Tremor frequency is time

varying and person specific

8-12 Hz

25 Hz 15 Hz 5 Hz

67

Rate-dependent PI Operator

Assume saturation is rate

independent

Sum of the backlash

weights up to ri (slope of the hysteresis curve at interval i) is linearly dependent on actuation rate Whi = Σwhi;

200 400 600 800 1000 1200

• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1

Whi

Actuation rate (µm/s)

( ) ( )

n i t x c x W t x W

i hi hi

... ), ( ) ( = + =

68

Rate Dependent PI Hysteresis Model

Rate dependent model: Also a PI type → Inverse exists Rate dependent inverse model

) ]]( , [ )) ( ( [ ) ]( , [ ) ( t y x H t x w S w t x x t z

r T h d T s

• ⋅

⋅ = Γ =

( )

) ]( ], ˆ [ [ )) ( ( ] ˆ [

, , )) ( ( , 1

,

t y z S w H t x w t z

d T s t x r T h

• ′

−

⋅ ⋅ = Γ

69

Open-Loop Feedforward Controller with Inverse Rate-Dependent PI Hysteresis Model

Measured Desired

0.05 0.1 0.15 0.2

• 2

2 4 6 8 10 12 14

Displacement (µm)

Error

Rate

• dependent

Time (s)

0.05 0.1 0.15 0.2

• 2

2 4 6 8 10 12 14 Error

Rate

• independent

Time (s) Displacement (µm)

0.05 0.1 0.15 0.2

• 2

2 4 6 8 10 12 14

Time (s) Displacement (µm) Without Model

• Tracking single frequency

stationary sinusoids

70

0.05 0.1 0.15 0.2

• 2

2 4 6 8 10 12 14

Open-Loop Feedforward Controller with Inverse Rate-Dependent PI Hysteresis Model

Tracking multiple frequency

non-stationary sinusoids

0.05 0.1 0.15 0.2

• 2

2 4 6 8 10 12 14

Time (s)

Displacement (µm)

Error Error

Measured Desired Without model. Rate

• independent.

0.05 0.1 0.15 0.2

• 2

2 4 6 8 10 12 14

Displacement (µm)

Time (s)

Error

Displacement (µm) Rate

• d

ependent.

71

Dynamic Motion Tracking Results

5.3 8.0 17.3 0.59 ± 0.06 0.89 ± 0.04 1.91 ± 0.08 max error ± σ (µm) 1.4 2.8 9.2 0.15 ± 0.003 0.31 ± 0.03 1.02 ± 0.07 rmse ± σ (µm) Rate- dependent Rate- independent Without model

(%) amplitude p

• p

rmse (%) amplitude p

• p

error max

rms noise of interferometer = 0.01 µm

72

Tremor Tracking Results

Tracking recordings of real tremor using 1 piezoelectric stack

Rmse = 0.64% of max ampl.; Max error = 2.4% of max ampl.

0.2 0.4 0.6 0.8 2

• 2

2 4 6 8 10 12 14 Desired Obtained Error 0.2 0.4 0.6 0.8 1

• 2

2 4 6 8 10 12 14 Desired Obtained Error

Without Model Rate-Dependent Controller

Time (s) Time (s) Displacement (µm) Displacement (µm)

73

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback MICRON

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

• High precision tracking control
• Mechanism design

74

Design of Parallel Mechanism

75

Manipulator Design

3 DOF piezoelectric-driven parallel manipulator

1 actuator per axis, max effective stroke = 12.5 µm Motion amplification = 9.4x, total stroke > 100 µm

Tool tip approximated as a point, hence only 3 DOF

manipulation

Parallel manipulator design because

Rigidity, compactness, and design simplicity

Located at the front end to balance the weight of the

instrument

76

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

77

Manipulator Kinematics

Inverse kinematics

Modeled as Lee &

Shah RS-type

Closed-form

solution

No internal

singularity

78

Workspace Analysis

Xmax, Ymax = 650 µm Zmax = 100 µm Tremor Space = ∅ 50 µm

Tremor Space Manipulator Workspace

79

Manipulator 3D Tracking Result

Tracking planar circle

• f ∅200 µm

Mean tracking rmse ~

12.1 µm

80

Microsurgery with Active Handheld Instrument

Visuomotor Control System

Noisy, Tremulous Motion Motion Sensing

Visual Feedback Micron

Vitreoretinal Microsurgery Estimation of erroneous motion Manipulation of tip for active error compensation

81

Motion Canceling Experiment

• Translation only
• Generated motion: 9 Hz,

91 µm p-p

• Ave compensated tip motion
• ver 10 runs = 60 µm p-p
• 34.3% reduction
• 3D optical sensing system
• < 1.0 µm rms accuracy

8.8 9 9.2 9.4 9.6 9.8 10

• 40
• 30
• 20
• 10

10 20 30 40 Tip Displacement in Z time (seconds) Displacement (microns)

5 10 15 20 25 5000 10000 15000 Frequency Response without Compensation Magnitude 5 10 15 20 25 5000 10000 15000 Frequency Response with Compensation Frequency (Hz) Magnitude

82

Motion Canceling Experiment

83

Micron Canceling Hand Tremor

Total range: 52% reduction RMS amplitude: 47% reduction

1 2 3

• 60
• 30

30 60

time (s) displacement (µm) compensated uncompensated

84

Other Applications

Surgery and Diagnostics

Active 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 devices

Handheld, vehicle & ship mounted

Consumer camera/camcorder

85

Other Applications: Cell Manipulation / Dissection

86

Questions & Comments

Wei Tech Ang

School of Mechanical & Aerospace Engineering Nanyang Technological University Singapore wtang@ntu.edu.sg