research objective wearable, high-speed, and compliant...

1

Jun Ueda Ph.D.Assistant Professor

Mechanical EngineeringGeorgia Institute of Technology

LargeLarge--Strain Piezoelectric Cellular Actuators Strain Piezoelectric Cellular Actuators inspired by Biological Muscles: Design, inspired by Biological Muscles: Design,

Modeling, and ControlModeling, and Control

2

Rehabilitation robotics researchRehabilitation robotics research[1] Exoskeleton for muscle diagnosis and physical therapy

Computer algorithm for muscle functional test Neuromuscular model Wearable robot with multiple actuators

[2] Robot components for rehabilitation and healthcare “Muscle-like” fast-moving piezoelectric actuator Nonmagnetic optical sensor

Robotic surgery and intervention in MRI/fMRI

3

Research Objective Research Objective Robot-assisted diagnosis of neurological

movement disorders The use of an exoskeleton robot provides a wider variety of

muscle activities Motor-task planning to induce a desired muscle activation

pattern using individual muscle control

4

Wearable, highWearable, high--speed, and speed, and compliant actuator is the keycompliant actuator is the key

Exoskeleton has more Exoskeleton has more ““hands.hands.””Control is more accurate (feedback)Control is more accurate (feedback)

CompactCompliantLight weightContractiveLarge strainHigh energy densityetc… Fast enough?

5

DC/AC motors?DC/AC motors?

DC motor + Harmonic drive

6

MultifingeredMultifingered RobotRobot--HandHand

Platform for manipulation research

4 fingers (12 DOF total)MP,PIP,DIP (flexion/extension)all DC motors embedded in palm

(no motor in the middle of finger link)No wire: Gear & Link transmission

2

7

NAISTNAIST--Hand finger moduleHand finger module

MP Joint

PIP JointDIP Joint (coupled with PIP)

Motor3: PIP (flexion/extension)

Motor2: MP (flexion/extension)Motor1: MP (adduction/abduction)

1

3

2

rodPIP

DIP

MPaa

MPfe

33

22

11

/

/

/

110

012

001

n

n

n

rod

MPfe

MPaa

8

Gear mechanism Gear mechanism (Japan Patent 4100622 B)(Japan Patent 4100622 B)

MPaa

MPfe

rod

PIP(DIP) Flexion

-A novel three-axis gear driving mechanism that enables the placement of all three electrical motors that drive the finger joints in the palm region without the use of tendons.

-The mechanism requires less space for the actuators than tendon mechanisms and reduces the burden on the motors in terms of finger-tip force generation.

9 10

Recognition Experiment (DP Matching)Recognition Experiment (DP Matching)

Average Recognition Rate [%] (9 subjects, 10 trials for each primitive)

93.7 92.4 96.2 90.4 28.3 77.1

Primitive A Primitive B Primitive C Primitive D Primitive E Primitive F

11

Recognition Experiment (Rolling contact)Recognition Experiment (Rolling contact)

12

3

13

UnderUnder--actuated robotactuated robot 1 DOF ball pitching robot that independently

controls velocity, angular velocity and direction of a ball

release point

start

L

d

ddv

d

ss

d

L

d

ddv

d

ss

d

14

1 DOF Planar 1 DOF Planar ““PitchingPitching”” RobotRobot

DC motor with an encoder

Air table(air hockey toy)

Single link arm

Disc (ball)

15

Experimental results Experimental results (Control of velocity and direction)(Control of velocity and direction)

ｔｈrow3

ｔｈrow1ｔｈrow2120018001160Spin [deg/s]

168178179Direction [deg.]

1.82.61.8Velocity [m/s]

Throw3Throw2Throw1

Single control input changes (at least) 2 outputs independently.

16

17

Independent control of (1) velocity, (2) Independent control of (1) velocity, (2) angular velocity and (3) directionangular velocity and (3) direction

Throwing at the same velocity and direction, but at different angular velocities

18

Mobility Manipulation Perception

““MuscleMuscle--likelike”” robot actuator research at Georgia Techrobot actuator research at Georgia Tech

4

19

PiezoelectricityPiezoelectricityPiezoelectricity is the ability of materials to generate an electric field or

electric potential in response to applied mechanical stress.

Direct Piezoelectric Effect Converse Piezoelectric Effect

Stress Electric potential Electric potential Stress (displacement)

Load cells (force measurement)

Piezopickups

http://www.physikinstrumente.de

Piezoelectric actuators

20

New Actuator MaterialsNew Actuator Materials

Stress

PZTPZT SMA (shape memory alloy)

Reliability, Stability

Efficiency Speed

Strain

PolypyrroleConducting Polymer

ElectrostrictivePolymer

(Elastomer)

Temperature

Strain

0.1%, ~ 10ms

21

Strain Amplification MechanismStrain Amplification Mechanism

)1(2

)2(42 222

d

w

w

wdda

Amplification of displacement:

Amplification of strain:

hd

wa

2

=[Amplification of displacement] x [aspect ratio]

d

w/2

(1+)w/2

d’h

Typically, 5 ~ 20 times: Strain 0.1% 1 ~ 2%

input

output

Cerdat Inc. Conway, Kim, MEMS actuator Janker et al.

Our goal: 20%

22

““Nested RhombusNested Rhombus”” for Exponential Strain for Exponential Strain AmplificationAmplification

PZT stack actuator

0.1%

1.6%

23.9%

1.6%

0.1% x 15 x 15

Ueda, Asada, Secord, US patent application 20090115292

Our goal: 20%

(Amplification gain)^Layerby “Power-law”

23

Principle of strain amplificationPrinciple of strain amplificationConventional proportional

amplificationPower-law (exponential)

amplification

Layer

Strain

Nanomuscle actuator

0

0.1

0.2

0.3

1

Str

ain

(abs

olut

e va

lue)

2 3

0.1%

24%

0

200

400

600

800

f1 f2 f3

Blo

ckin

g fo

rce

[N]

15.1N141.8N

1.6 %

24

Contractive, 33% strain

33.4%

11.0 x 23.1 x 15.3 [mm]

Contractive PZT cellular actuatorContractive PZT cellular actuatorby three amplifying layersby three amplifying layers

1 2 3 40

0.1

0.2

0.3

0.1% 0.31%2.83%

Am

plif

ied

Str

ain

NEC Tokin: PZT stack (AE0203D04F)

L x W x H: 5.1±0.1mm x 4.5mm x 3.5mmDisplacement@150V: 4.6 ± 1.5µm

5

Mechanical Design & DevelopmentMechanical Design & Development

21% effective strain, 1.7N, 15g

30mm

12mm

3.5mm

3.5mm0.1mm

4.97 deg

1.3mm

26

Mechanical Design (cont.)Mechanical Design (cont.)Maximum Stress 324MPa(<550MPa, Phosphor Bronze, C54400)

M

b

h

L

Eh

L yieldmax

2

L

Ebhk

12

3

(1) Lower joint stiffness

(2) Avoid yield

0.53 550103Phosphor Bronze(C54400)

0.28 27597Brass(C3604)

0.77 880113.8Ti 6AL-4V

0.11 215195SUS304

0.13 96.572.4AL2014

(%)(MPa)E (GPa) yield E/yield

Free-cutting brass

6-4 Ti, for aircraft

Free-cutting Bronze H08 spring

27

Cellular piezoelectric actuatorsCellular piezoelectric actuators Pros

Fast motion (over 100 Hz) Zero backlash Large displacement (over 20%

strain) Natural compliance Wearable robots

Non magnetic MRI/fMRI compatibility

Energy efficient Cons

Machining and assembly Control and wiring

28

Miniature Flapping RobotMiniature Flapping Robot

56Hz86Hz

Resonance

29

MRIMRI--Compatible Compatible PiezoPiezo TweezersTweezers

Possible telesurgery device• Nonmagnetic (MRI compatible)• 1N, >30Hz • Force/displacement sensing capability

Sugihara, Kurita, Ueda, Ogasawara, "MRI Compatible Robot Gripper Using Large-Strain Piezoelectric Actuators,“Japan Society of Mechanical Engineers. 30

Bilateralcommunication

Nonmagnetic sensing system (Georgia Tech)

MRI/MRI/fMRIfMRI compatible roboticscompatible robotics

MRI compatible fluid actuator (Vanderbilt)

National Science FoundationCenter for Compact and EfficientFluid Power

6

31

Piezoelectric material for sensing Piezoelectric material for sensing displacement/forcedisplacement/force

PZT

Differential amp Charge ampTrue valueSensor output

Actuator

Sensor

Yuichi Kurita, Fuyuki Sugihara, Jun Ueda, Tsukasa Ogasawara, "Piezoelectric Tweezers with Force- and Displacement-Sensing Capability for MRI, " IEEE/ASME Transactions on Mechatronics, submitted, 32

SensorimotorSensorimotor Enhancer based on Enhancer based on Stochastic ResonanceStochastic Resonance Piezoelectric stack actuator with amplification

mechanism Stochastic resonance “White-noise” ~300Hz

Fingernail mount Side mount

Attachment

Tactile Receptors

Fingernail as a“speaker cone”

Collaborating with Prof. Shinohara, Applied Physiology, GT

33 34

Experimental resultsExperimental results Sensory test (one-point touch test)

Motor test (grasping test)

More sensitive

Less effort(more efficient)

35

Cellular piezoelectric actuatorsCellular piezoelectric actuators

Pros Large displacement (over 20% strain) Fast motion Natural compliance ( rehabilitation robots) Non magnetic ( MRI/fMRI compatible)

Cons Machining and assembly tolerance Control and wiring Reliability (?)

36

33--spring static lumped parameter model for spring static lumped parameter model for design and analysis design and analysis

aloadk

Jk

pztf

pztk

1xBOk

BIk

PZTk

loadkPZT stackactuator

pztf

pztf

1x

1f

1f

Applicable to ANY shape of amplification mechanisms

7

37

Parameter calibrationParameter calibration

pztf=10N

10N

blockf1

blockpztx free

pztx

Blocked Free-load

pztf=10N

freex1

pztf

1f

pztx

1x

11 x

x

f

f pztpzt S

2-port model

38

12

2

Xkkka

kkkka

x

f

BIJBO

BIJBOBIblockout

blockpzt

22

21 X

kkka

kka

x

f

BIJBO

BOBIblockpzt

block

41

Xa

k

x

fJ

free

freepzt

31 X

kk

ak

x

x

BIJ

BIfreepzt

free

Parameter calibration (cont.)Parameter calibration (cont.)

2-port model

1132

21

1 / x

x

XXX

XX

f

f pztpzt

akkk JBOBI ,,,a

Jk

pztf1x

BOk

BIk

39

Structure 1 (Moonie) Structure 2 (Rhombus)

pztfpztx

1x

Validation by connecting to a compliant beam (external load)

40Hill-type Muscle Model

MuscleMuscle--like compliance (Hill model??)like compliance (Hill model??)

PZTf

PZTk

PZT stack actuator

Amplification mechanism

Lumped Model for Piezoelectric Cellular Actuators

41

Lumped parameter model: Design guideLumped parameter model: Design guide

aloadk

a

Jk

pztf

pztk

1xBOk

BIk

loadk

Ideal rhombus

pzt

pzt

Rigid beam

Free joint

(1) Minimize Parallel Stiffness (constrained space)(2) Maximize Serial Stiffness (admissible space)

pztf

42

Reconfigurable cellular actuatorReconfigurable cellular actuator

252 PZT stack actuators7 bundles 6 stacks

288 PZT stack actuators4 bundles 12 stacks

Jun Ueda, Tom Secord, Harry Asada, "Design of PZT Cellular Actuators with Power-law Strain Amplification," IROS 2007.

8

43

PZT stack actuator

N1 serial connection

N2 serial connectionEquivalent model for each nested unit

1BOk

1BIk1a

2a

3a

1st layer

2nd layer

3rd layer

2

~k

2

~f

2BIk

3BIk

1Jk

2Jk

3Jk2BOk

3BOkRecursive Formula for Nested RhombusRecursive Formula for Nested Rhombus

44

ComponentComponent--level modeling and level modeling and controlcontrol

45

Human Skeletal Muscle possesses:

Quantization due to finite enervation rates

Resonant modes due to flexibility and mass of muscle tissue.

However, despite these effects, humans are able to produce smooth motion with simple on-off commands to discrete groups of muscle fibers.

The biological mechanisms by which the switching times are chosen are not well known.

PhysiologicallyPhysiologically--inspired impulse excitation inspired impulse excitation method for fast and compliant actuators: method for fast and compliant actuators: MotivationMotivation

Quantization in actuation (# of motor units) butHigh precision in time (very fast contraction time)

46

Vibration suppression by redundant Vibration suppression by redundant ONON--OFF actuationOFF actuation

0 5 10 15-1

0

1

2

3

4

Time [s]

Dis

plac

emen

t [m

m]

ONON--OFFOFF

ON‐OFF Power Switching Network

(1) Serially-connected PZT actuators (redundant discrete actuation)(2) Fast response of PZT (good resolution in time) Linear actuation (amplifiers) may not be necessary

Motivation

47

Experimental Bode PlotExperimental Bode Plot

47

101 102 103

-200

-150

-100

-50

frequency [rad/s]

Mag

nitu

de [d

B]

101 102 103

-300

-200

-100

0

100

frequency [rad/s]

Pha

se [d

eg]

Mode 1Mode 2

48

““Input shapingInput shaping”” for redundant actuationfor redundant actuation

Input-shaping Singer and Seering, Input Shaping, 1990. Singhose and Seering, Vector Diagrams, 1994. Singhose, Mills, and Seering, On-Off Control, 1998.

Pulse 1 Response

Pulse 2 Response

Resulting Motion0

Past research: Either linear or All On-All Off control

Quantization in actuation, high-precision in time

ONON--OFFOFF

ON‐OFF Power Switching Network

9

49

Step Input (0 Step Input (0 5 Units ON)5 Units ON)

49

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

Time (sec)

Nu

mb

er

of A

ctu

ato

rs O

n

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

x 10-3

Time (sec)

Act

ua

tor

Po

sitio

n, m

Residual oscillation is significant

50

All On/All Off Input (0 All On/All Off Input (0 5 Units ON)5 Units ON)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

Time (sec)

Num

ber

of A

ctua

tors

On

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

x 10-3

Time (sec)

Act

uato

r P

ositi

on, m

* All on/ all off control is not the only solution.Vibration suppression by input-shaping

51

[Proposed] [Proposed] Minimum Switching Input (0Minimum Switching Input (05 Units ON)5 Units ON)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

1

2

3

4

5

6

Time (sec)

Num

ber

of A

ctua

tors

On

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.5

1

1.5

x 10-3

Time (sec)

Act

uato

r P

ositi

on, m

(1) Vibration suppression by input shaping & (2) Minimization of switching

Minimum Switching Discrete Switching Vibration Suppression (MSDSVS)

* Input command is not always “stair step”

Joshua Schultz and Jun Ueda, "Discrete Switching Vibration Suppression for Flexible Systems With Redundant Actuation, " 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2009), Singapore, July 2009. 52

Experimental SetupExperimental Setup

Silicon Laboratories C8051F120DKMicrocontroller Development Kit

RS232-USB adapter

Control Circuit

MicroEpsilonlaser position

sensor

Cellular actuator

52

53

Discrete ONDiscrete ON--OFF CommandsOFF Commands Limit commands to actuators to completely on or completely off. No linear amplifiers required. Smaller system board footprint. No hysteresis compensation necessary. Less vulnerable to noise.

53

DC-DC converter (150V)6 Fast ON-OFF switching transistors

6 Linear amplifier(bulkey!)

Step MSDSVS (proposed)

10

55

Switching Comparisons: Energy efficiencySwitching Comparisons: Energy efficiency

Goal Number of Actuators

Number switches, All on/All offAll on/All off

Number switches, MSDSVS

2 6 66

5 15 55

6 18 88

dtRiE 2

56

Robustness against modeling errorRobustness against modeling error

56

Vibration suppression designed to suppress frequency 40% belowactual lowest natural frequency

(0 units on 6 units on)

-0.05 0 0.05 0.1 0.15 0.2 0.25

0

0.2

0.4

0.6

0.8

1

Time [seconds]

Dis

plac

emen

t [m

m]

Step response

MSDSVS responseAll On/All Off response

0 200 400 600 800 10000

100

200

300

400

Un-modeled mode Frequency [Hz]

Re

sidu

al O

scill

atio

n[%

]

Low

ro

bust

nes

sH

igh

H

igh

ro

bust

nes

sro

bust

nes

s

MSDSVSAll On/All Off

57

0

3

1

2

T 2T

Nominal input (discrete-time control theory)

PWM Quantization

Intersample Discretized

(1)

(2)

(3)

OFF

ON

58

From From ““Quantization in time, highQuantization in time, high--precision in actuationprecision in actuation””toto““Quantization in actuation, highQuantization in actuation, high--precision in timeprecision in time””

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time [sec]

Pos

itio

n [m

]

ReferencePWM QuantizationIntersample Discretized

0 0.2 0.4 0.6 0.8 1 1.2Time [sec]

0

2

4

-2

-4

-6

Qua

ntiz

atio

n le

vel

OFF

ON

PWM Quantization

0 0.2 0.4 0.6 0.8 1 1.2

Qua

ntiz

atio

n le

vel

Time [sec]

0

2

4

-2

-4

-6

-8OFF

ON

Intersample Discretized

59

Modeling and Characterization of Modeling and Characterization of actuator array topologiesactuator array topologies

60

Different actuator array topologiesDifferent actuator array topologies

Consists of: Piezoelectric Actuator Amplification Structure

Modeled as: Spring Pure Force Generator

Spring

Pure Force Generator

Cell Model

RelaxedActuated

60

11

61

1

1

3&

1

2

3&

1

2

3&

1

2

1&

L1 L2 Lk-1 Lk

L1 L2 L3 L4

1

1

F1&

000

122

8&6&1&

000

211

01&E&1&

0

5

1&

L1 L2 L3 L4

L1 L2 Lk-1 Lk

Connection Fingerprint

(a)

(b)

““FingerprintFingerprint”” method for modeling and method for modeling and characterizing reconfigurable actuator characterizing reconfigurable actuator array topologiesarray topologies

David MacNair and Jun Ueda, "A Fingerprint Method for Variability and Robustness Analysis of Stochastically Controlled Cellular Actuator Arrays," The International Journal of Robotics Research, accepted. 62

2 Cells : 2 Arrays

Automatic generation of actuator Automatic generation of actuator topologies using the fingerprint methodtopologies using the fingerprint method

plot_fingerPrintGrid(fingerPrintBuild(# of cells))

63

3 Cells : 4 Arrays

64

4 Cells : 9 Arrays

65

5 Cells : 23 Arrays

66

6 Cells : 65 Arrays

12

67

7 Cells : 199 Arrays

68

# Cells

Com

puta

tion

Tim

e (s

)

1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

350

# Cells

# A

ctua

tor

Arr

ays

1 2 3 4 5 6 7 8 9 100

1000

2000

3000

4000

5000

6000

7000

8000

9000

Computational loadsComputational loads

69

Actuator array network representationActuator array network representation

Actuator Array

= Node

= Cell

= Spacer

& = Expanders

Ni,f Ni,f

Node i

Ni,x

Cell j

kj

FjNi Ni+1

Xj

dj

Element Type Variables Equations Constants

Node iPosition (Ni,x)

Force (Ni,f)None None

Cell j Displacement (dj)Ni+1,x ‒ Ni,x ‒ dj = Xj

Ni,f ‒ kj(dj) = Fj

Ni+1,f ‒ kj(dj) = Fj

Spring Constant (kj)Unforced Length (Xj)

Pure Force Generator Force (Fj)

Spacer m NoneNi+1,x ‒ Ni,x = qm

Ni+1,f ‒ Ni,f = 0Length (qm)

Expander None

Ni,x ‒ Ni+1,x = 0Ni,x ‒ Ni+2,x = 0Ni,x ‒ Ni+3,x = 0

…Ni,f ‒ Ni+1,f ‒ Ni+2,f ‒ Ni+3,f ‒ … = 0

None

70

Analysis: Force RelationshipAnalysis: Force Relationship[A] N1,d N1,f N2,d N2,f N3,d N3,f N4,d N4,f N5,d N5,f N6,d N6,f d1 d2 [B] [C]

Eqn1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 N1,d 0Eqn2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 N1,f XtotalEqn3 0 0 -1 0 1 0 0 0 0 0 0 0 -1 0 N2,d X1Eqn4 0 0 0 1 0 0 0 0 0 0 0 0 -bk1 0 N2,f bF1Eqn5 0 0 0 0 0 1 0 0 0 0 0 0 -bk1 0 N3,d bF1Eqn6 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 N3,f X2Eqn7 0 0 0 0 0 0 0 1 0 0 0 0 0 -bk2 N4,d bF2Eqn8 0 0 0 0 0 0 0 0 0 1 0 0 0 -bk2 N4,f bF2Eqn9 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 N5,d 0Eqn10 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 N5,f 0Eqn11 0 1 0 -1 0 0 0 -1 0 0 0 0 0 0 N6,d 0Eqn12 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 N6,f 0Eqn13 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 d1 0Eqn14 0 0 0 0 0 -1 0 0 0 -1 0 1 0 0 d2 0

Sp

ring

Eq

ns.P

ara

llel L

ink E

qu

ation

s

Mo

un

tP

oin

ts

N1

N2

N4

C1

C2

N3

N5

N6

P1 P2

[B] = [A]‐1[C]

70











Expander None


…Ni,f ‒ Ni+1,f ‒ Ni+2,f ‒ Ni+3,f ‒ … = 0

None

Operational Cell: b=1Broken Cell: b=0

71

OutputReference

0 1 22

4

6

8

10

12

14

Time [sec]

forc

e [N

]

kf

Variability analysis (stochastic control)Variability analysis (stochastic control)

0 0.2 0.4 0.6 0.8 10

0.02

0.04

0.06

0.08

Normalized command

Var

ianc

e of

Out

put F

orce

Muscle A

Muscle B

Muscle C

Muscle D

Muscle E

A B

C D

ENode

Actuator unit

72

Robustness analysisRobustness analysis[A]

N1,d N1,f

N2,d N2,f N3,d N3,f N4,d N4,f N5,d N5,f N6,d N6,f d1 d2 f [B] [C]

Eqn1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 N1,d 0Eqn2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 N1,f

Xtotal

Eqn3 0 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 N2,d X1Eqn4 0 0 0 1 0 0 0 0 0 0 0 0 -bk1 0 -1b N2,f 0Eqn5 0 0 0 0 0 1 0 0 0 0 0 0 -bk1 0 -1b N3,d 0Eqn6 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 0 N3,f X2Eqn7 0 0 0 0 0 0 0 1 0 0 0 0 0 -bk2 -1b N4,d 0Eqn8 0 0 0 0 0 0 0 0 0 1 0 0 0 -bk2 -1b N4,f 0Eqn9 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 N5,d 0Eqn10 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 N5,f 0Eqn11 0 1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 N6,d 0Eqn12 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 N6,f 0Eqn13 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 d1 0Eqn14 0 0 0 0 0 -1 0 0 0 -1 0 1 0 0 0 d2 0Eqn15 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 f 0

Sp

ring

Eq

ns.P

ara

llel L

ink E

qu

ation

s

Mo

un

tP

oin

ts

N1

N2

N4

C1

C2

N3

N5

N6

P1 P2











Expander None


…Ni,f ‒ Ni+1,f ‒ Ni+2,f ‒ Ni+3,f ‒ … = 0

None

[B] = [A]‐1[C]

Operational Cell: b=1Broken Cell: b=0

13

73

Percent of Original Force

Remaining: 0.0%


Remaining:28.52%


Remaining: 69.25%

Active unit

Disconnected unit

Robustness analysis (cont.)Robustness analysis (cont.)

1

1

F1&

000

122

8&6&1&

000

211

01&E&1&

0

5

1&

74

NEXT Challenge:NEXT Challenge:How can we control a vast number of actuators? How can we control a vast number of actuators?

1,500,000,000 Sarcomeres / Motor neuron (controller)

Actuators >>> Controllers > SensorsSkeletal muscle:

Skeletal muscle shows a good performance in the presence of:(1) Limited communication, sensing(2) Non-functional (dead or damaged) cells(3) Non-uniformity of cells (displacement, activity level, etc.)

MEMS-PZT Cellular Actuator Unit

75

Idea: Stochastic broadcast controlIdea: Stochastic broadcast control

Ion diffusion process

Motor Neuron

Sarcomeres

Stochastic !

2 m

2 - 8 m

Sarcomere

actuator

on/off

OFF

ON

actuator

on/off

OFF

ON

actuator

on/off

OFF

ON

actuator

on/off

OFF

ON

actuator

on/off

OFF

ON

actuator

on/off

OFF

ON

N

i

iyy1

actuator

on/off

OFF

ON

Dead cell

actuator

on/off

OFF

ON

Dead cell

Stochastic Recruitment

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Signal dependent noise in muscles and Signal dependent noise in muscles and generation of generation of ““naturalnatural”” robot movements robot movements

x yO

z

Force VariabilityEllipsoid (FVE)

Stochastic actuator arrays

Actuator-level variability analysis

National Science Foundation: Cyber-Physical Systems #0932208

PI: Ueda, September 2009- August 2012

Jones, Hamilton, and Wolpert, Sources of Signal-Dependent Noise During Isometric Force Production, J. Neurophysiology, 2002

Harris, and Wolpert, Signal-dependent noise determines motor planning, Nature, 1998

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Optimal trajectory of a robot arm with Optimal trajectory of a robot arm with stochastically controlled actuator arrays stochastically controlled actuator arrays

Uno, Y., Kawato, M. & Suzuki, R. Biol. Cybern. 61, 89–101 (1989).

Observation: human-arm trajectories, 4 trials

Mr. Teraoka, NAIST, Japan 78

AcknowledgementAcknowledgement National Science Foundation NSF Center for Compact and Efficient Fluid Power General Motors Korea Institute for Advancement of Technology NAIST Robotics Lab Robotics and Intelligent Machines @ GA Tech My lab members

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Thank you !!Thank you [email protected]

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