research objective wearable, high-speed, and compliant...
TRANSCRIPT
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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
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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
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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
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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?
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DC/AC motors?DC/AC motors?
DC motor + Harmonic drive
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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
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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
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22
11
/
/
/
110
012
001
n
n
n
rod
MPfe
MPaa
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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.
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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
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Recognition Experiment (Rolling contact)Recognition Experiment (Rolling contact)
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3
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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
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1 DOF Planar 1 DOF Planar ““PitchingPitching”” RobotRobot
DC motor with an encoder
Air table(air hockey toy)
Single link arm
Disc (ball)
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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.
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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
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Mobility Manipulation Perception
““MuscleMuscle--likelike”” robot actuator research at Georgia Techrobot actuator research at Georgia Tech
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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
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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
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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%
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““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”
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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 %
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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
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Mechanical Design & DevelopmentMechanical Design & Development
21% effective strain, 1.7N, 15g
30mm
12mm
3.5mm
3.5mm0.1mm
4.97 deg
1.3mm
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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
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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
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Miniature Flapping RobotMiniature Flapping Robot
56Hz86Hz
Resonance
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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
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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
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Experimental resultsExperimental results Sensory test (one-point touch test)
Motor test (grasping test)
More sensitive
Less effort(more efficient)
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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 (?)
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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
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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
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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
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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
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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
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ComponentComponent--level modeling and level modeling and controlcontrol
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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)
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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
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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
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
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
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
[B] = [A]‐1[C]
Operational Cell: b=1Broken Cell: b=0
13
73
Percent of Original Force
Remaining: 0.0%
Percent of Original Force
Remaining:28.52%
Percent of Original Force
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
76
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
77
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
78
Thank you !!Thank you [email protected]