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Biomimetic Robots for Robust Operation in Unstructured Environments
M. Cutkosky and T. KennyStanford University
R. Full and H. KazerooniU.C. Berkeley
R. HoweHarvard University
R. ShadmehrJohns Hopkins University
http://cdr.stanford.edu/touch/biomimetics
Site visit -- Stanford University, Sept. 2, 1990
Main ideas:• Study insects to understand role
of passive impedance (structure and control), study humans to understand adaptation and learning(Full, Howe,Shadmehr)
• Use novel layered prototyping methods to create compliant biomimetic structures with embedded sensors and actuators (Cutkosky, Full, Kenny)
• Develop biomimetic actuation and control schemes that exploit “preflexes” and reflexes for robust locomotion and manipulation (Full, Cutkosky, Howe, Kazerooni, Shadmehr)
BioMimetic Robotics
MURIBerkeley-HarvardHopkins-Stanford
Low-LevelControl
Design & Fabrication
High-LevelControl
MURI
BiomimeticRobots
Issues in studying, designing and building biomimetic robots(and the basic outline for today’s site visit)
1. 2.
3.
Low-LevelControl
Fabrication
High-LevelControl
MURI
What passive properties are found in Nature?
What properties in mechanical design?
How should properties be varied for changing tasks, conditions ?Matching ideal impedance for unstructured dynamic tasks (Harvard)
Guiding questionsGuiding questions
Preflexes: Muscle and Exoskeleton Impedance Measurements (Berkeley Bio.)
Biological implications for RoboticsBasic Compliant Mechanisms for Locomotion (Stanford)Variable compliance joints (Harvard, Stanford)Fast runner with biomimetic trajectory (Berkeley ME)
Fabrication
MURILow-LevelControl High-Level
Control
What strategies are used in insect locomotion and what are their implications?Insect locomotion studies (Berkeley Bio)New measurement capabilities (Stanford)
What motor control adaptation strategies do people use and how can they be applied to robots?
Compliance Learning and Strategies for Unstructured Environments (Harvard & Johns Hopkins)Implications for biomimetic robots (Harvard, Stanford)
Guiding questionsGuiding questions
1 cmdt=10ms dt=30msdt=10msAre preflexes enough?
High-LevelControlMURI
Low-LevelControl
Fabrication
How do we build robust biomimetic structures and systems?Shape deposition manufacturing of integrated parts, with embedded actuators and sensors (Stanford)
How do we build-in tailored compliance and damping?
Effects of Compliance in simple running machine (Stanford, Berkeley ME)
Structures with functionally graded material properties (Stanford)
Guiding questionsGuiding questions
9:30-11:00 Low Level Biomimetic Control
• Results on measurements of muscles, exoskeleton,
compliance, damping (Full ~30)
• Implications for biomimetic robots (Bailey ~20min)
• Matching leg trajectory and scaling (Kazerooni ~15)
• Matching impedance to dynamic task (Matsuoka ~15)
Low-LevelControl
Fabrication
High-LevelControl
MURI
What passive properties are found in Nature?
What properties in mechanical design?
How should properties be varied for changing tasks, conditions ?Matching ideal impedance for unstructured dynamic tasks (Harvard)
Preflexes: Muscle and Exoskeleton Impedance Measurements (Berkeley Bio.)
Biological implications for RoboticsBasic Compliant Mechanisms for Locomotion (Stanford)Variable compliance joints (Harvard, Stanford)Fast runner with biomimetic trajectory (Berkeley ME)
MURI Year One Meeting 1999
University of California at BerkeleyDepartment of Integrative Biology
[email protected]://polypedal.berkeley.edu
University of California at BerkeleyDepartment of Integrative Biology
[email protected]://polypedal.berkeley.edu
Lower Level ControlProfessor Robert J. FullDaniel DudekDr. Kenneth Meijer
Lower Level Control
Mechanical
HigherCenters Environment
aero- , hydro, terra-dynamic
FeedforwardController
(CPG)
AdaptiveController Sensors
Closed-loop
Open-loop
System(Actuators, limbs)
FeedbackController
Sensors
Behavior
Chain of Reflexes
Cruse Controller
Inspired by
Stick Insects
Rough Terrain
Fractal Surface
Variation -3 times the height of the center of mass
Control Challenge
NeuralNeural
MechanicalMechanical
PreciseNovelSlow
Static
Feedforward
ContinuousFeedback(Reflexes)
ControlControl
Dynamic
Feedforward
GrossRepetitiveRapid
ContinuousFeedback(Preflexes)
PolyPEDAL Control
Musculoskeletal units, leg segments and legs do computations on their own.
Control results from propertiesof parts and their morphology.
Control algorithms embeddedin the form of animal itself.
Lower Level Control
Mechanical
HigherCenters Environment
aero- , hydro, terra-dynamic
FeedforwardController
(CPG)
AdaptiveController Sensors
Closed-loop
Open-loop
System(Actuators, limbs)
FeedbackController
Sensors
Behavior
Contribution to Control
FeedforwardIntrinsic musculo-skeletal properties
PreflexMotor program acting through moment arms
Passive DynamicSelf-stabilization
Mechanical System
Predictive Rapid acting
Neural SystemReflex
ActiveStabilization
Neuralfeedbackloops
Slow acting
MURI Interactions
Muscles and
Rapid PrototypingStanfordMotor Control
& LearningJohns Hopkins
Sensors / MEMSStanford
ManipulationHarvard
MURI
LocomotionUC Berkeley
Robot & Leg MechanismsUC Berkeley
Manufactured Legs
What properties should legs possess? Why?
Act as springs to store and return energy? How?
Act to reject disturbances?
What properties should legs possess? Why?
Act as springs to store and return energy? How?
Act to reject disturbances?
Road Map
1. System Impedance
2. Leg Impedance
3. Muscle Impedance
Spring-Mass SystemsLeggedSIX-
Human
TWO-Legged
Cockroach Crab
LeggedEIGHT-
Dog
LeggedFOUR-Vertical
ForceBody
Weight
ForceTime
Fore-aft
Blickhan 1989
Virtual Leg Stiffness
10
100
0.010.001 0.1 1 10 100Mass (kg)
1
Cockroach
Crab
Quail
Hare
Human
Kangaroo
Dog
rel,legk
HOPPERS
TROTTERSRUNNERSkrel =
F
mg
xx
Blickhan and Full, 1993
Sagittal Plane Model
ORGANISM
Multi-Leg
Spring Loaded Inverted
Pendulum k
m
Leg Springs ?
Road Map
1. System Impedance
2. Leg Impedance
3. Muscle Impedance
Leg as Spring & Damper
∆x
Force
Stiffness, kDamping coefficient, c
Restorative Forcesand Perturbation Damping
. ..
For an Oscillating System:Force = force due to + force due to + force due to mass stiffness damping
Force = kx + cx + mx
Experimental Setup
Oscillate Leg
At Multiple
Frequencies
To Determine
k and c
Oscillate Leg
At Multiple
Frequencies
To Determine
k and c
Servo Motor
Roach leg
Length and Force recording
Leg Oscillation Experiments
Time (s)
Dis
plac
emen
t (m
m)
For
ce (
N)
Small Deflection at 12 Hz
-0.3
0
0.3
0 0.05 0.1 0.15 0.2
-0.03
0
0.03
Displacement Force
Leg Is Spring and Damper
Displacement (mm)
For
ce (
N)
Small Deflection at 12 Hz
-0.03
0.03
-0.3 0.3
Slope ≈ Impedance
Effect of Frequency
Displacement (mm)
For
ce (
N)
k25 Hz > k0.08 Hz
Impedance Increases with Frequency
-0.035
0.035
-0.3 0.3
Force @0.08 Hz Force @25 Hz
45
50
55
60
65
70
75
0.01 0.1 1 10 100
Impedance
Preferred Stride Frequency12 Hz
Impedance of Metathoracic Limb of Cockroach
Impe
danc
e (N
/m)
Frequency (Hz)
Leg Model
• At high frequencies:Force (k1+k2)*(displacement)
• At low frequencies:Force k2*(displacement)
Standard Linear Solid
c k1
k2
Frequency vs Speed
Speed (m/sec)
0
5
10
15
20
0 0.2 0.4 0.6
Cockroach
Str
ide
freq
uen
cy (
Hz)
ImpedanceIncreases
ImpedanceConstant
Alter Leg Spring AngleTake Longer Strides
*
NaturalFrequency?
Impedance
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
-1.25 -0.75 -0.25 0.25 0.75 1.25
Displacement (mm)
Forc
e (
N)
0.25 Hz24 Hz
k24 Hz > k0.25 HzLarge Deflection Non-linear
Perturbation Rejection
RestorativeForce
4x Body Mass
Perturbation
Discoveries
1. Insect leg behaves like a spring and damper system.
2. Strain energy is stored in the leg and returned.
3. Force – displacement relationship shows hysteresis with significant energy dissipation (50% or more).
Discoveries
4. Leg impedance increases with frequency up to 12 Hz, the preferred speed of the animal.
5. Leg impedance remains constant at frequencies above 12 Hz.
6. The leg’s natural frequency is near the frequency used by the animal at its preferred speed.
Discoveries
7. Insect leg could simplify control by rejecting perturbations.
For a deflection of only one mm, the leg produces a force of 0.75-4x body mass.
Road Map
1. System Impedance
2. Leg Impedance
3. Muscle Impedance
MURI Interactions
Muscles and
Rapid PrototypingStanfordMotor Control
& LearningJohns Hopkins
Sensors / MEMSStanford
ManipulationHarvard
MURI
LocomotionUC Berkeley
Robot & Leg MechanismsUC Berkeley
Manufactured LegsWhat properties
should actuators possess? Why?
Act as springs to store and return energy? How?
Act to reject disturbances?
Power generation?
What properties should actuators possess? Why?
Act as springs to store and return energy? How?
Act to reject disturbances?
Power generation?
Horizontal Plane Model
ORGANISM
Multi-Leg
Lateral Leg Spring
Muscle-Apodeme Damped Springs ?
k
m
Muscle Lever
Servo andForce
Transducer
Stimulation Stimulation
Strain
Frequency
- pattern- magnitude- phase
- pattern- magnitude
ControlControl
Workloop Technique
Muscle Capacity
4 6 8 10 12 14
++in vivoin vivo conditions conditions
2 Muscle Action Potentials
in vivoin vivoconditionsconditions**
205 10 15
3 Muscle Action Potentials
Muscle Strain %
179 Powerspace
100
80
60
40
20
0
-200.0
-100.0
0.0
Power(W/kg)
177c Powerspace
Sti
mu
lati
on p
has
e (%
)
Spring
Spring
Damper
Damper
Motor
Musculo-skeletal Model
Force
VelocityInsect Leg
Intrinsic musculo-skeletal properties
Preflexes
Brown and Loeb, 1999
Active+Passive Force
Passive Force
Length Increase
Perturbation Experiments
Servo and ForceTransducer
Stimulation
Passive Muscle Stiffness Significant
Effect of Step Length Increase
Stimulated (Twitch)
Relaxed
Passive resistance
is significant in muscle
177c
Passive resistance
is significant in muscle
177c
(n = 4)
0 1 2 30
20
40
60
Step size (%)
For
ce in
crea
se (
mN
)
Oscillatory Perturbations
0 200-5
0
5
0.5 %
Muscle strain (%)
Force (mN)
Time (ms)
-0.25 0 0.25
-5
5
Muscle strain (%)
Force (mN)
Phase angle
Ecomplex =(Force/Area)/strain
Eviscous/Eelastic=tan(phase angle)
Visco-elastic PropertiesPassive Muscle
Impedance increases with frequency in muscle 179 Impedance independent of frequency in muscle 177cSignificant viscous damping in both muscles.
Passive MuscleImpedance increases with frequency in muscle 179 Impedance independent of frequency in muscle 177cSignificant viscous damping in both muscles.
Frequency (Hz)
tan(phase angle)Ecomplex (N/m2)
Frequency (Hz)0 50 100 150
0
1
2
3
4
5 x 105
0 50 100 1500
0.2
0.4
0.6
0.8
1
M177c (n=3)M179 (n=2)
L=1.075
Effect of Length
0.9 1 1.1 1.2 1.3 1.40
2
4
6
8
10x 10
5
0.9 1 1.1 1.2 1.3 1.40
0.2
0.4
0.6
0.8
1
Length
tan(phase angle)Ecomplex (N/m2)
Length
M177c (n=3)M179 (n=2)
f= 50 Hz
Passive MuscleImpedance increases with lengthContribution viscous damping decreases with length
Passive MuscleImpedance increases with lengthContribution viscous damping decreases with length
Perturbation experiments
00
300
100
Locomotion cycle (%)
Force (mN)
0 100
+
Locomotion cycle (%)
Strain
Locomotor pattern
Sinusoid (A=0.5%,f=200 Hz)
7%
Impedance during workloop.
Multiple Muscle System
Anatomically similar muscles provide
impedance during
different phases of the locomotion
cycle!
Anatomically similar muscles provide
impedance during
different phases of the locomotion
cycle!
Muscle strain (%)
0 100
Impedance (mN)
Locomotion cycle (%)
m177c
m179
Stimulation Phase {
Discoveries1. Passive muscle can reject perturbations.
2. Preflexes comprise passive (fixed) and active
components (adjustable).
3. Passive muscle acts like a visco-elastic
actuator.(Viscous damping is responsible for a significant part of total
force response to perturbation.)
4. Impedance of anatomically similar muscles
is distributed over the locomotion cycle.
Impact on Deliverables
1. Energy storage
2. Reject perturbations
3. Simplify control
4. Penetrate new environments
5. Increase robustness
1. Energy storage
2. Reject perturbations
3. Simplify control
4. Penetrate new environments
5. Increase robustness
Low-LevelControl
Fabrication
High-LevelControl
MURI
What passive properties are found in Nature?
What properties in mechanical design?
How should properties be varied for changing tasks, conditions ?Matching ideal impedance for unstructured dynamic tasks (Harvard)
Guiding questionsGuiding questions
Preflexes: Muscle and Exoskeleton Impedance Measurements (Berkeley Bio.)
Basic Compliant Mechanisms for LocomotionBiological implications for Robotics (Stanford)Variable compliance joints (Harvard, Stanford)Fast runner with biomimetic trajectory (Berkeley ME)
Low-LevelControl
MURILocomotion:
Biomimetic Ideology
• Goal:– Navigate rough terrain with simple, robust, compliant robots
• Mindset shaped by Biology – Tunable, passive mechanical properties– Purpose-specific geometry – Simple control scheme – Robust components
Low-LevelControl
MURI Variable Compliance?: Interpreting Biological Findings
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
-1.25 -0.75 -0.25 0.25 0.75 1.25
Displacement (mm)
Forc
e (
N)
0.25 Hz24 Hz
Force
Displacement
Load
Unload
k24 Hz > k0.25 Hz
• Idea– Desired reaction forces depend on the environment and locomotion speed
• How do we represent these findings?– Not traditional spring or damper elements– Energy spent per cycle independent of frequency (area enclosed by curve is the energy spent)
• Results suggest hysteretic damping
Low-LevelControl
MURIVariable Impedance:
New Design Direction• What’s the difference between compliance and impedance?
– Impedance refers to the relationship: dF/dx– Stiffness refers to particular impedance relationship, namely: dF/dx = k
• Hysteretic Damping– Characteristic of some heterogeneous materials– Loading and unloading create different stress-strain paths– Stress-strain curve is independent of frequency
• Design Implications– Compliance is mainly a function of displacement– Damping has a significant frequency dependant term
-0.025
-0.020
-0.015
-0.010
-0.005
0.000
0.005
0.010
0.015
0.020
0.025
-1.25 -0.75 -0.25 0.25 0.75 1.25
Displacement (mm)
Forc
e (N
)
0.25 Hz
24 Hz
Force
Displacement
Load
Unload
k24 Hz > k0.25 Hz
Low-LevelControl
MURIVariable Impedance: Design Approach
• Traditional Robotic Compliance– Actuator powered– Proportional feedback control - variable compliance– Complex
• multiple control laws with different objectives must work together
• Low bandwidth - controller delays
k-
+SetPoint
PlantActuatorPosition
Low-LevelControl
MURIVariable Impedance: Design Approach
• Different Approach– Compliant member powered– Adjustable geometry - variable impedance– Simple
• mechanical properties are more predictable
• separate from control law
• intrinsic low level stability
• Biology is telling us what mechanical properties we really need
SDM robot limb withcompliance and damping
Stiffness
Variable Stiffness Joint Concept
Low-LevelControl
MURISprawl 1.0:
Legged Testbed
• Capture the essential locomoting elements in a low DOF robot
• Explore the roles of compliance and damping in locomotion
• Identify areas which can be improved by SDM
Low-LevelControl
MURISprawl 1.0: Biomimetic, not just a copy
• Full’s research highlights certain important locomoting components– Power-producing thrust muscles– Supporting/repositioning hip joints
Low-LevelControl
MURISprawl 1.0:
Thrusting
• Full’s research on power-producing muscles 177a,c,d,e (Ahn, Meijer)
• Thrust production - Decoupled, compliant system
Cockroach Geometry
Force andWorkspace
Femur
Tibia
12
Force andWorkspace
F1 r1 0 1
=F2 0 r2 2
Robotics Analysis
Force andWorkspace
Sprawl 1.0 Geometry
Very LowFrictionPneumaticPiston
Sprawl 1.0 Geometry
Damped, CompliantRC Servo Actuator
Low-LevelControl
MURISprawl 1.0:
Repositioning/Supporting
• Full’s research on Trochanter-Femur joint (Dudek)
• Repositioning/Supporting - Decoupled, compliant system
Cockroach Geometry
g
Actuated Body-Coxa joint
Compliant Trochanter-Femur joint
Low-LevelControl
MURI Sprawl 1.0: Findings
• Good design and passive mechanical properties take burden off control– Compliance and damping– Simple alternating tripod locomotion scheme– Built-in posture control
• Low bandwidth geometry changes– Walking, stopping, turning, and running
• Need for robust components– Traditional components are not robust - poster child for SDM
Low-LevelControl
MURI Sprawl 1.0: Future Work
• Suggestions from Full– Change location of center of mass– Increase gait frequency– Dynamically control middle leg set points– Weaken front leg force
• Work in Progress– Add compliant springs in parallel with constant force pistons– Replace RC servo hip actuators with more biomimetic components