Biomimetic Robots for Robust
Operation in Unstructured
Environments
M. Cutkosky and T. Kenny
Stanford University
R. Full and H. Kazerooni
U.C. Berkeley
R. Howe
Harvard University
R. Shadmehr
Johns Hopkins University
Site visit -- Stanford University, Sept. 2, 1990
http://cdr.stanford.edu/touch/biomimetics
BioMimetic Robotics
MURI
Berkeley-Harvard
Hopkins-Stanford
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)
Issues in studying, designing and building biomimetic robots
(and the basic outline for today’s site visit)
2.
1.
Low-Level
Control
Biomimetic
Robots
High-Level
Control
MURI
3.
Design & Fabrication
Guiding questions
What passive properties are
found in Nature?
Preflexes: Muscle and Exoskeleton
Impedance Measurements (Berkeley Bio.)
Low-Level
Control
High-Level
Control
MURI
What properties in mechanical design?
Biological implications for Robotics
Basic Compliant Mechanisms for Locomotion
(Stanford)
Variable compliance joints (Harvard, Stanford)
Fast runner with biomimetic trajectory (Berkeley ME)
How should properties be varied for changing
tasks, conditions ?
Matching ideal impedance for unstructured
dynamic tasks (Harvard)
Fabrication
Guiding questions
Low-Level
Control
1 cm
What strategies are used in insect
locomotion and what are their
implications?
MURI
High-Level
Control
Fabrication
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)
dt=10ms
dt=10ms
dt=30ms
Are
preflexes enough?
Guiding questions
Low-Level
Control
MURI
High-Level
Control
How do we build robust biomimetic
structures and systems?
Fabrication
Shape deposition manufacturing of
integrated parts, with embedded actuators
and sensors (Stanford)
How do we build-in tailored
compliance and damping?
Structures with functionally graded
material properties (Stanford)
Effects of Compliance in simple running machine
(Stanford, Berkeley ME)
Low Level
Biomimetic Control
9:30-11:00
• 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)
What passive properties are
found in Nature?
Preflexes: Muscle and Exoskeleton
Impedance Measurements (Berkeley Bio.)
Low-Level
Control
High-Level
Control
MURI
What properties in mechanical design?
Biological implications for Robotics
Basic Compliant Mechanisms for Locomotion
(Stanford)
Variable compliance joints (Harvard, Stanford)
Fast runner with biomimetic trajectory (Berkeley ME)
How should properties be varied for changing
tasks, conditions ?
Matching ideal impedance for unstructured
dynamic tasks (Harvard)
Fabrication
MURI Year One Meeting 1999
Lower Level Control
Professor Robert J. Full
Daniel Dudek
Dr. Kenneth Meijer
University of California at Berkeley
Department of Integrative Biology
rjfull@socrates.berkeley.edu
http://polypedal.berkeley.edu
Lower Level Control
Higher
Centers
Sensors
aero- , hydro, terra-dynamic
Open-loop
Feedforward
Controller
(CPG)
Mechanical
System
(Actuators, limbs)
Feedback
Controller
Adaptive
Controller
Environment
Closed-loop
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
Precise
Novel
Slow
Static
Control
Mechanical
Gross
Repetitive
Rapid
Dynamic
Neural
Feedforward
Continuous
Feedback
(Reflexes)
Feedforward
Continuous
Feedback
(Preflexes)
PolyPEDAL Control
Control algorithms embedded
in the form of animal itself.
Control results from properties
of parts and their morphology.
Musculoskeletal units, leg segments
and legs do computations on
their own.
Lower Level Control
Higher
Centers
Sensors
aero- , hydro, terra-dynamic
Open-loop
Feedforward
Controller
(CPG)
Mechanical
System
(Actuators, limbs)
Feedback
Controller
Adaptive
Controller
Environment
Closed-loop
Sensors
Behavior
Contribution to Control
Mechanical System Neural System
Feedforward Preflex
Motor program
acting through
moment arms
Predictive
Intrinsic
musculo-skeletal
properties
Rapid acting
Passive Dynamic
Self-stabilization
Reflex
Neural
feedback
loops
Slow acting
Active
Stabilization
MURI Interactions
Motor Control
& Learning
Johns Hopkins
Rapid Prototyping
Stanford
Muscles and
Locomotion
UC Berkeley
MURI
Manipulation
Harvard
Sensors / MEMS
Stanford
Robot & Leg
Mechanisms
UC Berkeley
Manufactured Legs
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 Systems
EIGHT- Legged
SIX- Legged
Cockroach
TWO-Legged
Crab
Body
Weight
Vertical
Force
FOUR- Legged
Fore-aft
Force
Time
Blickhan 1989
Human
Dog
Virtual Leg Stiffness
k rel =
100
F
mg
TROTTERS
RUNNERS
HOPPERS
Dx
x
Blickhan and Full, 1993
Human
Quail
10
Dog
Cockroach
krel,leg
1
0.001
Hare
Crab
0.01
0.1
Mass (kg)
1
Kangaroo
10
100
Sagittal Plane Model
ORGANISM
Spring Loaded
Inverted
Pendulum
Multi-Leg
m
b
k
Leg
Springs ?
Road Map
1. System Impedance
2. Leg Impedance
3. Muscle Impedance
Leg as Spring & Damper
∆x
Force
Stiffness, k
Damping coefficient, c
Restorative Forces
and 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
Servo Motor
Roach leg
Length and
Force recording
Leg Oscillation Experiments
Small Deflection at 12 Hz
0.03
0
0
-0.3
-0.03
0
0.05
0.1
Displacement
Time (s)
0.15
Force
0.2
Force (N)
Displacement (mm)
0.3
Leg Is Spring and Damper
Small Deflection at 12 Hz
0.03
Force (N)
Slope ≈ Impedance
-0.3
0.3
-0.03
Displacement (mm)
Effect of Frequency
Impedance Increases with Frequency
0.035
Force (N)
k25 Hz > k0.08 Hz
-0.3
0.3
-0.035
Force @0.08 Hz
Force @25 Hz
Displacement (mm)
Impedance
Impedance of Metathoracic Limb of Cockroach
Impedance (N/m)
75
70
Preferred Stride Frequency
12 Hz
65
60
55
50
45
0.01
0.1
1
10
Frequency (Hz)
100
Leg Model
Standard Linear Solid
k1
c
• At high frequencies:
Force a (k1+k2)*(displacement)
k2
• At low frequencies:
Force a k2*(displacement)
Stride frequency (Hz)
Frequency vs Speed
Cockroach
20
Natural
Frequency?
15
Impedance
Increases
10
*
Impedance
Constant
Alter Leg Spring Angle
Take Longer Strides
5
0
0
0.2
0.4
Speed (m/sec)
0.6
Impedance
Large Deflection
Non-linear k
24 Hz > k0.25 Hz
Perturbation Rejection
Perturbation
Restorative
Force
4x Body Mass
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 0.754x body mass.
Road Map
1. System Impedance
2. Leg Impedance
3. Muscle Impedance
MURI Interactions
Motor Control
& Learning
Johns Hopkins
Rapid Prototyping
Stanford
Muscles and
Locomotion
UC Berkeley
MURI
Manipulation
Harvard
Sensors / MEMS
Stanford
Robot & Leg
Mechanisms
UC Berkeley
Manufactured Legs
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
k
Lateral Leg Spring
b
Multi-Leg
m
MuscleApodeme
Damped
Springs ?
Muscle Lever
Control
Stimulation
Servo and
Force
Transducer
Stimulation
- pattern
- magnitude
- phase
Strain
- pattern
- magnitude
Frequency
Workloop Technique
Muscle Capacity
179 Powerspace
177c Powerspace
2 Muscle Action Potentials
Power
3 Muscle Action Potentials (W/kg)
Stimulation phase (%)
100
60
0.0
Damper
80
Damper
Spring
-100.0
+
40
Motor
in vivo
conditions
20
Spring
*
in vivo
conditions
0
4
6
8
10
12
14
5
Muscle Strain %
10
15
20
-200.0
Musculo-skeletal Model
Preflexes
Intrinsic musculo-skeletal
properties
Force
Insect
Leg
Velocity
Brown and Loeb, 1999
Perturbation Experiments
Passive Muscle Stiffness Significant
Length Increase
Stimulation
Servo and Force
Transducer
Active+Passive Force
Passive Force
Force increase (mN)
Effect of Step Length Increase
Passive
resistance
is
significant
in muscle
177c
60
Stimulated (Twitch)
(n = 4)
40
20
0
0
Relaxed
1
2
Step size (%)
3
Oscillatory Perturbations
Force (mN)
5
Muscle strain (%)
0.5 %
Force (mN)
5
Muscle strain (%)
-0.25
0
0.25
Phase angle
0
-5
Ecomplex =(DForce/Area)/strain
-5
0
Time (ms)
200
Eviscous/Eelastic=tan(phase angle)
Visco-elastic Properties
Passive Muscle
Impedance increases with frequency in muscle 179
Impedance independent of frequency in muscle 177c
Significant viscous damping in both muscles.
Ecomplex (N/m2)
5 x 10
tan(phase angle)
5
1
4
0.8
3
0.6
2
0.4
M179 (n=2)
M177c (n=3)
1
0.2
L=1.075
0
0
50
100
Frequency (Hz)
150
0
0
50
100
Frequency (Hz)
150
Effect of Length
Passive Muscle
Impedance increases with length
Contribution viscous damping decreases with length
10
Ecomplex (N/m2)
x 10
tan(phase angle)
1
5
8
0.8
6
0.6
4
0.4
M179 (n=2)
M177c (n=3)
2
0.2
f= 50 Hz
0
0.9
1
1.1
1.2
Length
1.3
1.4
0
0.9
1
1.1
1.2
Length
1.3
1.4
Perturbation experiments
Impedance during workloop.
Force (mN)
300
7%
Locomotor pattern
+
Sinusoid (A=0.5%,f=200 Hz)
0
0
100
Locomotion cycle (%)
0
100
Locomotion cycle (%)
Multiple Muscle System
Muscle strain (%)
Stimulation Phase {
m177c
0
Anatomically
similar
muscles
provide
Impedance (mN)
impedance
m179
during
different
phases of the
locomotion
cycle!
100
Locomotion cycle (%)
Discoveries
1. 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
Guiding questions
What passive properties are
found in Nature?
Preflexes: Muscle and Exoskeleton
Impedance Measurements (Berkeley Bio.)
Low-Level
Control
High-Level
Control
MURI
What properties in mechanical design?
Basic Compliant Mechanisms for Locomotion
Biological implications for Robotics (Stanford)
Variable compliance joints (Harvard, Stanford)
Fast runner with biomimetic trajectory (Berkeley ME)
How should properties be varied for changing
tasks, conditions ?
Matching ideal impedance for unstructured
dynamic tasks (Harvard)
Fabrication
MURI
Locomotion:
Biomimetic Ideology
Low-Level
Control
•
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
MURI
Low-Level
Control
•
Variable Compliance?:
Interpreting Biological Findings
Idea
– Desired reaction forces depend on the environment and locomotion speed
Unload
Force
k24 Hz > k0.25 Hz
Load
Displacement
•
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
MURI
Low-Level
Control
•
Variable 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
MURI
Low-Level
Control
•
Variable 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
Set +
Point -
k
Plant
Actuator
Position
MURI
Low-Level
Control
•
Variable 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
SDM robot limb with
compliance and damping
•
Stiffness
Variable Stiffness Joint Concept
Biology is telling us what mechanical properties we really need
MURI
Low-Level
Control
Sprawl 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
MURI
Low-Level
Control
•
Sprawl 1.0:
Biomimetic, not just a copy
Full’s research highlights certain important locomoting components
– Power-producing thrust muscles
– Supporting/repositioning hip joints
MURI
Sprawl 1.0:
Thrusting
Low-Level
Control
Cockroach Geometry
Sprawl 1.0 Geometry
Robotics Analysis
F1
r1
0
1
0
r2
2
=
F2
Femur
2
Very Low
Friction
Pneumatic
Piston
1
Tibia
Force and
Workspace
•
•
Force and
Workspace
Force and
Workspace
Full’s research on power-producing muscles 177a,c,d,e (Ahn, Meijer)
Thrust production - Decoupled, compliant system
MURI
Sprawl 1.0:
Repositioning/Supporting
Low-Level
Control
Cockroach Geometry
Sprawl 1.0 Geometry
Compliant Trochanter-Femur joint
g
Damped, Compliant
RC Servo Actuator
Actuated Body-Coxa joint
•
•
Full’s research on Trochanter-Femur joint (Dudek)
Repositioning/Supporting - Decoupled, compliant system
MURI
Low-Level
Control
•
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
Sprawl 1.0:
Future Work
MURI
Low-Level
Control
•
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