Low-Level

1
Low-Level Control
Cockroach Locomotion Results and Implications
New Measurement Techniques and Results
Fabrication
Adaptation and Impedance Matching Strategies
2
Road Map
1. System Impedance 2. Skeletal Impedance
3.
Musculo-skeletal Impedance
3
MURI Interactions
Rapid Prototyping
Stanford
Muscles and
Motor Control
Learning
Locomotion UC Berkeley
Johns Hopkins
MURI
Robot Leg Mechanisms
Manipulation
Harvard
UC Berkeley
Sensors / MEMS
Stanford
4
System Impedance
Compliant Legs
What is the system impedance? Fixed? Adjustable?
Where does the control reside?
1 DOF Robot
5
Spring-Mass Systems
Legged
SIX-
6
Virtual Leg Stiffness
F
mg
TROTTERS

RUNNERS
Dx
HOPPERS
x
100
Blickhan and Full, 1993
Human
Quail
Dog
Cockroach
10
k
Hare
rel,leg
Kangaroo
Crab
1
0.01
0.001
0.1
1
10
100
Mass (kg)
7
Sagittal Plane Model
ORGANISM
Spring Loaded Inverted Pendulum
m
k
b
Leg Springs ?
Multi-Leg
8
System Impedance
Spring Constant from Force data (k 10 kg/s)
Double animal mass (2.4 g to 4.8g)
9
System Natural Frequency
Leg Spring Adjustable
10
Discoveries
System Impedance 1. Insects do prefer to run at
their natural frequency (10 Hz). 2. Animals run
with loads equal to body weight. Experiment can
suggest if the animals natural frequency is a
control target. 3. Stride frequency does not
decease to values predicted for loading 4. Leg
spring stiffness could be adjustable.
11
Road Map
1. System Impedance 2. Skeletal Impedance
3.
Musculo-skeletal Impedance
12
MURI Interactions
Rapid Prototyping
Stanford
Muscles and
Motor Control
Learning
Locomotion UC Berkeley
Johns Hopkins
MURI
Manipulation
Harvard
Sensors / MEMS
Stanford
13
Leg Impedance
Compliant Legs
How to model leg impedance? Where does the
control reside?
14
Leg as Spring Damper
?x
Force
Stiffness, k Damping 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
15
Experimental Setup
Oscillate Leg At Multiple Frequencies To
Determine k and c
Servo Motor
Roach leg
Length and Force recording
16
Leg Oscillation Experiments
Small Deflection at 12 Hz
Force (N)
Displacement (mm)
Time (s)
17
Leg Is Spring and Damper
Small Deflection at 12 Hz
Slope Impedance
Force (N)
Displacement (mm)
18
Impedance
Large Deflection
Non-linear
k24 Hz gt k0.25 Hz
19
Discoveries
1. Insect leg behaves like a spring and damper
system. 2. Leg impedance increases with frequency
up to 10 Hz, the preferred speed of the
animal. 3. Leg impedance remains constant at
frequencies above 10 Hz. 4. The legs natural
frequency is near the frequency used by the
animal at its preferred speed.
20
Relaxation History
Give step displacements and measure force over
time
21
New Leg Models
Xiaorong Xu , Wendy Cheng , Daniel Dudek ,
Motohide Hatanaka , Mark R. Cutkosky, and Robert
J. Full. Material Modeling for Shape Deposition
Manufacturing of Biomimetic Components. ASME
22
Impact on Deliverables
Development methodology to use biological
inspiration to determine robot leg impedance
23
Road Map
1. Skeletal Impedance 2. System Impedance
3.
Musculo-skeletal Impedance
24
Horizontal Plane Model
Muscle-Apodeme Damped Springs ?
25
Musculo-skeletal Model
Preflexes
Intrinsic musculo-skeletal properties
Force
Insect Leg
Velocity
Brown and Loeb, 1999
26
Perturbation Experiments
Passive Muscle Stiffness Significant
27
Oscillatory Perturbationsof Muscle
Ecomplex (DForce/Area)/strain Eviscous/Eelastic
tan(phase angle)
28
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.

29
Next Step - Natural Musculo-skeletal Loading
Muscle
Axial Loading in Nature includes Muscle and
Skeletal Components
Natural Loading includes Perpendicular and Axial
Components
30
Experimental Setup
Tethered animal

• Leg impedance measurements
• - oscillation of leg at range of frequencies
  (2-25 Hz) and amplitudes (1-5 mm)
• Study of preflex
• - sudden perturbation
• time course of force development

Reordings of single leg movement and forces
31
Experimental Setup

• Tethered animal
• All legs on the ground
• Single leg oscillations
• High speed video of joint angles
• Force vector can be aligned

32
Leg Oscillation in Relaxed Cockroach
Forces per cycle are almost identical for the
first 2 seconds. No active response to leg
oscillations !!
33
Impedance Calculation
Whole Leg Oscillations
2
0
1
5
1
0
Impedance (mN/mm)
5
DF
0
-
5
-
1
0
Dl
-
1
5
-
2
0
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
2
-
0
.
1
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
Amplitude (mm)
Impedance DF/Dl
34
Effect of Oscillation Frequency
L
e
g

O
s
c
i
l
l
a
t
i
o
n
s
2
0
2
0

H
z

1
5
1
0

H
z

1
0
2

H
z

Impedance (mN/mm)
5
0
-
5
-
1
0
-
1
5
-
2
0
-
0
.
5
-
0
.
4
-
0
.
3
-
0
.
2
-
0
.
1
0
0
.
1
0
.
2
0
.
3
0
.
4
0
.
5
Amplitude (mm)
35
Single Leg Impedance
Impedance increases with frequency
7
/
2
7
/
0
0
Impedance (mN/mm)
Frequency (Hz)
36
Discoveries

• 1. Forces exerted on muscle lever (5-15 mN)
  during single leg oscillations are within range
  reported for single leg ground reaction forces
  (3-12 mN, Full et al 1991).
• 2. Small active response of the animal to the leg
  oscillation.
• 3. Whole leg impedance of relaxed cockroach
  increases with frequency.
• 4. Hind leg of relaxed cockroach functions as
  spring-damper system.

37
Future Experiments

• 1. Model passive whole leg. Determine effect of
  frequency and strain. Compare to muscle and
  perpendicular oscillations.
• 2. Determine the effect of active muscle.
  Stimulate and record EMG from particular muscles.
• 3. Study preflex and reflex components of force
  during sudden perturbations.

38
MURI Interactions
Rapid Prototyping
Stanford
Muscles and
Motor Control
Learning
Locomotion UC Berkeley
Johns Hopkins
MURI
Manipulation
Harvard
Sensors / MEMS
Stanford
39
Single Leg Forces
How are single legs loaded during perturbations?
A THREE-AXIS PIEZORESISTIVE MICROMACHINED FORCE
SENSOR FOR STUDYING COCKROACH BIOMECHANICS.
Michael S. Bartsch. Aaron Partridge, Beth L.
Pruitt, Robert J. Full, Thomas W. Kenny ASME
40
MURI Interactions
Rapid Prototyping
Stanford
Muscles and
Motor Control
Learning
Locomotion UC Berkeley
Johns Hopkins
MURI
Manipulation
Harvard
Sensors / MEMS
Stanford
41
Lower Level Control
aero- , hydro, terra-dynamic
Higher
Sensors
Environment
Centers
Open-loop
Mechanical
Feedforward
Behavior
System
Controller
(CPG)
(Actuators, limbs)
Feedback
Closed-loop
Controller
Adaptive
Sensors
Controller
42
Progress Report
Muscle and Artificial Muscle Impedance First
direct comparison of SRI Electroactive Polymers
(EAPs) to natural muscle.
1. Muscles have a broad range of potential
function. 2. Realized function in nature shows
multiple roles Muscle function cannot be
predicted from neural activity. Muscles
innervated by the same motor neuron do NOT
necessarily function similarly. Muscles of the
same anatomical group can have many similar
intrinsic muscle properties, but still function
differently. History-dependent properties may
play an important role in determining muscle
function. 3. Can not refute EAP as artificial
muscle EAP has more rapid kinetics than
muscle. EAP has a linear Force-Length curve as
does the operational portion of the curve in
muscle. EAP produced and absorbed energy. As in
muscle, EAPs only produce power over a particular
range of strains and stimulation phases. Work
per cycle lower than mean for muscle. Stress
higher and strain lower than mean for
muscle. Power output of EAP within range of
natural muscle.
43
Progress Report
Leg Impedance New analysis of insect leg
properties (Cutkosky Lab and PolyPEDAL Lab) 1.
Insect legs that exhibit viscoelasticity that can
be matched by polymer materials used in SDM. 2.
Developed a simple lumped parameter model to
characterize cockroach leg behavior in relaxation
experiments and a linear model for characterizing
leg response to sinusoidal excitations. 3.
Models fit results of experiments at low
frequencies and small displacements but not at
higher frequencies and displacements as nonlinear
effects become pronounced. At very low
frequencies dynamic tests on cockroach legs
indicate a higher loss modulus than that
predicted by a standard linear model. Next step
is to develop a new material constitutive law to
better simulate the viscoelastic behavior of the
leg in a wide frequency range. 4. New apparatus
designed to measure axial leg impedance is
functional. This apparatus loads the leg in a
manner more similar to that observed that in
running.
44
Effect of Step Length Increase
Passive resistance is significant in muscle 177c
Stimulated (Twitch)
(n 4)
Force increase (mN)
Relaxed
Step size ()
45
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)
tan(phase angle)
Frequency (Hz)
Frequency (Hz)
46
Effect of Length
Passive Muscle Impedance increases with
length Contribution viscous damping decreases
with length
47
Perturbation experiments
Impedance during workloop.
48
Multiple Muscle System
Anatomically similar muscles provide impedance
during different phases of the locomotion cycle!
Muscle strain ()
49
Impact on Deliverables
1. Energy storage 2. Reject perturbations 3.
Simplify control 4. Penetrate new environments 5.
Increase robustness
50
Approach
1. What is impedance in nature? 2. Impedance
matching 3. Learning and adapting impedance.