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SICB10 Talia Yuki Moore 1/7/2010
Adding Inertia and Mass to Test Stability Predictions in Rapid
Running Insects
Talia Yuki Moore*, Sam Burden, Shai Revzen, Robert Full
PolyPEDAL LabUniversity of California Berkeley
1
SICB10 Talia Yuki Moore 1/7/2010
(Gerald and Buff Corsi, Visuals Unlimited)
(Pauline Smith)
(Tim Flach Stone/Getty Images)
(Flagstaffotos)
Animals compensate for large changes in
mass and moment of
inertia.
Natural Changes in Moment of Inertia
2
SICB10 Talia Yuki Moore 1/7/2010
Differences in Body Mass & Form
3
Animals have evolved diverse and successful body forms that differ in mass
and moment of inertia.
(Aivar Mikko) (Sophia Moore)
(http://dcydiary.blogspot.com) (http://academic.ru) (John S. Reid)
SICB10 Talia Yuki Moore 1/7/2010
Lateral Leg Spring (LLS) Template
3 Legs Acting as
One
Animal
Schmitt & Holmes, (2000)
Bouncing Side to Side
SICB10 Talia Yuki Moore 1/7/2010
Model Parameters
β
k
m
d
Schmitt & Holmes (2000)
- leg stiffness
- leg length
- center of pressure position
- body mass
- inertia
- leg angle
k
L
d
m
I
β
SICB10 Talia Yuki Moore 1/7/2010
Input Parameters
β
k
Schmitt, Holmes, Garcia, Razo & Full (2001)
k = 2.25 Nm
β = 1 rad
I = 2.04 10-7 kgm2
L = 0.1 m
m = 0.0025 kg
SICB10 Talia Yuki Moore 1/7/2010
Model State Variables
Rotational velocity
Body orientation
Heading
v Velocity
Schmitt, Holmes, Garcia, Razo & Full (2002)
SICB10 Talia Yuki Moore 1/7/2010
Self-Stabilization
11
Passive, mechanical self-stabilizing with minimal neural feedback
Heading
Velocity
Orientation
Rotational Velocity
Schmitt, Holmes,Garcia, Razo & Full (2002)
SICB10 Talia Yuki Moore 1/7/2010
0.2 1 2 43 5
Perturbation remaining per
stride [Eigenvalue, ]
0.4
0.6
0.8
1.0
Vary Body Mass
Nondimensional Body Mass
Animal
More Stable
Less Stable
Schmitt, Holmes, Garcia, Razo & Full (2000)
Stability of Body Orientation &
Rotational Velocity to
Lateral Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Vary Leg Angle - Stride Length
Vary Leg Length- Sprawl
Vary Leg Stiffness
Perturbation remaining per
stride [Eigenvalue, ]
0.8 0.9 1 1.1 1.2 1.3Nondimensional Leg angle
Animal
0.20.40.60.81.0
0.005 0.01 0.015Nondimensional Leg length
AnimalPerturbation remaining per
stride [Eigenvalue, ]
0.2
0.4
0.60.8
1.0
0.2 0 1 32 4
Perturbation remaining per
stride [Eigenvalue, ] 0.4
0.60.81.0
Nondimensional Spring stiffness
Animal
Tuning for Self-Stabilization
Schmitt, Holmes, Garcia, Razo & Full (2000)
More Stable
Less Stable
More Stable
Less Stable
More Stable
Less Stable
β
SICB10 Talia Yuki Moore 1/7/2010
Perturbation remaining per
stride [Eigenvalue, ]
Moment of Inertia
0 0.5 1.51 2Nondimensional Moment of Inertia
Animal
More Stable
Less Stable
0.2
0.4
0.6
0.8
1.0Animal & Inertia
Hypothesis:A cockroach with added mass and increased moment of inertia will
recover from perturbations slower and be unstable.
14
Schmitt, Holmes, Garcia, Razo & Full (2000)
SICB10 Talia Yuki Moore 1/7/2010
Control InertiaAdded Mass 40% 90% 90%
Added Inertia 20% 30% 960%
Mass
Each cockroach was its own
control
Perturbation remaining per
stride [Eigenvalue, ]
0 0.5 1.51 2Non-Dimensional Moment of Inertia
More Stable
Less Stable
0.2
0.4
0.6
0.8
1.0
Control
Mass
Inertia
Changing Moment of Inertia & Mass
15
Treatment
SICB10 Talia Yuki Moore 1/7/2010
Rapid Impulse Perturbation Device
Evidence for Mechanical Feedback
16
Recovery begins <10ms after perturbation
Jindrich and Full (2002)Slowed 30X
Challenges fastest neural reflexes
SICB10 Talia Yuki Moore 1/7/2010
Platform accelerates laterally at 0.6±0.1 g in a
0.1 sec interval providing a 50±3 cm/sec specific
impulse, then maintains velocity.
Lateral Perturbation
17
Cockroach runs at: 31±6 cm/sec
Stride Frequency: 12.5±1.7 Hz
trackway
camera
diffusermirror
magnetic lock
animal motion
cart
cart motion
rail
pulley
mass
cable
elastic
ground
SICB10 Talia Yuki Moore 1/7/2010
Lateral Perturbation
Criteria for trial rejection: 1. >15° deviation in heading
pre-perturbation2. Contact with the cart sides3. >50% Change in forward
velocity pre-perturbation
Cart impulse
Equal and opposite impulse
on animal
Measured:1. Distal tarsal (foot) position2. Pitch, roll, yaw3. Forward, lateral, rotational
velocity4. Heading, body orientation
SICB10 Talia Yuki Moore 1/7/2010
Raw Data
Model
Residual
Phase
χ
χ
χ
Compare Response to Pre-Perturbation Behavior
21
Onset of Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Residual Orientation
Animals Recover Orientation
Inertia Changes Body Orientation Less
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Residual Forward Velocity
All Treatments Decrease Speed
Aft
Fore
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Carrier et al. 2001 J. Experimental Biology
Increase Moment of InertiaLimits Maneuverability
35% Decrease in Speed
Horizontal Plane Instability
Reject Lateral Leg Spring Prediction
Increased Moment of Inertia Treatment Recovers & Does
Not Lead to Instability
Limit ManeuverabilityDecrease Speed
SICB10 Talia Yuki Moore 1/7/2010
Residual Roll
25
Mass Rolls Most Animals Overcompensate in Recovery
Lean Into Impulse
Roll From Impulse
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Residual Pitch
26
Mass Pitches More than Inertia
Animals Remain Pitched Down in Recovery
Nose down
Nose up
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Residual Lateral Velocity
Inertia Lateral Velocity Changes Less
Animals Overcompensate & Move Into Perturbation
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Residual Lateral Tarsal Position
Inertia Recovery SlowerAnimals Overcompensate & Place Feet
as if to Resist Next Perturbation
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Feedback Response
Frequency Change
Neural FeedbackR
esid
ual P
hase
TimeTime
Tars
al F
ore-
Aft
Posi
tion
Mechanical FeedbackNo Frequency Change
Frequency Change
Revzen, Bishop-Moser, Spence, Full (2007)
Perturbation
Perturbation
Perturbation
Perturbation
Tars
al F
ore-
Aft
Posi
tion
Feedback - Mechanical, Neural or Both?
Time Time
Res
idua
l Pha
se
SICB10 Talia Yuki Moore 1/7/2010
No Frequency Change Supports Mechanical
Feedback
Residual Phase Response
Mechanical Feedback Followed by Neural Feedback to the Central Pattern Generator
Frequency Change Supports Neural
Feedback
Peak Perturbation
SICB10 Talia Yuki Moore 1/7/2010
Conclusions
1. Changes in body mass and form affect response to perturbations. Mechanical feedback important early in response.
2. Increased moment of inertia reduces and delays response to perturbation, but limits maneuverability.
3. Passive horizontal plane model (Lateral Leg Spring) is insufficient to explain response to lateral perturbations. Higher degree of freedom models needed.
32
SICB10 Talia Yuki Moore 1/7/2010
Three Dimensional Models
Spring-Loaded Inverted Pendulum (SLIP)
Lateral Leg Spring (LLS) Seipel 2005
Spring Loaded Inverted Pendulum (SLIP)
Lateral Leg Spring (LLS)
SICB10 Talia Yuki Moore 1/7/2010
Conclusions
4. Hexapods overcompensate in recovery perhaps providing greater stability to another perturbation from the same direction. Neural feedback to CPG may assist.
5. Placement of payload in legged robots can learn from nature.34
1. Changes in body mass and form affect response to perturbations. Mechanical feedback important early in response.
2. Increased moment of inertia reduces and delays response to perturbation, but limits maneuverability.
3. Passive horizontal plane model (Lateral Leg Spring) is insufficient to explain response to lateral perturbations. Higher degree of freedom models needed.