SICB10 Talia Yuki Moore 1/7/2010 Adding Inertia and Mass to Test Stability Predictions in Rapid...

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

[email protected]

1


(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


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)


Different View of Stability

Sagittal Plane

Horizontal Plane


Instability in the Horizontal Plane

5


Instability in the Horizontal Plane

6


Lateral Leg Spring (LLS) Template

3 Legs Acting as

One

Animal

Schmitt & Holmes, (2000)

Bouncing Side to Side


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


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


Model State Variables

Rotational velocity

Body orientation

Heading

v Velocity



Self-Stabilization

11

Passive, mechanical self-stabilizing with minimal neural feedback

Heading

Velocity

Orientation

Rotational Velocity

Schmitt, Holmes,Garcia, Razo & Full (2002)


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


Stability of Body Orientation &

Rotational Velocity to

Lateral Perturbation


Vary Leg Angle - Stride Length

Vary Leg Length- Sprawl

Vary Leg Stiffness



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


0.2

0.4

0.60.8

1.0

0.2 0 1 32 4


stride [Eigenvalue, ] 0.4

0.60.81.0

Nondimensional Spring stiffness

Animal

Tuning for Self-Stabilization


More Stable

Less Stable

More Stable

Less Stable

More Stable

Less Stable

β




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.

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Control InertiaAdded Mass 40% 90% 90%

Added Inertia 20% 30% 960%

Mass

Each cockroach was its own

control



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

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Treatment


Rapid Impulse Perturbation Device

Evidence for Mechanical Feedback

16

Recovery begins <10ms after perturbation

Jindrich and Full (2002)Slowed 30X

Challenges fastest neural reflexes


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.


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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



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


Real time

Lateral Perturbation Experiment

19


Slowed 40xLeg and Body Tracking

20

Cart Velocity


Raw Data

Model

Residual

Phase

χ

χ

χ

Compare Response to Pre-Perturbation Behavior

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Onset of Perturbation


Residual Orientation

Animals Recover Orientation

Inertia Changes Body Orientation Less

Peak Perturbation


Residual Forward Velocity

All Treatments Decrease Speed

Aft

Fore

Peak Perturbation


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


Residual Roll

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Mass Rolls Most Animals Overcompensate in Recovery

Lean Into Impulse

Roll From Impulse

Peak Perturbation


Residual Pitch

26

Mass Pitches More than Inertia

Animals Remain Pitched Down in Recovery

Nose down

Nose up

Peak Perturbation


Residual Lateral Velocity

Inertia Lateral Velocity Changes Less

Animals Overcompensate & Move Into Perturbation

Peak Perturbation


Residual Lateral Tarsal Position

Inertia Recovery SlowerAnimals Overcompensate & Place Feet

as if to Resist Next Perturbation

Peak Perturbation


Overcompensation in Humans

Welch and Ting (2009)


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


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


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.

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Three Dimensional Models

Spring-Loaded Inverted Pendulum (SLIP)

Lateral Leg Spring (LLS) Seipel 2005

Spring Loaded Inverted Pendulum (SLIP)

Lateral Leg Spring (LLS)


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.


Guidance, Input, and Advice:Berkeley Biomechanics GroupProf. Robert FullPolyPEDAL Lab

Think Tanks,Matlab Wizards:Sam BurdenShai Revzen

Tarsus Trackers:Debbie LiBrian McRae

Cockroach Wrangler:Jessie Ding

Acknowledgements

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SICB10 Talia Yuki Moore 1/7/2010 Adding Inertia and Mass to Test Stability Predictions in Rapid...

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