Preserving the Planar Dynamics of a Compliant Bipedal Robot with a Yaw-Stabilizing Foot DesignAn HBS Thesis by Andy Abate

Ball Toe

Chatter

Point Contact

Stabilizing Foot

Revision

Testing

Compliance

Line Contact

Current Humanoids

Construction

Weight

Ground Clearance

Disturbance Force

Contact Stiction

Contact Stiffness

Future

Motivation Design Prototype Testing

Outline Enabling 3D Walking

Motivation:Humanoid Walking in 3D

Background:

• Humanoids picking up speed• General trend toward spring-mass running• Excellent machines, lots of promise• They all have point toes!

Motivation Design Prototype Testing

Raibert Hopper ARL Monopod

MABEL ATRIAS

Present1986 1997 1999 2008

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Spring-Mass Walking in 3D:

Motivation Design Prototype Testing

Dynamical template*

ATRIAS bipedon Planarizing boom

• Designed with a spring-mass template- Has very specific dynamics

• Matches human walking• Literal design means point-contact

- Okay on a boom, but bad for 3D

* Adapted from: W. J. Schwind and D. E. Koditschek, “Approximating the Stance Map of a 2-DOF Monoped Runner,” Journal of Nonlinear Science.

Two Instabilities at the Ground Interface:

Motivation Design Prototype Testing

3D space

Point contact

Yaw axis

Air Time

Touchdown Error

(2) Chatter

(1) Yaw Oscillation

≠

A Stabilizing Foot Design

Remove Yaw Instability Limit Chatter

Preserve Spring-Mass Dynamics

Minimal massFree pivot

Does not trip

• Passive• Does not affect COM trajectory

Yaw Stabilization: Only permit 2 degrees of freedom

Point: 3-DOF Line: 2-DOFPlane: 2-DOF

Motivation Design Prototype Testing

0 @ ground+ 2 mechanical

1 @ ground+ 1 mechanical

3 @ ground+ 0 mechanical

• Ball toes• Under-constrained

• Over-constrained footprint• Mechanical complexity

• Perfect compromise

NO CONTACT

Chatter Reduction:

Motivation Design Prototype Testing

Limits rebound

Interface Stiffness

Leg Stiffness

Leg Mass

Robot Mass

Ground Reaction Force

Interface Deflection

Stiff Rubber

Linear Spring

Progressive Spring

Oscillation

Prototype

Foot Pads:

• Cylinder → Linear Footprint• Compliant Sorbothane• Tear-resistant composite skin

Motivation Design Prototype Testing

3

4

51

2

Nylon

Sorbothane

Weave

Urethane

Epoxy

Support Structure: Aluminum arch supports the pads

Motivation Design Prototype Testing

Aluminum arch

Free pivot

Robot

Return Mechanism: Single DOF reeds to be reset after each step

RobotArch Restoring Torque

Leaf Spring

Motivation Design Prototype Testing

Adjustable Stiffness

Ankle Body: Pulling it all together

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Motivation Design Prototype Testing

Testing

280 g

Passed

0.33 N

29 N.m

250 N/mm

Weight

Ground Clearance

Disturbance Force

Contact Stiction

Contact Stiffness

Contact Stiction:

• Resists at least 29 N.m of torque• Limit cause by jig failure!

0 100 200 300 400 500 6000

5

10

15

20

25

30

Normal Force [N]

Stic

tion

Torq

ue [N

.m]

Loading

Incr

easi

ng T

orqu

e

Unloading

Peak Torque = 29 N.m

Motivation Design Prototype Testing

Jig axis

Force plate

Contact Stiffness:

Measured at 250 N/mmMuch higher than the 75 N/mm maximum

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Compression Force

Separation

Motivation Design Prototype Testing

Ground Clearance:

Reset mechanism prevents ground contact during swing phase

0 0.1 0.2 0.3 0.4 0.5−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

Dis

plac

emen

t [ra

d]

0 0.1 0.2 0.3 0.4 0.5−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1Foot System Characterization

Time [s]

0 0.1 0.2 0.3 0.4 0.5−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

Best FitExperimental Data

Damping Ratio = 0.1295Natural Frequency = 31.0055 [rad/s]

Damping Ratio = 0.1775Natural Frequency = 30.0589 [rad/s]

Damping Ratio = 0.1572Natural Frequency = 32.5143 [rad/s]

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

−0.5

0

0.5

1

x [m]

y [m

]

Ankle PositionToe PositionHeel Position

0 1 2 3 4 5 6−1

−0.5

0

0.5

1

Time [s]

Foot

Ang

le [r

ad]

0 1 2 3 4 5 6−10

−5

0

5

10

Foot

Spe

ed [r

ad/s

]

Motivation Design Prototype Testing

Disturbance:Reset mechanism does not affect COM trajectory

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Deflection Angle [rad]

Torq

ue [N

.m]

Torque−Deflection Curve Linear Fit, 0.488 N.m / rad

Motivation Design Prototype Testing

Max Torque: 0.33 N.mMax Lever Arm: 1 mMax Disturbance Force: 0.1 lbf << 150 lbf

Revision

Increased Compliance

ReducedWeight

Revision:

• Weight reduced from 280g to 120g• Modular fiberglass arch• Internalized reset mechanism

Motivation Design Prototype Testing

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Next

ATRIAS’s 3-Dimensional Debut:

Motivation Design Prototype Testing

Thanks!Questions?