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Preserving the Planar Dynamics of a Compliant Bipedal Robot with a Yaw-Stabilizing Foot DesignAn HBS Thesis by Andy Abate
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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
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Motivation:Humanoid Walking in 3D
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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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N NS S
N NS
S
⌧
⌧
?
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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.
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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
≠
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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
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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
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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
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Prototype
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Foot Pads:
• Cylinder → Linear Footprint• Compliant Sorbothane• Tear-resistant composite skin
Motivation Design Prototype Testing
3
4
51
2
Nylon
Sorbothane
Weave
Urethane
Epoxy
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Support Structure: Aluminum arch supports the pads
Motivation Design Prototype Testing
Aluminum arch
Free pivot
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Robot
Return Mechanism: Single DOF reeds to be reset after each step
RobotArch Restoring Torque
Leaf Spring
Motivation Design Prototype Testing
Adjustable Stiffness
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Ankle Body: Pulling it all together
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Motivation Design Prototype Testing
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Testing
280 g
Passed
0.33 N
29 N.m
250 N/mm
Weight
Ground Clearance
Disturbance Force
Contact Stiction
Contact Stiffness
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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
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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
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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
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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
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Revision
Increased Compliance
ReducedWeight
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Revision:
• Weight reduced from 280g to 120g• Modular fiberglass arch• Internalized reset mechanism
Motivation Design Prototype Testing
N NS
S
⌧
N NS S
⌧
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Next
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ATRIAS’s 3-Dimensional Debut:
Motivation Design Prototype Testing
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Thanks!Questions?