v

Dynamic Robotics Lab

Enabling Real-World Locomotion for the ATRIAS Biped:A Passive, Naturally Stabilizing Foot DesignA Thesis by Andy Abate, advised by Dr. Jonathan Hurst, MIME

College of Engineering

N NS

S

⌧

N NS S

⌧

The ATRIAS Humanoid

ATRIAS stands for “Assume The Robot Is A Sphere,” describing the key design goal: having the robot behave like a spring-loaded, inverted pendulum (SLIP). This concept is what makes ATRIAS relatively agile compared to other walking robots, such as Honda’s ASIMO.

X

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

� ��� � ��� � ��� ��

���

���

���

���

���

���

���

'LVSODFHPHQW�>PP@

)RUFH�>1@

�

�)RUFHí'LVSODFHPHQW�6DPSOHV/LQHDU�)LW������1�PP�

Off-Boom Operation A Stabilizing Foot

The spring-loaded, inverted pendulum (SLIP) is a biologically-inspired template model which can accurately describe walking and running in humans. SLIP has many valuable features, so ATRIAS reaps the same benefits:• Self-stable under disturbances (like

changing ground height or composition) without requiring a complicated feedback and control system.

• Naturally energy-conservative, having a spring to cycle gait energy, and zero impact losses.

Runner with SLIP model, adapted from [1]

ATRIAS on the planarizing boom

Revised Foot

When taken off the support boom, ATRIAS has a yaw instability which leads it to spin like a top around a single contact point.

• Lightweight• Senses ground contact• Compliant to reduce chatter• Removes yaw degree of freedom• Return mechanism resets after each cycle

Need for a Foot

References1. W. J. Schwind and D. E. Koditschek, “Approximating the Stance

Map of a 2-DOF Monoped Runner,” Journal of Nonlinear Science, vol. 10, no. 5, pp. 533–568, 2000.

2. R. M. Alexander and M. B. Bennett, “Mechanical properties and function of the paw pads of some mammals,” Journal of Zoology, vol. 209, no. 3, pp. 405–419, 1986.

A foot is necessary to stabilize ATRIAS when it is ultimately taken outside the laboratory. It will need to carefully preserve the existing favorable dynamics of ATRIAS while removing the spin instability.Soft foot pads prevent harmful “chattering” of the foot on impact, where ground contact is repeatedly broken and re-established.

Traction testing is performed using a force plate and a jig which restricts the foot to translation and rotation in the vertical direction only. The prototype has a measured peak stiction torque of 29 N.m, more than enough to stabilize ATRIAS.

[2] suggests that the foot stiffness should be no more than five times the leg stiffness to prevent chatter.ATRIAS leg stiffness: 15 N/mmMax foot stiffness: 15x5 = 75 N/mmMeasured stiffness: 250 N/mm - Needs more compliance!

Impulse and step responses of the return mechanism characterize the oscillation of the foot. A simulation of the foot’s behavior under a real ATRIAS gait shows the mechanism to be very effective at preventing ground contact during swing phase.

Foot Design Requirements

The revised foot design includes non-laminated layers of fiberglass composite to increase compliance. This allows a high degree of modularity in the number of layers and what materials are used.Friction between the sliding layers has a damping effect, further reducing chatter.

Additionally, a magnetic return mechanism is designed to be fully enclosed in the foot, preventing damage and ensuring operation in uncontrolled environments.

N NS

S

⌧

N NS S

⌧An ankle and a linear footprint remove the yaw instability without affecting the behavior of ATRIAS. A spring return is used to reset the foot after each step.

Magnetic return mechanism?

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]

� � � � � �

�

���

� �

��

���� ����������� ������������ ��������

y [m]

x [m]

Ret

urn

Mec

hani

smG

roun

d C

lear

ance

Testing

Spring return

Compliant Sorbothane foot pads

Contact sensor

Fiberglass arch

Robot

Strong rubber pads

Foot rotation induces a restoring torque T

Impulse Response Impulse Response

Step Response

The SLIP Model