H. Kazerooni Human Engineering Laboratory (HEL) University of California at Berkeley

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H. Kazerooni Human Engineering Laboratory (HEL) University of California at Berkeley

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H. Kazerooni Human Engineering Laboratory (HEL) University of California at Berkeley

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ONR Site VisitAugust 9, 2000

H. Kazerooni

Human Engineering Laboratory (HEL)

University of California at Berkeley

f

g

b

c

a

d

- One motor powers all legs

2

4

3

2

1

1

2

4

3

4

3

- Shape Deposition Modeling (SDM)
- Simple Spring Legs
Control system is embedded in hardware

(Elasticity, Damping, and Mass of Legs)

Trajectory of center of mass

- Inverse Pendulum Model
- Frequency of Walking (pendulum) α
Natural Frequency of Leg (spring)

- In fact, for cockroach,
Freq. of Walking ≈ fnof 3 legs / 3 ≈ 14Hz

Ground Reaction Force Control

The only external force on a walking machine is imparted by the ground.

Considering Newtonian Mechanics, zero Ground Reaction Forces lead to zero motion (f = m α)

Large Ground Reaction Forces lead to large acceleration and large speed

A leg during stance phase

Infinitely Rigid Ground

Ground Reaction forces = f (T1, T2)

A leg during swing phase

A leg during swing phase does

not contribute to motion of the

machine.

Zero Stiffness Ground

Ground Reaction forces = 0

A leg during stance phase

The fundamental method of creating locomotion for the walking machine is the generation of appropriate ground reaction forces on the machine leg that is in contact with the ground, not the leg which is swinging; in fact, the leg during the swing phase should not be powered to save energy.

Actual Ground

Ground Reaction Forces = f ( T1, T2 and K)

The Ground Reaction Forces are the “Actuators” of a Walking Machine

W

ηW

The Horizontal Ground Reaction

Forces are controlled to be larger than ηW

Inclined Maneuvers

ηW Cos () +W Sin ()

The Ground Reaction Forces must be controlled

to be larger than ηW Cos () +W Sin ()