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

1. ONR Site VisitAugust 9, 2000 H. Kazerooni Human Engineering Laboratory (HEL) University of California at Berkeley

2. Topics1. Ground Reaction Force Control2. Frequency Matching Control

4. EXAMPLE f g b c a d

5. Path Generation

6. Power Terrain • One motor powers all legs

7. 2 4 3 2 1 1 2 4 3 4 3 Flexible Feet Construction • Shape Deposition Modeling (SDM) • Simple Spring Legs Control system is embedded in hardware (Elasticity, Damping, and Mass of Legs)

8. Trajectory of center of mass Frequency Matching • 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

9. Mechanical Walker

13. 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

14. A leg during stance phase Infinitely Rigid Ground Ground Reaction forces = f (T1, T2)

15. 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

16. 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)

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

20. W ηW The Horizontal Ground Reaction Forces are controlled to be larger than ηW

22. Electronic Schematic

23. Inclined Maneuvers ηW Cos () +W Sin ()  The Ground Reaction Forces must be controlled to be larger than ηW Cos () +W Sin ()