1. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 H. Kazerooni Human Engineering Laboratory (HEL) University of California at Berkeley ONR Site Visit August 9, 2000

2. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Topics 1. Ground Reaction Force Control 2. Frequency Matching Control

4. EXAMPLE a b c d f g

5. Path Generation

6. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Power Terrain One motor powers all legs

7. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Flexible Feet Construction Shape Deposition Modeling (SDM) Simple Spring Legs Control system is embedded in hardware (Elasticity, Damping, and Mass of Legs) 2 34 1 2 3 4 12 3 4

8. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Frequency Matching Inverse Pendulum Model Frequency of Walking (pendulum) α Natural Frequency of Leg (spring) In fact, for cockroach, Freq. of Walking ≈ f n of 3 legs / 3 ≈ 14Hz Trajectory of center of mass

9. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Mechanical Walker

10. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000

11. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000

12. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000

13. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Ground Reaction Force Control The only external force on a walking machine is imparted by the ground. Large Ground Reaction Forces lead to large acceleration and large speed Considering Newtonian Mechanics, zero Ground Reaction Forces lead to zero motion (f = m α)

14. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Infinitely Rigid Ground Ground Reaction forces = f (T1, T2) A leg during stance phase

15. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Zero Stiffness Ground Ground Reaction forces = 0 A leg during swing phase A leg during swing phase does not contribute to motion of the machine.

16. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Actual Ground Ground Reaction Forces = f ( T1, T2 and K) 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.

17. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 The Ground Reaction Forces are the “Actuators” of a Walking Machine

18. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000

19. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000

20. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 W ηW The Horizontal Ground Reaction Forces are controlled to be larger than ηW

21. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000

22. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 Electronic Schematic

23. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000 ηW Cos (  ) +W Sin (  ) The Ground Reaction Forces must be controlled to be larger than ηW Cos (  ) +W Sin (  ) Inclined Maneuvers 

24. MURI Fabrication Biomimetic Robots - ONR Site Visit - August 9, 2000