Emergence of Gait in Legged Systems

1. Emergence of Gait in Legged Systems André Seyfarth ISB conference Cleveland, 2005

2. Emergence of Gait in Legged Systems André SeyfarthLocomotion Laboratory Friedrich-Schiller University, Jena

3. Arrival at Cleveland Jürgen Suzi Hartmut

4. Robots • Springs • Screws • Metal parts • Servos • Rubber Models • Springs • Joints • Segments • Muscles simple, fast, easy to understand

5. Central questions What are the common design and control principles of legged locomotion? Internal Leg Function Global Leg Function

6. Central questions What are the common design and control principles of legged locomotion? What are the movement primitives of legged locomotion? STABILITY MECHANICS CONTROL

7. Outline • Jumping for distance • Stable operation of a segmented leg • Generation of muscle activity • Stable running with elastic legs • From running to walking • Exploration of simple legged robots • Conclusions 1 2 3 4 5 6 7

8. 1Jumping for distance

9. Ground reaction force (N) time (ms) m1 Energetic losses may increase performance! Nonlinear spring-damper element k m2 Dynamics of the long jump Seyfarth et al. (1999) J. Biomech.

10. m1 Nonlinear spring-damper element k m2 Dynamics of the long jump Is this model able to predict jumping distance? Is this model able to predict maximum jumping distance? Seyfarth et al. (1999) J. Biomech.

11. eccentric operation Muscle operation in long jump Tendon compliance (SE) shifts eccentric muscle operation (CE) into midstance Seyfarth et al. (2000) J. Exp. Biol.

12. Take home message(long jump) • The dynamics of long jump can well be described by a simple two-mass model • Energetic losses due to impacts and eccentric muscle operation can improve jumping distance • Tendon complianceshifts eccentric muscle operation into midstance

13. 2Stable operation of a segmented leg

14. Control of a segmented leg Idea Global Leg Function Local Leg Function

15. Control of a segmented leg Idea

16. Control of a segmented leg Idea

17. 1 2 3 3b 3a Control of a segmented leg

18. + • Biarticular Structures (e.g. Muscles) • Geometric Constraints (e.g. Heel pad) Control of a segmented leg Solutions Seyfarth et al. (2001) Biol. Cybern.

19. Take home message(internal leg stability) • With three or more leg segments, internal stability becomes important • At certain leg length, symmetric joint flexion becomes unstable • Different safety strategies do exist to resolve the intrinsic stability problem

20. 3Generation of muscle activity

21. Generation of muscle activity Positive Force Feedback Geyer et al. (2003) Proc.Roy.Soc.B.

22. Generation of muscle activity

23. Take home message(positive force feedback) • In hopping or running tasks, the generation of extensor muscle activity could be facilitated by positive force feedback • This control regime imitates spring-like leg behavior and is robust with respect to environmental changes

24. 4Stable Running with elastic legs

25. fixed angle of attack fixed leg stiffness Spring Mass Running PERIODICITY SYMMETRY ELASTICITY Seyfarth et al. (2002) J. Biomechanics

26. RETRACTION Spring Mass Running Seyfarth et al. (2003) J. Exp. Biol.

27. Spring Mass Running Seyfarth & Geyer (2002) CLAWAR Meeting, Paris.

28. Take home message(spring mass running) • For a given leg stiffness and angle of attack, self-stable running can be found. • The stability of running is largely increased, if leg retraction is applied.

29. 5From Running to Walking

30. Spring Mass Walking Geyer et al. (2005) ISB Conference

31. FY FY stiffness k stiffness 0 stiffness k stiffness 0 YCOM YCOM SS DS stiffness k stiffness 2k stiffness k stiffness 2k mass m mass m/2 mass m mass m/2 Spring Mass Running &Walking RUNNING WALKING POSTER #197

32. Stable solutions E k 0 Spring Mass Walking

33. Ground Reaction Forces A B C Spring Mass Walking E=const.

34. Running Walking Walking andRunning withElastic Legs GAP Speed vX angle of attack 0 stiffness k

35. Take home message(spring mass walking) • In bipedal spring-mass model, self-stable walking can be found. • The model predicts the experimentally observed force pattern. • Running and walking are behaviors of one and the same system.

36. 6Exploration of simple legged robots

37. Our Approach • Experiments • Theory • Simulations • Robotics

38. Experiments

39. Robotics

40. Hip Control

41. CPG Experimental Robotics

42. human Comparison with Biology robot

43. Human Walking & Running walking running

44. Take-home message(hip control) • Sinusoidal hip oscillations applied to an elastic leg may result in stable hopping patterns • Elastic joints are important to master impacts and to keep control simple.

45. Movement Direction ?

46. Hopping direction? High Speed200Hz Rummel et al. (2005) ISB Conference

47. Frequency Bias Angle ?

48. CPG Hopping direction? v

49. CPG FLEG M = c (0 – ) Influence of Hip Retraction v

50. Take-home message(movement direction) Leg segmentation and motor frequency defines preferred locomotion direction. Leg compliance supported by the hip action Leg stiffness supported by the hip action