1. of the Simplest Walking Model
Basin of Attraction
of the Simplest Walking Model
A. L. Schwab1 and M. Wisse2
1Laboratory for Engineering Mechanics
2Delft Biped Laboratory
Delft University of Technology
The Netherlands
DETC’01 ASME 2001, Sep 9-12, Pittsburgh PA, 2001

2. Walking Robots Anthropomorphic Design Energy Efficient
Passive Dynamic Walking ( T. McGeer 1990 )

3. Passive Dynamic Walking
G.T.Fallis
Patent (1888)

4. Problem Mostly Falls Down Hard to Start (initial conditions)
Sensitive to Small Disturbances
Why?

5. Simplest Walking Model
Garcia, Chatterjee, Ruina and Coleman (1998)
Scaling with: M, l and g
Limit case: m/M
Leaves one free parameter: g

6. Walking Motion Walking Motion in Phase Plane Cyclic Motion if
Swing phase
Stance phase
Cyclic Motion if

7. Cyclic Motions How Stable ? Stable Cyclic Motions
Stability of Cyclic Motion Determined by Characteristic Multipliers |l|<1
How Stable ?

8. Basin of Attraction Failure Modes Fixed Point (Cyclic Motion):
Poincare Section
Fixed Point (Cyclic Motion):

9. Basin of Attraction
(continued)
Basin of Attraction, askew & enlarged

10. Towards Cyclic Motion A Number of Steps in the Basin of Attraction
x = Fixed Point
1 = Start

11. Effect of Slope
Basin of Attraction > Slope Angle g

12. How Stable? Basin of Attraction < > Stability Cyclic Motion
l Characteristic Multiplier

13. Conclusion Simplest Walking Model Very small Basin of Attraction
No Relation between Basin of Attraction and Cyclic Motion Stability l
Increase the Basin of Attraction ?