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Research Papers

Passive Dynamic Biped Walking—Part II: Stability Analysis of the Passive Dynamic Gait

[+] Author and Article Information
Christine Q. Wu

Department of Mechanical Engineering,
University of Manitoba,
Winnipeg MB R3T 5V6, Canada

Difference between the next estimate and current estimate.

Normalized with the leg length, total mass, and average hip velocity.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received December 11, 2012; final manuscript received March 1, 2013; published online March 26, 2013. Assoc. Editor: Parviz Nikravesh.

J. Comput. Nonlinear Dynam 8(4), 041008 (Mar 26, 2013) (10 pages) Paper No: CND-12-1220; doi: 10.1115/1.4023933 History: Received December 11, 2012; Revised March 01, 2013

Passive dynamic walking is an excellent tool for evaluating biped stability measures, due to its simplicity, but an understanding of the stability, in the classical definition, is required. The focus of this paper is on analyzing the stability of the passive dynamic gait. The stability of the passive walking model, validated in Part I, was analyzed with Lyapunov exponents, and the geometry of the basin of attraction was determined. A novel method was created to determine the 2D projection of the basin of attraction of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of gait was examined. The angular momentum of the passive walker was not found to correlate to the stability of the gait.

Copyright © 2013 by ASME
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References

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Figures

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Fig. 2

Evolution of an initial (hyper)sphere of initial conditions

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Fig. 3

Effect of kv on Sv

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Fig. 4

Points of interest (POI) labeled on the θ-θ· phase portrait

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Fig. 5

Offset correction visualization

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Fig. 6

Finding the first point on the BoA edge

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Fig. 7

Finding the first edge on the BoA

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Fig. 8

Without the reverse protocol

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Fig. 9

Relative error between the current Lyapunov exponent λ(t) to the final Lyapunov exponent λ

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Fig. 10

BoA edge algorithm validation case: b/l = 0.35, POI 1

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Fig. 11

BoA for point of interest one

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Fig. 12

Visualization of the swing leg BoA abnormality

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Fig. 13

Area of the BoA swing leg

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Fig. 14

Area of the BoA stance leg

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Fig. 15

Torque and angular momentum versus the center of mass

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Fig. 16

Normalized torque and angular momentum versus the center of mass

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Fig. 17

Angular momentum of the walker about the center of mass over one step

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Fig. 18

Ground reaction torque over one step

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Fig. 19

BoA for point of interest one

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Fig. 20

BoA for point of interest two

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Fig. 21

BoA for point of interest three

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Fig. 22

BoA for point of interest four

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Fig. 23

BoA for point of interest five

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Fig. 24

BoA for point of interest six

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Fig. 25

BoA for point of interest seven

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Fig. 26

BoA for point of interest eight

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