IN-SILICO ASSESSMENT OF ORBITAL STABILITY ANALYSIS APPLIED TO WALKING

Federico Riva (1), Rita Stagni (1)

1. DEIS, Department of Electronics, Computer Sciences and Systems, University of

Bologna, Italy

Introduction

Orbital stability analysis is an approach to quantify

stability of periodic limit cycle systems; widely

applied to robotics, this technique has recently

gained interest as a method to quantify stability of

locomotion [Dingwell, 2007], but still the use of

this technique in the assessment of fall risk has

been deemed controversial [Hamacher, 2011]. A

possible cause of this controversy could lie in the

lack of a “standard” implementation of this

technique, and simulations represent an important

instrument to explore how implementation

differences affect the analysis. The aim of this

study was to explore how different state space

compositions affect kinematic orbital stability

analysis of a stable walking model and the

influence of simulated experimental noise on the

results.

Methods

A 2-dimensional, 5-link (trunk, thighs and shanks)

stable bipedal walking model was implemented

[Solomon, 2010]. Model orientation was described

by stance and swing knee angles, stance and swing

hip angles and upper body angle. Orbital stability

analysis was performed on two 2-dimensional state

spaces, composed by knee and hip joint

flexion/extension angles. Noisy signals were also

analysed. A simulated CAST protocol [Cappozzo,

1995] was implemented in the model; joint angles

were then obtained adding stereophotogrammetric

noise and anatomical landmarks misplacement

errors. Fundamental indicators of orbital stability

are maximum Floquet multipliers (maxFM), that

quantify how periodic systems respond to small

perturbations discretely from one cycle to the next.

If maxFM have magnitude < 1, perturbations tend

to shrink by the next repetition, and the system

remains stable. Mean values of maxFMs across the

gait cycle were calculated on increasing number of

steps (from 3 to 300).

Results

Mean values of maxFMs across the gait cycle for

non-noisy kinematic data (hip/knee angles) had

values close to 0.34, independently from the

number of cycles upon which the analysis was

conducted (Fig. 1). Values of maxFM calculated

upon state spaces composed by noisy kinematic

signals tend to gradually decrease towards zero

while the number of cycles increases.

Figure 1: Mean maxFM values calculated across

the gait cycle on kinematic data upon increasing

number of cycles, with their Standard Deviation

(Black: noisy data, Grey: non-noisy data). For

graphic convenience, results from 20 cycles on are

showed.

Discussion

Non-noisy signals analysis on both kinematic state

spaces (knee and hip joint angles) led to coherent

stability results (walking resulted to be stable,

maxFM < 1). A few number of cycles seem

sufficient to obtain a reliable result for maxFM.

State spaces composed by noisy kinematic signals

didn’t seem to show reliable stability results; noise

seems to overcome useful information. Further

studies are needed to determine if experimental

noise on kinematic variables can compromise

orbital stability results in experimental trials.

Acknowledgements

The authors gratefully thank Dr. Martijn Wisse for

References

Cappozzo et al, Clin Biomech 10(4);171-178, 1995.

Dingwell et al, J Biomech Eng 129(4):586-593,

2007.

Hamacher et al, J R Soc Interface 8(65):1682-1698,

2011.

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his contribution in the implementation of the model.

S226 Presentation 1180 − Topic 20. Gait and posture

Journal of Biomechanics 45(S1) ESB2012: 18th Congress of the European Society of Biomechanics