The gait sensitivity norm in human walking 1
2
2
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Sjoerd M. Bruijn , Martijn Wisse , Eras Draaijers , Jaap H. van Dieën , Onno G. Meijer & Peter J. Beek
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Research Institute MOVE, Faculty of Human Movement Sciences, VU University Amsterdam, The Netherlands 2 Mechanical Engineering, Delft University of Technology, The Netherlands
Gait sensitivity norm
Results
Stability is a main boundary condition of legged locomotion. Quantifying stability in human walking has proven rather complicated. The recently developed Gait Sensitivity Norm (Hobbelen & Wisse, 2007) predicts stability in Passive Dynamic Walkers, but it remains to be investigated whether it can be applied to quantify stability in human walking. The gait sensitivity norm is calculated as:
Steptime as gait indicator Perturbationsize and GSN (step time)
0.35
Walking speed and GSN (Step time)
0.08 2 km/h 4 km/h 6 km/h
0.3
0.07 0.06
0.25
2
1 = e0
q
∞
2
* g i − g ∑∑ ( k ( ) (i ))
GSN step time
∂g ∂e
GSN step time
0.05 0.2
0.15
i =1 k = 0
0.1
Where e are disturbances, and g gait indicators. A meaningful selection of e and g is crucial for the success of the gait sensitivity norm.
0.03 0.02
0.05
0.01
0
0 50
In the current experiment, we tested the gait sensitivity norm on human walking. e was chosen as a lateral perturbation, while we were searching for a g that remained constant with varying perturbation sizes (note that this is a necessity for the gait sensitivity norm to contain any useful information), while still showing an effect of walking speed.
0.04
100
150 force [N]
200
250
300
2
4 Speed (km/h)
6
We found no significant effect of perturbation size (maximum force during the perturbation) nor walking speed on the gait sensitivity norm using steptime as a gait indicator. However, steptime may not be an adequate gait indicator for lateral perturbations, as it does not seem to be ”directly related to failure” after such a perturbation.
COM as gait indicator
Methods
5
x 10
-3
Perturbationsize and GSN (COM position)
4 2 km/h 4 km/h 6 km/h
4.5
x 10
-3
Walking speed and GSN (COM)
3.5
4 3 3.5
We tested 1 subject using different perturbation sizes, at 3 different walking speeds. At each speed, the subject performed 5 minutes of steady state walking, followed by 5 minutes during which perturbations were applied.
2.5 GSN COM
GSN COM
3 2.5 2
2 1.5
1.5 1 1 0.5
0.5
0
0 50
100
150 force [N]
200
250
300
2
4 Speed (km/h)
6
When using COM position as gait indicator, we found no significant effects of perturbation size, but a significant effect of walking speed, indicating that walking faster is more stable. Subject during a perturbation. Perturbations were timed to occur during the reversal of side to side trunk movement. Full body 3D Kinematics were recorded using Optotrak, and perturbation forces were sampled using 1 dimensional force transducers.
0.35 Marker 1 Marker 2 Marker 3
Marker position (m)
0.3 0.25 0.2 0.15 0.1 0.05 0 -0.05 0
5
10
15 20 Time (s)
25
30
35
Example of thorax marker time series during two perturbations.
Gait indicators chosen were steptime and position of centre of mass (COM) with respect to the feet. Future analysis will also use other gait indicators, such as the extrapolated centre of mass measures (Hof et al., 2006).
Our preliminary analysis showed that in human walking reactions to perturbations scale with perturbation size, as was reported in passive walkers. Thus, the gait sensitivity norm may thus be a usefull measure. Moreover, the effect of walking speed that we found agree with observations from robot experiments (Hobbelen, 2008). It should be kept in mind that humans have the ability to change their movement strategy after a sudden perturbation of walking, possibly making the gait sensitivity norm only useful to predict how stable subjects are in terms of their steady state walking pattern, without quantifying how well they are in performing other compensatory behavior after a perturbation. This would however still give an indication about how often this compensatory behavior needs to be employed.
1
0.5
0
1 0.8 0.6 0.4
-0.5
Literature
0.2
0.8
0
0.6
-0.2
0.4 0.2
-0.4
0
-0.6
-0.2 -0.4 -0.6
-0.8
Stick figure of a subject during a perturbation. Blue line indicates the force.
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Conclusion & Discussion
Hobbelen, D. G. E. and M. Wisse (2007). "A disturbance rejection measure for limit cycle walkers: The Gait Sensitivity Norm." IEEE Transactions on Robotics 23, 1213-1224. Hobbelen, D.G.E.(2008) "Limit Cycle Walking", PhD Thesis, Delft University of Technology, ISBN 978-90-9023121-1. Hof, A. L., Gazendam, M. G. and Sinke, W. E. (2005) “The condition for dynamic stability.” Journal of Biomechanics. 38, 1-8.
