skdh.gait.StepLengthModel2

class skdh.gait.StepLengthModel2

The distance traveled during a step (heel-strike to opposite foot heel-strike). A basic asymmetry measure is also computed as the difference between sequential step lengths of opposite feet.

Methods

predict(*, fs, leg_length, gait, gait_aux)

Predict the gait event-level endpoint

Notes

The step length for model 2 is computed using the double inverted pendulum model from [1] per

\[L_{step} = 2 \sqrt{2l_{leg}h - h^2} + 2\sqrt{2l'h' - h'^2}\]

where \(L_{step}\) is the step length, \(l_{leg}\) is the leg length, \(h\) is the center of mass (COM) change in height during the single support phase of a step, \(l'\) is the double support pendulum length, and \(h'\) is the change in height of the COM during the initial double support phase of a step.

However, now because we don’t have an exact measurement of \(l'\), we have to estimate it. From [2], the actual estimation would rely on the distance covered during initial double support (ids) and single support (ss) phases, per

\[\frac{L_{ids}}{L_{ss}} = \frac{l'}{l_{leg}}\]

However, since the distances are what we are trying to estimate, we have to approximate this. The most obvious would be to see if the ratio of time in ids and ss would work:

\[\frac{T_{ids}}{T_{ss}} \approx \frac{l'}{l_{leg}}\]

And from experimental results, this approximation is close, but needs to be scaled slightly on a quadratic:

\[1.12 \left(\frac{T_{ids}}{T_{ss}}\right)^2 + 0.547\frac{T_{ids}}{T_{ss}} + 0.066\]

References

[1]

W. Zijlstra and A. L. Hof, “Assessment of spatio-temporal gait parameters from trunk accelerations during human walking,” Gait & Posture, vol. 18, no. 2, pp. 1–10, Oct. 2003, doi: 10.1016/S0966-6362(02)00190-X.

[2]

W. Zijlstra and A. L. Hof, “Displacement of the pelvis during human walking: experimental data and model predictions,” Gait & Posture, vol. 6, no. 3, pp. 249–262, Dec. 1997, doi: 10.1016/S0966-6362(97)00021-0.