The effect of noise on the dynamics of a 2-D walking model

Abstract

Walking models have been used to explore concepts such as energy, step variability, control strategies and redundancy in walking. A 2-D dynamic walking model was used to determine the levels of variability in gait while being perturbed. The perturbations were added in the form of randomly added noise applied at different magnitudes. The model was comprised of two equal length legs and masses at the feet and hips. The model walked on a flat surface and each step was initialed by an impulse at the swing leg. The magnitude of the impulse determined the size of the model's steps. In this study, the walker took steps with lengths that were than were analogous to humans. An attempt to offset the effect of the noise was made by adding a proportional controller to correct the errors of the applied impulse. The control equation was comprised of gain, A, and noise, [xi], term. The step length, time and speed were calculated to analyze how the model walks. It was hypothesized that the model would use a strategy similar to humans on a treadmill and follow a goal equivalent manifold. The manifold was all possible solutions of step length and step time for maintaining constant speed. Any fluctuations in step length and time would still result in constant speed. The results showed that the model's gait became more variable as noise was added. When the control was added through the gain being increased, the model steps became more variable. The model did not follow the same control strategy as humans and coordinate steps along the GEM. As the model began taking longer step lengths the step time decreased.