A template for the exploration of chaotic locomotive patterns

Inverted pendulum and spring-mass models have been successfully used to explore the dynamics of the lower extremity for animal and human locomotion. These models have been classified as templates that describe the biomechanics of locomotion. A template is a simple model with all the joint complexities, muscles and neurons of the locomotor system removed. Such templates relate well to the observed locomotive patterns and provide reference points for the development of more elaborate dynamical systems. In this investigation, we explored if a passive dynamic double pendulum walking model, that walks down a slightly sloped surface (γ<0.0189 rad), can be used as a template for exploring chaotic locomotion. Simulations of the model indicated that as γ was increased, a cascade of bifurcations were present in the model's locomotive pattern that lead to a chaotic attractor. Positive Lyapunov exponents were present from 0.01839 rad <γ<0.0189 rad (Lyapunov exponent range=+0.002 to +0.158). Hurst exponents for the respective γ confirmed the presence of chaos in the model's locomotive pattern. These results provide evidence that a passive dynamic double pendulum walking model can be used as a template for exploring the biomechanical control parameters responsible for chaos in human locomotion.