Modeling of longitudinal human walking force using self-sustained oscillator

The paper proposes a self-sustained single-degree-of-freedom oscillator to accurately generate the longitudinal contact force between a pedestrian's feet and the supporting flat rigid surface. The model is motivated from the self-sustained nature of pedestrian walking, i.e. a pedestrian produces the required internal energy to maintain a repetitive body motion. It is derived by adding two nonlinear terms to the conventional Rayleigh oscillator to yield odd as well as even harmonics, as observed in experimentally recorded longitudinal force data. For the dynamic analysis of the oscillator, two methods are adopted: the energy balance method and the Lindstedt-Poincare perturbation technique. Moreover, the least-squares identification procedure is used to identify values of the oscillator parameters from the force records of 12 different pedestrians walking on an instrumented treadmill at 10 walking speeds. The results generated by the proposed oscillator agree well with the experimental data.