Comparison of the Lagrangian approach for modelling the heel-to-toe contact in passive dynamic walkers with the discrete pivot point method

Traditional biped walkers based on passive dynamic walking usually have flat or circular feet. This foot contact may be modelled with an effective rocker represented as a roll-over shape to describe the function of the knee-ankle-foot complex in human ambulation. Mahmoodi et al. [1] has modelled this roll-over shape as a discretized set of pivot points. In this paper, Lagrangian mechanics are used to formulate non-discrete ordinary differential equations for the stance phase that conserve mechanical energy. Qualitative insight can be gained by studying the bifurcation diagrams of gait descriptors such as average velocity, step period, mechanical energy and inter-leg angle for different gain and length values for the feet, as well as different mass and length ratios. The results from both approaches are compared and discussed. This research is not only useful for understanding the stability of bipedal walking, but also for the design of prosthetic feet.