Comparison of point foot, collisional and smooth rolling contact models on the bifurcations and stability of bipedal walking

Abstract

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. has represented this rollover shape as a polygon with a discretised set of collisions. In this paper point foot, collisional and smooth rolling contact models are compared. An approach based on the Lagrangian mechanics is used to formulate the equations for the swing phase that conserves mechanical energy. Qualitative insight can be gained by studying the bifurcation diagrams of gait descriptors such as average velocity, step period, mechanical energy and interleg angle for different gain and length values for the feet, as well as different mass and length ratios. The results from the three approaches are compared and discussed. In the case of a rolling disk, the collisional contact model gives a negligible energy loss; incorporated into the double inverted pendulum system, however, reveals much greater errors. This research is not only useful for understanding the stability of bipedal walking, but also for the design of rehabilitative devices such as prosthetic feet and orthoses.