Modelling the effect of 'heel to toe' roll-over contact on the walking dynamics of passive biped robots

The 'heel to toe' rolling contact has a great influence on the dynamics of biped robots. Here this contact is modelled using the roll-over shape defined in the local co-ordinate system aligned with the stance leg. The roll-over shape is characterised by six constants: forefoot, midfoot and hindfoot gains and length values. A piecewise parabolic polynomial constructed from these six values is able to match the realistic roll-over shape with continuous slope and variable curvature. The effect of these constants and the roll-over shape arc length has been studied on various gait descriptors such as average velocity, step period, inter-leg angle (and hence step length), mechanical energy. The bifurcation diagrams have been plotted for point feet and different gain values. The insight gained by studying the bifurcation diagrams for different gain and length values is not only useful in understanding the stability of the biped walking process but also in the design of prosthetic feet. The discovery of 'critical values' for the length and mass ratios for the inter-leg angle δ (and hence step length) bifurcation diagrams, or a 'critical value' for forefoot gain in the step period bifurcation diagram, is of particular interest as it would mean a constant step length or step period for a range of acceptable values of forefoot and hindfoot gains. The dependence of the horizontal roll-over shape length and hindfoot/forefoot gains on the actual stance leg angular velocity θ̇s and angular displacement (θs) values along with the corresponding existence of critical values has also been demonstrated.