Figure 2. Model of dynamic walking over a single Up- (or Down-) step.

(a) Model behaves like an inverted pendulum. Momentum and speed fluctuate in each step (numbered ${\displaystyle i}$), and are particularly disrupted by an uneven step (at ${\displaystyle i=0}$). (b) Dynamic walking model has a point mass ${\displaystyle M}$ at pelvis, supported by an inverted pendulum stance leg (massless, length ${\displaystyle L}$, gravitational acceleration ${\displaystyle g}$, fixed or constrained step length ${\displaystyle S}$ and inter-leg angle ${\displaystyle 2\alpha }$). (c) Level nominal walking has discrete step-to-step transition where COM velocity (dark arrow) is redirected from forward-and-downward to forward-and-upward by active, impulsive trailing leg push-off (PO), immediately followed by an inelastic, impulsive, leading leg collision (CO). Both PO and CO are directed along the corresponding leg. (d, e) The model walks Up or Down a step by modulating the sequence of discrete push-offs surrounding and including the uneven step. The model’s compensatory response is therefore summarized as a time-varying trajectory of speeds ${\displaystyle v_i}$, discretely sampled once per step ${\displaystyle i}$.