Optimum Push-off for Uneven Walking Based on the Just-in-Time Strategy: Walking with Interrupted Push-Off is Mechanically Costly.

Using a powered simple walking model (point mass with rigid massless legs), the optimal analytical push-off was derived based on walking speed and step elevation changes. It was observed that higher speeds increased the available push-off to attain greater step-up e.g., a walker at 1.4 m/s could manage a step-up amplitude of ∆h = 0.106 m with a push-off only. Step-up amplitude also required a minimum walking speed for the required push-off. When post step transition energy compensation was necessary, delayed push-off exerted along the trailing leg led to some wasted work. Walking over smooth surfaces, the delayed push-off cost was up to 7.5 times higher than the optimal push-off, whereas hip-driven compensation was lower at 3.2 times the optimal work. A similar pattern was also observed for step-ups. Our simulation results match young adult walking when terrain view was unrestricted. We utilized available empirical data to quantify the incremental energetic cost of disrupted push-off. It showed that the frequency and post step transition compensation costs were comparable. As step length further decreased, the cost of post step transition compensation rose more rapidly, possibly defining a lower limit for step length. The post step transition compensation rose by 0.18 W/kg/%∆Hz in young adults and 0.2 W/kg/%∆Hz in older adults. Additionally, visual constraints amplified the cost by 0.05 W/kg/%∆Hz.