Optimum Push-off During Uneven Walking for Just-in-Time Strategy; Delayed Push-off Exertion is Mechanically Costly

It is shown that step mechanical work roughly describes walking energetics, and optimal walking economy is achieved by pre-emptive step work. We suggest this is also true for uneven walking. Using a simple powered walking model, we estimated the preferred pre-emptive push-offs to cover the entire step energy. The maximum push-off is exerted when the subsequent heel-strike dissipation is zero, setting an upper bound for step-up amplitude achievable with pre-emptive push-off. For instance, at a walking speed of 1.4 m {middle dot} s-1, the maximum step-up is 0.106 m. Conversely, for any step-up amplitude, there is a minimum walking speed. For a step-up height ({Delta}h) of 0.06 m, the minimum walking speed is 1.06 m {middle dot} s-1. The importance of pre-emptive push-off and optimal timing of push-off and collision is widely discussed. However, there are cases where this timing is undermined, such as during uneven walking, necessitating post-transition mechanical energy compensation. The ankle (via delayed push-off) or hip can provide mid-flight energy, but no mechanical determinant prefers one source over the other. Our modeling demonstrates that delayed push-off entails mechanical energy waste, likely converted to heat by stretching the stance leg. This stretch may also release energy stored during the heel-strike (e.g., in the Achilles tendon), exacerbating the required mechanical work performance in the subsequent step transition. Hence, we propose that during the double support phase, when the stance leg is switched, hip actuation becomes mechanically preferable. Physiological observations also support our proposition.