Optimization of energy and time determines dynamic speeds for human walking

Abstract

Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual's movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts speed vs. time trajectories with inverted U shapes. Model and human experiment (N=10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster due to energy-per-distance. Individual-dependent vigor is characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone has similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs predict transient, steady, and vigor-related aspects of walking.

A biomechanics dataset of healthy human walking at various speeds, step lengths and step widths

“…Further, it must be noted that because this dataset uses controlled, treadmill walking, its application should be limited to research questions regarding these applications. Considering biomechanical differences between treadmill and overground walking 14 as well as between steady and non-steady walking 15 , the dataset does not address changes in self-selected, spontaneous walking speeds during overground walking 16 .…”