A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait

Whether humans minimize metabolic energy in gait is unknown. Gradient-based optimization could be used to predict gait without using walking data but requires a twice differentiable metabolic energy model. Therefore, the metabolic energy model of Umberger et al. (2003) was adapted to be twice differentiable. Predictive simulations of a reaching task and gait were solved using this continuous model and by minimizing effort. The reaching task simulation showed that energy minimization predicts unrealistic movements when compared to effort minimization. The predictive gait simulations showed that objectives other than metabolic energy are also important in gait.

人类行走时是否以代谢能量最小化为目标，目前尚无定论。基于梯度的优化方法可在无需采集步行数据的前提下预测步态，但需要构建二阶可微的代谢能量模型。为此，本研究对Umberger等人2003年提出的代谢能量模型进行适配改造，使其满足二阶可微的要求。基于该连续模型，通过最小化运动代价的方式，本研究完成了伸手任务与步态的预测仿真优化求解。伸手任务的仿真结果显示，相较于以运动代价最小化为目标的预测结果，仅以代谢能量最小化为目标会得到不符合生物力学实际的运动轨迹。步态预测仿真结果则表明，除代谢能量最小化目标外，其他优化目标在步态规划中同样具有重要意义。