Department of Kinesiology, University of Texas, Austin, Texas, United States of America.
PLoS Comput Biol. 2010 Jul 15;6(7):e1000856. doi: 10.1371/journal.pcbi.1000856.
It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely "optimal," but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability.
人们普遍认为，人类和动物在行走时会将能量消耗最小化。虽然这些原则可以预测平均行为，但它们并不能解释行走中观察到的可变性。为了稳健的表现，行走运动必须在每一步都进行适应，而不仅仅是平均水平。在这里，我们提出了一个分析框架，该框架调和了最优性、冗余性和随机性问题。对于人类在跑步机上的行走，我们定义了一个目标函数，以对一种可能的控制策略进行精确的数学定义：保持每步的速度恒定。我们记录了健康受试者在五种速度下行走时的步时和步长。指定的目标函数将步与步之间的变化分解为与实现假设策略明确相关的新步态变量。受试者在与实现该策略直接相关的目标相关的步态波动方面表现出大大降低的可变性，但在与目标无关的波动方面则表现出更大的可变性。更重要的是，人类会立即在每个连续的步伐中纠正与目标相关的偏差，同时允许与目标无关的偏差在多个步伐中持续存在。为了证明这不是人们成功完成任务的唯一策略，我们创建了三个替代数据集。每个数据集都测试了一个特定的替代假设，即受试者使用了一种与假设的目标函数没有任何关系的不同策略。人类没有采用任何这些可行的替代策略。最后，我们根据最小干预原则，为行走的步与步之间的可变性开发了一系列随机控制模型。我们证明，健康的人类并不是完全“最优”的，而是在每一步都略微过度纠正行走速度的小偏差。我们的结果揭示了一种新的调节原则，用于调节人类行走中的步与步之间的波动，该原则独立于但平行于最小化能量消耗。因此，人类利用任务冗余来实现稳健的控制，同时最小化努力并允许潜在有益的运动可变性。
