Data from: Do humans optimally exploit redundancy to control step variability in walking?

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.

学界普遍认为，人类与动物在行走时会尽可能降低能量消耗（energetic cost）。这类原则虽能预测行走的平均行为，却无法解释行走过程中出现的变异性。为实现稳健的运动表现，行走动作需在每一步都进行适配，而非仅在整体层面调整。为此，我们提出了一套分析框架，可调和最优性、冗余性与随机性之间的矛盾。针对人类跑步机行走（treadmill walking）场景，我们定义了一个目标函数，以精确数学形式界定了一种可行的控制策略：在每一步都保持恒定的行进速度。我们记录了健康受试者在五种不同速度下行走的步幅时长（stride times）与步幅长度（stride lengths）。基于指定的目标函数，我们可将步间变异分解为若干新的步态变量（gait variables），这些变量与实现上述假设策略直接相关。受试者在与目标策略直接相关的步态波动上表现出显著降低的变异性，而在与目标无关的波动上则呈现出更高的变异性。更关键的是，人类会在每一步即时修正与目标相关的偏差，却允许与目标无关的偏差在多步中持续存在。为证明这并非受试者唯一可行的成功完成任务的策略，我们构建了三组替代数据集。每组数据集均对应一个特定的备选假设，即受试者采用了不涉及上述目标函数的其他控制策略。结果显示，人类并未采用任何这些可行的备选策略。最后，基于最小干预原则（Minimum Intervention Principle），我们开发了一系列描述行走步间变异性的随机控制模型（stochastic control models）。研究表明，健康人类并非严格意义上的“最优”，反而会在每一步对行进速度的微小偏差进行略微过度的修正。我们的研究揭示了调控人类行走步间波动的全新支配原则：该原则独立于降低能量消耗的机制，但与之并行运作。由此可见，人类会利用任务冗余性实现稳健的运动控制，在降低运动能耗的同时，保留潜在有益的运动变异性。