[论文解读] On the Principled Description of Human Movements

Stuart Hagler|arXiv (Cornell University)|Jan 1, 2015

Motor Control and Adaptation参考文献 21被引用 5

一句话总结

本文提出了一种基于最小化 jerk 的人类运动原理性最优控制模型，采用类似于分析力学的数学形式。该模型推导出一个类似于经典力学中能量的运动常数，通过鼠标追踪和手指敲击数据验证了模型，恢复了 Fitts 法则，并展示了震颤样振荡如何从 jerk 的不连续性中自然产生。

ABSTRACT

While the use of technology to provide accurate and objective measurements of human movement performance is presently an area of great interest, efforts to quantify the performance of movement are hampered by the lack of a principled model that describes how a subject goes about making a movement. We put forward a principled mathematical formalism that describes human movements using an optimal control model in which the subject controls the jerk of the movement. We construct the formalism by assuming that the movement a subject chooses to make is better than the alternatives. We quantify the relative quality of movements mathematically by specifying a cost functional that assigns a numerical value to every possible movement; the subject makes the movement that minimizes the cost functional. We develop the mathematical structure of movements that minimize a cost functional, and observe that this development parallels the development of analytical mechanics from the Principle of Least Action. We derive a constant of the motion for human movements that plays a role that is analogous to the role that the energy plays in classical mechanics. We apply the formalism to the description of two movements: (1) rapid, targeted movements of a computer mouse, and (2) finger-tapping, and show that the constant of the motion that we have derived provides a useful value with which we can characterize the performance of the movements. In the case of rapid, targeted movements of a computer mouse, we show how the model of human movement that we have developed can be made to agree with Fitts' law, and we show how Fitts' law is related to the constant of the motion that we have derived. We finally show that solutions exist within the model of human movements that exhibit an oscillatory character reminiscent of tremor.

研究动机与目标

• 开发一种基于最优控制的原理性数学形式，用于描述人类运动。
• 将人类运动建模为基于 jerk 控制的成本泛函最小化。
• 在运动模型中推导出一个类似于经典力学中能量的守恒量。
• 使用来自计算机鼠标操作和手指敲击的实验数据验证该模型。
• 解释震颤样振荡如何从 jerk 的不连续性中自然产生。

提出的方法

• 基于 jerk 的平方积分构建成本泛函，以建模最优人类运动。
• 应用欧拉-拉格朗日方程与哈密顿力学，从成本泛函推导运动方程。
• 在系统中识别出一个守恒量，其作用类似于经典力学中的能量。
• 采用成本泛函的二次形式以简化分析，并推导出闭式解。
• 将震颤建模为由 jerk 不连续性引发的振荡解，对应于加速度的尖点。
• 通过展示运动时间与距离如何根据推导出的守恒量缩放，将模型与 Fitts 法则关联起来。

实验结果

研究问题

• RQ1 如何通过基于 jerk 最小化的最优控制模型，形式化描述人类运动？
• RQ2 基于 jerk 的成本泛函最小化所得到的运动解具有怎样的数学结构？
• RQ3 所推导出的守恒量与经典力学中的能量及运动表现之间有何关系？
• RQ4 该模型能否在类似鼠标控制的快速、目标导向性运动中重现 Fitts 法则？
• RQ5 动作性震颤与静止性震颤如何从模型的动力学中自然产生，特别是在 jerk 不连续性处？

主要发现

• 该模型通过将运动时间与距离与所推导出的守恒量关联，成功重现了 Fitts 法则。
• 识别出一个守恒量，其作用类似于经典力学中的能量，为运动分析提供了守恒量。
• 当成本泛函参数允许周期解时，震颤样振荡会自然地从模型中产生。
• 动作性震颤与静止性震颤被建模为在 jerk 不连续性瞬间被触发和终止的振荡，对应于加速度的尖点。
• 震颤样振荡的振幅取决于成本泛函参数以及初始和最终条件，且在 jerk 不连续性两侧可能具有不同的振幅。
• 该模型预测，经过滤波后的震颤样分量类似于加速度控制的运动，表明 jerk 控制可产生更平滑的运动。