Mathematical Sciences: Curve Estimation in Motion Analysis

这个项目是关于一个工作过程的扩展，其中非参数平滑和自举应用于生物力学和机器人的几个实际工作问题。动机和许多未来的应用来自步态分析，即研究人类在水平表面上的自由速度行走。我们利用一个模型，其主要方面是描述“主体”运动的标量或矢量函数。在拟合学习样本的数据并应用bootstrap之后，计算后续“测试对象”曲线的预测区域。对预测区进行了数值和理论研究。该项目的其他方面涉及通过核方法的方法，使用数据选择基础和模型，以及预测区域的条件版本。我们也将研究规定类型的多变量问题，因为它们适用于机器人和数控铣床。

This project is concerned with the expansion of a course of work in which nonparameteric smoothing and the bootstrap are applied to several real work problems in biomechanics and robotics. The motivation and many of the future applications come from gait analysis, ie, the study of free-speed human walking on a level surface. We utilize a model whose main aspect is a scalar or vectorial function that describes motion of a "subject". After fitting data from a learning sample, and applying the bootstrap, prediction regions for the curves of a subsequent "test subject" are computed. The prediction regions are to be studied numerically and theoretically. Other aspects of the project involve approaches through kernel methods, using data to pick bases and models, and conditional versions of the prediction regions. We also will study multivariate problems of the prescribed type as they apply to robots and numerically controlled milling machines.