Analysis of Uncertainty in Local and Telecollaborative Virtual Reality Applications in Design and Manufacturing

这笔拨款为一个框架提供资金，用于提前估计用户在虚拟现实环境中成功执行对对象操作的能力的概率（例如，拾取，放置，按压，持有，驾车通过，飞越），给定当前位置和时间的不确定性，基于环境中的设计（可控）和噪声（不可控）因素。对位置和时间的不确定性进行了表征。对于位置不确定性分析，使用六元素姿态向量（三个用于位置，三个用于沿三个直角坐标轴的方向），对于时间不确定性分析，使用六元素状态向量（三个用于位置，三个用于速度）。提出了一个6x6的协方差矩阵，即姿态或状态估计与真实向量之差的平方的期望，以表征不确定性。一个有用的协方差矩阵的解释可以通过假设误差是联合高斯得到。该研究项目是迭代预测协方差矩阵，并通过在所有可能的感官信息线性组合中最小化不确定椭球的几何体积，通过融合新的传感器测量值来校正协方差矩阵。如果成功，本研究的结果将提高对虚拟环境的标称对象大小阈值，标称用户交互速度阈值和虚拟分析任务结果的概率密度的理解，然后可用于更准确地估计成本预测。基于结果，可以建立一个实用函数，用于在虚拟环境中根据嵌入的不确定性表达用户的态度。不确定性分析将能够解决设计因素，如：物体边界解释错误，真实环境-虚拟环境映射/配准错误，盲点和遮挡，低帧率错误和由于用户或物体的快速运动而发生的错误。

This grant provides funding for a framework for estimating, in advance, the probability of the user's ability to successfully execute an operation on an object in a virtual reality environment (e.g. picking, placing, pressing, holding, drive-through, fly-through), given the current positional and temporal uncertainties based on design (controllable) and noise (uncontrollable) factors in the environment. The positional and temporal uncertainties are characterized. For positional uncertainty analysis a six-element pose vector (three for position and three for orientation along three cartesian coordinate axes) is used, and for temporal uncertainty a six-element state vector (three for position and three for velocity) is used. A 6x6 covariance matrix, which is the expectation of the square of the difference between the pose or state estimate and the true vector, is proposed to characterize the uncertainty. A useful interpretation of the covariance matrix can be obtained by assuming that the errors are jointly Gaussian. The research project is to iteratively predict the covariance matrix and correct it by fusing new sensor measurements as they arrive by minimizing the geometric volume of the ellipsoid of uncertainty among all possible linear combinations of sensory information.If successful, the results of this research will improve the understanding of nominal object size threshold for virtual environments, nominal user interaction speed threshold, and probability densities of virtual analysis task outcomes, which can then be used to more accurately estimate the cost projections. A utility function for expressing user attitude in virtual environment in light of the embedded uncertainties is possible based on the results. The uncertainty analysis will be able to address design factors such as: object boundary interpretation errors, real environment-virtual environment mapping/registration errors, blind spots and occlusions, and low frame rate errors and errors that occur because of fast movement of user or object.