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

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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.