Efficient Uncertainty Quantification for Intelligent Autonomous Systems

Linear Covariance Analysis (LCA) is a computationally efficient method for uncertainty quantification that yields direct statistical information about a nonlinear trajectory. LCA performs three orders of magnitude faster than the current method for uncertainty quantification, Monte Carlo Analysis (MCA), and yields direct statistical measures of uncertainty. Currently, uncertainty can only be propagated about a single reference trajectory in LCA, LCA can only model Gaussian noise, and LCA can only be applied to sufficiently linear systems. However, guidance algorithms like hazard avoidance with large diverts result in multiple nonlinear nominal trajectories that branch from the initial trajectory, each with their own uncertainty. By advancing the field of LCA to enable efficient, accurate UQ, the applicability of LCA will increase for mission design of intelligent autonomous systems; guidance, navigation, and control (GNC) analysis; and onboard navigation. To accomplish this goal, the limitations introduced above will be addressed. With the goal of integrating automatic trajectory branching into LCA, first, MCA will be used to find the branch point to use in LCA. Then, new method for representing uncertainty in LCA will be developed from statistical methods like Gaussian mixture models (GMMs), which can represent the uncertainty distributions at the branch point. GMMs can also be used to represent non-Gaussian distributions (i.e. uniform), which are useful for UQ of many autonomous systems. Third, Unscented Kalman filter theory will be applied to LCA to develop a method for autonomously predicting the location of a branch point or a recombination point. Fourth, the Koopman operator (KO) will be used to model nonlinear systems as high-dimensional linear systems, which can increase the accuracy of LCA. Note that these tasks will not be completed in series, but rather in parallel. Simultaneously, effort will be made to augment the computational efficiency of LCA by using autodifferention and computer algebra. Through these efforts, a single LCA simulation can be used to capture the uncertainty of a complex nonlinear multi-branched trajectory, representing a wide variety of NASA missions, from docking operations, to crater avoidance on Lunar landing, to obstacle avoidance for missions on Earth. This work will aid NASA mission design for many complex intelligent autonomous systems, such as human-class Martian vehicles, lunar landers, and planetary aircraft. LCA can be applied to both the mission planning phase, as a method for rapid trajectory analysis, and to the operational phase, as an onboard GNC scheme, for these and other missions. Onboard, robust, accurate UQ will be invaluable to increasing autonomy for many proposed and current missions, like Artemis, Mars Sample Return, and Dragonfly.

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