A Closed-Loop Linear Covariance Framework for Vehicle Path Planning in an Uncertain Obstacle Field

Path planning in uncertain environments is a key enabler of true vehicle autonomy. Over the past two decades, numerous approaches have been developed to account for errors in the vehicle path while navigating complex and often uncertain environments. An important capability of such planning is the prediction of vehicle dispersion covariances about candidate paths. This work develops a new closed-loop linear covariance (CL-LinCov) framework applicable to wide range of autonomous system architectures. Extensions to current CL-LinCov frameworks are made to accommodate 1) the cascaded architecture typical of autonomous vehicles and 2) the dual-use of continuous sensor information for both navigation and control. The closed-loop nature of the framework preserves the important coupling between the system dynamics, exogenous disturbances, and the guidance, navigation, and control algorithms. The developed framework is applied to a simplified model of an unmanned aerial vehicle and validated by comparison via Monte Carlo analysis. The utility of the CL-LinCov information is illustrated by its application to path planning in an uncertain obstacle field via a modified version of the rapidly exploring random tree algorithm.