Closed-Loop Linear Covariance Framework for Path Planning in Static Uncertain Obstacle Fields

Path planning in an uncertain environment 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 a candidate path. This work develops a new closed-loop linear covariance (CL-LinCov) framework applicable to a wide range of autonomous system architectures. Important features of the developed framework include 1) separation of high-level guidance from low-level control; 2) support for output-feedback controllers with internal states, dynamics, and output; and 3) multi-use continuous sensors for navigation state propagation, guidance, and feedback 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 a static, uncertain obstacle field via a modified version of the rapidly exploring random tree algorithm.