Monte Carlo Uncertainty Characterization & Chance Constraint Design in Motion Planning for Fielded sUAS

When a small uncrewed aircraft system (sUAS) follows a deterministic motion plan, the resulting aircraft behavior will contain uncertainty due to input uncertainty and changing conditions. In order to generate motion plans for sUAS that satisfy problem constraints concerning the aircraft trajectory, the motion planning system needs to reason over complex and uncertain models. Chance constraints offer a method for reasoning over problem constraints given trajectory uncertainty, and Monte Carlo approximations offer a method for empirically modeling complex uncertainty without requiring simplifications to complex distributions. However, the Monte Carlo approximation of the trajectory distribution will contain error given that a finite number of samples is used, which could lead to an incorrect evaluation of the chance constraint. Additionally, the lack of an analytical representation of the distribution limits the ability to validate whether the approximation represents the true distribution. This work addresses these limitations by exploring buffering chance constraints given approximation error using the Wald interval, and using the Mahalanobis distance to validate whether the Monte Carlo approximation of the trajectory distribution is representative of the true distribution. A motion planning system composed of a sampling-based planning algorithm, a Monte Carlo propagation algorithm, and a chance constraint assessment algorithm is interfaced with a fixed-wing sUAS leveraging dispersed computing to perform simulations and conduct fielded experiments. Results show that the Wald interval is only a sufficient method of buffering the chance constraint given specific distributions, and the state-wise and path-wise Mahalanobis values can be used to tune the system models and validate representative performance.