A key enabler of autonomous vehicles is the ability to plan the path of the vehicle to accomplish mission objectives. To be robust to realistic environments, path planners must account for uncertainty in the trajectory of the vehicle as well as uncertainty in the location of obstacles. The uncertainty in the trajectory of the vehicle is a difficult quantity to estimate, and is influenced by coupling between the vehicle dynamics, guidance, navigation, and control system as well as any disturbances acting on the vehicle. Monte Carlo analysis is the conventional approach to determine vehicle dispersion, while accounting for the coupled nature of the system. Due to the computational complexity of Monte Carlo analysis, this approach to calculating vehicle dispersion quickly becomes prohibitive for real-time applications, high dimensional systems. Modern or Closed-Loop Linear Covariance (LinCov) analysis linearizes the vehicle dynamics and GNC about a nominal trajectory, and computes the same information as Monte Carlo analysis but in a single run. This paper develops a LinCov framework capable of modeling the dynamics, guidance, navigation, and control of autonomous vehicles and validated the framework by comparison to Monte Carlo analysis. The developed framework is applied to the path planning of an unmanned aerial vehicle (UAV). The rapidly exploring random trees (RRT) algorithm is augmented with statistical information provided by the LinCov simulation and a model of the uncertainty of obstacles. It is demonstrated that the developed path planner efficiently guides the UAV through the obstacle field while maintaining the probability of collision below a user-specified value.
Christensen, R. and Leishman, R. C., "Real-Time Path Planning in Constrained, Uncertain Environments", ANT Center Tech Report, 2019.