Probably Approximately Correct Nonlinear Model Predictive Control (PAC-NMPC)

Approaches for stochastic nonlinear model predic- tive control (SNMPC) typically make restrictive assumptions about the system dynamics and rely on approximations to char- acterize the evolution of the underlying uncertainty distributions. For this reason, they are often unable to capture more complex distributions (e.g., non-Gaussian or multi-modal) and cannot provide accurate guarantees of performance. In this paper, we present a sampling-based SNMPC approach that leverages recently derived sample complexity bounds to certify the perfor- mance of a feedback policy without making assumptions about the system dynamics or underlying uncertainty distributions. By parallelizing our approach, we are able to demonstrate real-time receding-horizon SNMPC with statistical safety guarantees in simulation and on hardware using a 1/10th scale rally car and a 24-inch wingspan fixed-wing unmanned aerial vehicle (UAV).