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

TL;DR

This paper introduces a sampling-based stochastic nonlinear model predictive control method that provides real-time safety guarantees without restrictive assumptions on system dynamics or uncertainty distributions, demonstrated on vehicles.

Contribution

It presents a novel sampling-based SNMPC approach with performance certification using sample complexity bounds, enabling real-time implementation with statistical safety guarantees.

Findings

Successful real-time control on a rally car and UAV

Certifies performance without assumptions on uncertainty distributions

Demonstrates effectiveness in simulation and hardware

Abstract

Approaches for stochastic nonlinear model predictive control (SNMPC) typically make restrictive assumptions about the system dynamics and rely on approximations to characterize 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 performance 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).