Cautious Model Predictive Control using Gaussian Process Regression

TL;DR

This paper introduces a cautious model predictive control method that incorporates Gaussian process regression to model uncertainties in nonlinear dynamical systems, enhancing safety and performance in autonomous racing.

Contribution

It presents a novel MPC framework integrating GP-based residual uncertainty modeling with chance constraints for cautious control, demonstrated in simulation and real-world racing scenarios.

Findings

Improved safety and performance over nominal controllers.

Effective uncertainty quantification using Gaussian processes.

Successful hardware implementation in autonomous racing.

Abstract

Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and we describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Using additional approximations for efficient computation, we finally demonstrate the approach in a simulation example, as well as in a hardware implementation for autonomous racing of remote controlled race cars, highlighting improvements with regard to both performance and safety over a nominal controller.