Real-Time Online Learning for Model Predictive Control using a Spatio-Temporal Gaussian Process Approximation

TL;DR

This paper introduces an efficient, real-time capable spatio-temporal Gaussian process model for model predictive control, significantly improving control accuracy in dynamic systems like autonomous racing.

Contribution

It presents a novel approximate spatio-temporal Gaussian process model that enables constant-complexity online learning for GP-MPC, suitable for real-time applications.

Findings

Enhanced control performance in simulations and hardware experiments.

Real-time online learning with constant computational complexity.

Effective handling of time-varying system dynamics.

Abstract

Learning-based model predictive control (MPC) can enhance control performance by correcting for model inaccuracies, enabling more precise state trajectory predictions than traditional MPC. A common approach is to model unknown residual dynamics as a Gaussian process (GP), which leverages data and also provides an estimate of the associated uncertainty. However, the high computational cost of online learning poses a major challenge for real-time GP-MPC applications. This work presents an efficient implementation of an approximate spatio-temporal GP model, offering online learning at constant computational complexity. It is optimized for GP-MPC, where it enables improved control performance by learning more accurate system dynamics online in real-time, even for time-varying systems. The performance of the proposed method is demonstrated by simulations and hardware experiments in the exemplary application of autonomous miniature racing.