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

Lars Bartels, Amon Lahr, Andrea Carron, Melanie N. Zeilinger

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Key figure (auto-extracted from paper)

An efficient approximate spatio-temporal Gaussian process model enables real-time online learning for GP-MPC at constant computational cost, successfully demonstrated in autonomous miniature racing.

Gaussian Process Model Predictive Control Real-Time Learning Spatio-Temporal Modeling Autonomous Racing Online Adaptation

Problem

Exact Gaussian process inference scales cubically with data, making real-time online learning for GP-based Model Predictive Control computationally infeasible, particularly for systems with time-varying dynamics.

Approach

The authors combine spatial inducing points with a Markovian temporal state-space representation to enable constant-cost recursive updates via Kalman filtering, specifically optimized for integration into MPC solvers.

Key results

Constant computational complexity per time step for online GP learning
Open-source implementation integrated into the L4acados GP-MPC framework
Real-time adaptation to time-varying steering perturbations in simulation
Hardware validation through autonomous miniature racing experiments

Why it matters

Provides a computationally tractable path for deploying uncertainty-aware learning-based controllers in safety-critical, real-time robotic applications.

Abstract

Learning-based model predictive control (MPC) can enhance control performance by correcting for model inac- curacies, 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. Video: https://youtu.be/x4qo66R2-Ds

Index terms

Model Learning for Control Machine Learning for Robot Control Optimization and Optimal Control