# Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars

arXiv: https://arxiv.org/abs/1711.06586 · HTML: https://mlsanity.com/paper/1711.06586/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2017.

## Built on by (most cited first, 13 of 13)

- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [VisuoSpatial Foresight for Physical Sequential Fabric Manipulation](https://mlsanity.com/paper/2102.09754/) (2021)
- [Zero-Order Optimization for Gaussian Process-based Model Predictive Control](https://mlsanity.com/paper/2211.15522/) (2022)
- [Safe Machine-Learning-supported Model Predictive Force and Motion Control in Robotics](https://mlsanity.com/paper/2303.04569/) (2023)
- [Approximate Robust NMPC using Reinforcement Learning](https://mlsanity.com/paper/2104.02743/) (2021)
- [Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes](https://mlsanity.com/paper/2108.06430/) (2021)
- [Gaussian Processes with State-Dependent Noise for Stochastic Control](https://mlsanity.com/paper/2305.16229/) (2023)
- [Vehicle Dynamics Modeling for Autonomous Racing Using Gaussian Processes](https://mlsanity.com/paper/2306.03405/) (2023)
- [A Tutorial on Gaussian Process Learning-based Model Predictive Control](https://mlsanity.com/paper/2404.03689/) (2024)
- [Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics](https://mlsanity.com/paper/2604.26836/) (2026)
- [Learning Residual Model of Model Predictive Control via Random Forests for Autonomous Driving](https://mlsanity.com/paper/2304.04366/) (2023)
- [Physics-informed Gaussian Processes as Linear Model Predictive Controller](https://mlsanity.com/paper/2412.04502/) (2024)
- [Gradient-Enhanced Partitioned Gaussian Processes for Real-Time Quadrotor Dynamics Modeling](https://mlsanity.com/paper/2602.12487/) (2026)

## Abstract (arXiv)

This paper presents an adaptive high performance control method for autonomous miniature race cars. Racing dynamics are notoriously hard to model from first principles, which is addressed by means of a cautious nonlinear model predictive control (NMPC) approach that learns to improve its dynamics model from data and safely increases racing performance. The approach makes use of a Gaussian Process (GP) and takes residual model uncertainty into account through a chance constrained formulation. We present a sparse GP approximation with dynamically adjusting inducing inputs, enabling a real-time implementable controller. The formulation is demonstrated in simulations, which show significant improvement with respect to both lap time and constraint satisfaction compared to an NMPC without model learning.