# A Stochastic Nonlinear Model Predictive Control with an Uncertainty Propagation Horizon for Autonomous Vehicle Motion Control

arXiv: https://arxiv.org/abs/2310.18753 · HTML: https://mlsanity.com/paper/2310.18753/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2023.

## Built on by (most cited first, 4 of 4)

- [A Safe Reinforcement Learning driven Weights-varying Model Predictive Control for Autonomous Vehicle Motion Control](https://mlsanity.com/paper/2402.02624/) (2024)
- [Adaptive Stochastic Nonlinear Model Predictive Control with Look-ahead Deep Reinforcement Learning for Autonomous Vehicle Motion Control](https://mlsanity.com/paper/2311.04303/) (2023)
- [Analyzing the Impact of Simulation Fidelity on the Evaluation of Autonomous Driving Motion Control](https://mlsanity.com/paper/2602.07984/) (2026)
- [Accelerating Reinforcement Learning via MPC Solver-Gradient Guidance for Weights-varying MPC](https://mlsanity.com/paper/2609.01061/) (2026)

## Abstract (arXiv)

Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in high-dimensional systems with extended prediction horizons, such as autonomous vehicles. To enhance closed-loop performance in and feasibility in SNMPCs, we introduce the concept of the Uncertainty Propagation Horizon (UPH). The UPH limits the time for uncertainty propagation through system dynamics, preventing trajectory divergence, optimizing feedback loop advantages, and reducing computational overhead. Our SNMPC approach utilizes Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates nonlinear hard constraints on state expectations and nonlinear probabilistic constraints. We transform the probabilistic constraints into deterministic constraints by estimating the nonlinear constraints' expectation and variance. We then showcase our algorithm's effectiveness in real-time control of a high-dimensional, highly nonlinear system-the trajectory following of an autonomous passenger vehicle, modeled with a dynamic nonlinear single-track model. Experimental results demonstrate our approach's robust capability to follow an optimal racetrack trajectory at speeds of up to 37.5m/s while dealing with state estimation disturbances, achieving a minimum solving frequency of 97Hz. Additionally, our experiments illustrate that limiting the UPH renders previously infeasible SNMPC problems feasible, even when incorrect uncertainty assumptions or strong disturbances are present.